Research ArticlePredictive Analysis of Settlement Risk in TunnelConstruction A Bow-Tie-Bayesian Network Approach

Wen Liu 1 Shihong Zhai234 and Wenli Liu 5

1Post-Doctoral CCCC Second Harbor Engineering Co Ltd No 11 Jinyin Lake Road Dongxihu District Wuhan 430074 China2Professor-Level Senior Engineers Key Laboratory of Large-Span Bridge Construction Technology for Transportation IndustryNo 11 Jinyin Lake Road Dongxihu District Wuhan 430074 China3Professor-Level Senior Engineers Research and Development Center of Transportation Industry of Intelligent ManufacturingTechnologies of Transport Infrastructure No 11 Jinyin Lake Road Dongxihu District Wuhan 430074 China4Professor-Level Senior Engineers CCCC Highway Bridges National Engineering Research Centre Co LtdNo 11 Jinyin Lake Road Dongxihu District Wuhan 430074 China5Postdoctoral Research Fellow School of Civil Engineering ampMechanics Huazhong University of Science and Technology HubeiWuhan 430074 China

Correspondence should be addressed to Wenli Liu newheny2014hotmailcom

Received 18 January 2019 Accepted 23 June 2019 Published 10 July 2019

Academic Editor Dong Zhao

Copyright copy 2019Wen Liu et alis is an open access article distributed under the Creative CommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

A hybrid method consisting of bow-tie-Bayesian network (BT-BN) analysis and fuzzy theory is proposed in this research in orderto support predictive analysis of settlement risk during shield tunnel excavation We verified the method by running a prob-abilistic safety assessment (PSA) for a tunnel section in the Wuhan metro system Firstly we defined the ldquonormal excavationphaserdquo based on the fuzzy statistical test theory We eliminated the noise records in the tunnel construction log and extracted theoccurrence probability of facility failures from the denoised database We then obtained the occurrence probability of envi-ronmental failures operational errors andmultiple failures via aggregation of weighted expert opinionse expert opinions werecollected in the form of fuzzy numbers including triangular numbers and trapezoidal numbers Afterwards we performed theBT-BN analysis We mapped the bow-tie analysis to the Bayesian network and built a causal network PSA model consisting of 16nodes Causes of the excessive surface settlement and the resulting surface collapse were determined by bow-tie analysis e keynodes of accidents were determined by introducing three keymeasures into the Bayesian inference Finally we described the safetymeasures for the key nodes based on the PSA results ese safety measures were capable of reducing the failure occurrenceprobability (in one year) of excessive surface settlement by 66 thus lowering the accident probability caused by excessivesurface settlement

1 Introduction

ere are intrinsic risks associated with shield tunnel ex-cavation because of the limited knowledge about the existingsubsurface conditions [1 2] Although the majority of shieldtunnel construction projects have been completed safely thesurface collapse caused by excessive surface settlement didoccur in several tunneling projects which resulted in majordamage injury and loss of life e worst accident of metroconstruction in China took place on November 15 2008 inHangzhou [3] A massive cave-in during the construction of

Metro Line 1 near the Xianghu station caused 21 injuries and24 deaths and the direct economic loss amounted to 4961million Yuan A more recent accident took place on May 142017 in Nanchang [4] Excessive surface settlement duringthe construction of Metro Line 2 near the Bayi square stationcaused a cave-in more than 10m in diameter and led tosevere property losses erefore it is imperative to sys-tematically assess and manage the safety risks associatedwith shield tunnel excavation

Traditionally surface settlement in shield tunnel ex-cavation has been studied both empirically and analytically

HindawiAdvances in Civil EngineeringVolume 2019 Article ID 2045125 19 pageshttpsdoiorg10115520192045125

A number of empirical formulae have been proposed basedon extensive experiments and construction practices Peckproposed in his classic formula that the surface settlementtrough could be described by a normal distribution [5]Since then the Peck formula had been further improvedand modified by many scholars including Attewell et al [6]and Rankin [7] Attewell and Woodman proposed thecumulative probability curve [8] OrsquoReilly and New sug-gested a predictive formula to estimate trough widthformation loss and surface settlement [9] Mair et al andcoworkers established their formula to calculate subsurfaceformation displacement [10] Empirical formulae arewidely used in practical engineering because of theirsimplicity but their use is limited to crude estimations ofthe surface settlement because they are not accurateenough

In contrast analytical methods make reasonable sim-plifications of rock and soil to consider them as a mediumwith certain physical and mechanical properties and thenderive the surface settlement via well-established mathe-matical models and mechanical theories [1] e stochasticmedium theory considered rock and soil as a ldquostochasticmediumrdquo and regards the surface settlement caused bytunnel excavation as a stochastic process [11ndash13] Numericalanalysis integrates the elastic-viscoplastic theory into nu-merical calculations and reduces the dimension of the cal-culations with discrete interpolation and analytic functions[14ndash16] e primary problem with analytical methods is anoversimplification In most cases the task is reduced tosolving the plane strain that is uniform isotropic andaxisymmetric although the practical situation in engi-neering and the geological formation at the construction sitearemuchmore complicated In order to address those issuesartificial intelligence (AI) methods provide possible solu-tions which have been exploited in studying the risk evo-lution of surface settlement

is study aims to (1) clearly define the ldquonormal ex-cavation phaserdquo of shield tunneling based on the fuzzystatistical test theory and extract the occurrence proba-bility of facility failures from existing structured data (2)in the absence of available data determine the occurrenceprobability of environmental failure operational errorand multiple failures by aggregating fuzzy numbers(triangular numbers and trapezoidal numbers) of expertopinion (3) perform probabilistic safety assessment(PSA) of settlement failure in tunnel construction throughbow-tie-Bayesian network (BT-BN) analysis (4) identifythe key nodes for excessive surface settlement-causedsurface collapse and (5) develop appropriate safetymeasures

In this research we examined the tunneling log of theXiaodongmen-Wuchang section (XWS) during the con-struction of Metro Line 7 at Wuhan (Figure 1) Data werecollected from XWS and the key nodes that could causecave-in due to the excessive surface settlement wereextractedWe proposed safety measures that targeted the keynodes to reduce the likelihood of accidents e XWS wentfrom south to north mainly along the Zhongshan road eleft tunnel was 1115208m in length and was excavated with

a tunnel boring machine (TBM) e right tunnel was1107169m in length and was excavated with a Komatsutunnel boring machine Both tunnels were excavated byusing the earth pressure balance TBM e minimumhorizontal curve radius of the section was 400m and the linespacing was 126ndash505m e minimum longitudinal curveradius of the section was 3000m e section adopted aconcave slope with the overlying soil of 105ndash454m inthickness Figure 1 shows a picture taken during the exca-vation of the XWS

is paper is organized as follows Section 2 presents theexisting knowledge on the definitions of surface settlementincurred by shield tunnel excavation classifies existing re-search methods on surface settlement in metro constructionand introduces the dynamic safety analysis of the BT-BNmethodology Section 3 defines the ldquonormal excavationphaserdquo of shield tunneling and presents the detailed pro-cedures in carrying out the fuzzy BT-BN analysis Section 4examines the normal tunnel excavation in detail and appliesthe proposed fuzzy BT-BN method to the PSA analysis ofexcessive surface settlement-caused surface collapse in theXWS of Wuhan metro system e conclusions and futureworks are drawn in Section 5

2 Literature Review

21 Surface Settlement in Tunnel Construction Surface set-tlement caused by shield tunnel excavation is a three-di-mensional spatial process that involves the transformationdisplacement response and changing mechanical propertiesof different soil As an approximation an area of surfacesettlement can be seen to be developing as the TBM ad-vances e size of the area and the severity of settlementneed to be determined to evaluate the spatial distribution ofthe surface settlement Many countries have set out stan-dards and benchmarks to monitor surface settlement duringshield tunnel excavation (Table 1) Based on the Chinesestandard GB 50911-2013 ldquoCode for monitoring measure-ment of urban rail transit engineeringrdquo [17] as well as thestandards of other countries in this work we classified risklevels of the surface settlement for the soft soil in the XWS asshown in Table 2

In recent years the artificial intelligence methods havebeen exploited in studying the risk evolution of surfacesettlement Suwansawat and Einstein used artificial neuralnetwork (ANN) to evaluate the safety risks due to surfacesettlement in tunnel excavation by using the earth pressurebalance TBM [18] ey took various influence factors as theinputs to their ANNs and predicted the surface settlementSun et al introduced the theories and techniques of bothartificial intelligence and automatic control into geo-technical engineering [19] Specifically an ANN modelcalled ldquomultistep circulationrdquo was adopted for predicting thesafety risk of surface settlement in shield tunneling Fuzzylogic control was also applied to enable active safety controlof deformation displacement in real time However existingartificial intelligence methods cannot analyze the key nodeswith regard to surface settlement in shield tunnel excavation

2 Advances in Civil Engineering

Besides long learning time is needed and the requirementon known parameters can be demanding

Overall surface settlement in shield tunneling arisesfrom various risk factors that involve geology constructionmethod environment and management In order to thor-oughly study the safety risk of surface settlement it isnecessary to analyze in real time the uncertain informationin the risk factors from multiple sources However suchuncertainty including fuzziness and stochasticity is ubiq-uitous and restricts the application of traditional method-ologies such as empirical formula simulation and analyticalmodeling Other methods based on artificial intelligencesuch as neural networks also suffer from the memory effectbecause it is difficult to update the risk factors in real timewhen new information arises

22 Bayesian Network and Bow-Tie In recent years thebow-tie (BT) model has been combined with the Bayesiannetwork (BN) to tackle various problems in which un-certainty is deeply rooted e BT-BN approach has a solidfoundation in mathematical theory and has unique ad-vantages in dealing with complex dynamic uncertainty Ithas been considered as an ideal tool for knowledge repre-sentation inference and forecasting in an uncertainenvironment

Bow-tie analysis is a quantitative model that consists offault tree (FT) analysis and event tree (ET) analysis [20] andallows investigating the causes and consequences of a givenundesirable event Cherubin et al applied BT analysis as asimple and effective quantitative risk assessment (QRA)approach for the identification and evaluation of potential

Table 1 Standards for monitoring surface settlement in shield tunnel excavation

Country US Japan France Germany China

Acceptable surface settlement (mm) 10ndash15 25ndash50 Hard rock 10ndash20Soft rock 20ndash50 50 Hard soil 10ndash40

Soft soil 15ndash45

Table 2 Classification of risk levels

Level 1 2 3 4 5Description Negligible Alarming Serious Dangerous CatastrophicSurface settlement (mm) 0ndash10 5ndash15 10ndash25 20ndash35 30ndash45

Line 1Line 2Line 3Line 4Line 5

Location of Xiaodongmen-Wuchang section (XWS)

Site picture of theconstruction of XWS

Line 6Line 7Line 8Line 11Line 21

Ordinary stationTransfer stationTerminal station

Railway stationAirport

Figure 1 Location of XWS in the Wuhan metro system

Advances in Civil Engineering 3

hazards and associated risks with the baseline risk assess-ment tool (BART) [21] Targoutzidis argued that BTanalysisis an effective tool for identifying environmental risk sourcesbecause it can clearly show the connections between thecause the loss events (LEs) the conditional events (CEs)and the outcome events (OEs) [22] e BT approach hasbeen applied in the risk assessment of hexane distillation therisk management of harbor and maritime terminals and therisk assessment of airworthiness in military aviation [23ndash25]

e focus of these BT models is to depict the entirescenario of the accident to identify and evaluate the po-tential causes and consequences but does not readily revealthe actual causes through logical connections and occur-rence probability is caveat can be remedied by mappingBT to BN For example Badreddine and Amor improvedthe BTmodel by exploiting the advantages of BN dynamicanalysis ey built the BT chart in an automated anddynamic way to implement appropriate barriers to pre-vention and protection in dynamic systems [26] Khakzadet al made a dynamic risk analysis of systems whosephysical reliability is updated periodically [27] ey madeuse of the Bayes theorem to periodically update the failureprobability of safety barriers in the BT chart and estimatedthe probability of consequences based on the enhanced BTchart It was argued that mapping BT to BN [28] couldalleviate the limitations of BT caused by static factorsAbimbola et al used BT and BN to determine the keyfactors of the integrity model In their study the posteriorprobability was obtained through the Bayes theorem andthe key factors were determined by the ratio of the posteriorprobability to the prior probability [29]

In summary mapping BT to BN allows dynamic riskanalysis and the key factors of the system can be identifiedby calculating the posterior probability through the Bayestheorem Meanwhile since the conditional probability canbe calculated via the Bayes theorem the importance measureof PSA can also be introduced [30] and BN can be fitted withthese important measures very well to calculate the im-portance measures accurately and easily erefore the BT-BN analysis can not only analyze surface collapse caused byexcessive surface settlement in shield tunneling metroconstruction but also use PSA to confirm the critical causesof accidents by adding the importance measures

3 Methodology

BT analysis is used to display the scenario of the loss event(LE) in the system In the BTmodel the FTanalysis can revealthe cause of the LE and the consequences of LE can bedetermined by the ET analysis In the proposed BT-BNmethod the FT and ETanalyses in the BTmodel are mappedto the BN such that the nodes that give rise to accidents can bemore easily determined e BT-BN method requires explicitoccurrence probability of failure Data for the failure prob-ability of the TBM were extracted from construction logduring the ldquonormal excavation phaserdquo of the XWS Whenexisting data could not provide the required informationexpert opinion in the form of the fuzzy number was used todetermine the corresponding failure probability e

consequences were then predicted by the BT-BN analysis andthe critical nodes related to the consequences were obtainedFigure 2 shows the flowchart of the proposed methodology

31 ldquoNormal Excavation Phaserdquo of TBM

311 Fuzzy Statistical Test 9eory e concept of ldquofuzzysetrdquo introduced by Zadeh is a crucial extension of the classicset theory of Cantor [31] e fuzzy set theory has maturedover the past years to a well-established research area inmathematics and has found extensive applications in manyfields e fuzzy set A on domain X is in fact a function ofX⟶ [01] e primary task of dealing with fuzziness inpractical applications is to determine the membershipfunction A(x) Just like probabilistic theory cannot giveprecise but only approximate probability due to limitedknowledge and information the fuzzy set theory can onlyestablish the approximate degree of membership and con-sequently an estimatedmembership function Fuzzy statisticaltests that demonstrate the stability of frequency can be carriedout to characterize the objectivity of degree of membershipand to derive an approximate membership function

Two-phase fuzzy statistics divides the domain X (egTBM excavation speed) into two statistical sets ie A(ldquonormalrdquo) and Ac (ldquoabnormalrdquo) at is two opposite fuzzyconcepts compete for statistics in domain X e so-calledldquotwo-phaserdquo indicates P2 A Ac [32] ie each fuzzy testwill establish a mapping e X⟶ P2 is mapping dividesthe domain X ie forallx isinX A(x) +Ac(x) 1 e two-phasefuzzy statistical test contains four elements (1) domainX (2)a fixed element x0 in X (3) a varying classical set Alowast in X (Alowastreflects the flexible boundary of the fuzzy set A and allows todetermine if the x0 in each test conforms to the fuzzy conceptdescribed by A) and (4) condition S which restricts thechanges of Alowast

In fuzzy statistical tests x0 remains fixed while Alowast isvaried In each test a decision must be made as for whetherx0 belongs to Alowast Note that the changing Alowast is always asubset of X After n tests the membership frequency of x0belonging to the fuzzy set Alowast is calculated as ln(A)(x0)

ln(A) x0( 1113857 number of times that ldquox0 isin Alowastrdquo

n (1)

It has been experimentally found that ln(A)(x0) tends tostabilize as n increases e stabilized value is referred to asthe degree of membership that x0 belongs to A

ln(A) x0( 1113857 limx⟶infin

number of times that ldquox0 isin Alowastrdquon

(2)

312 Fuzzy Statistical Test of the Excavation Speed of TBMExcavation speed is a macroscopic measure of the workingstate of the TBM erefore the normal state of the TBM ischaracterized by the normal excavation speed In our casethe normal excavation speed during tunneling was obtainedby running a fuzzy statistical test with the construction logsof the XWS

4 Advances in Civil Engineering

In this work the excavation speed of the TBM had adomain ofV [1 96] (mmmin)e fuzzy setA represents thefuzzy concept of ldquonormal excavation speedrdquo For the purpose ofillustration select an arbitrary excavation speed v0 23mmmin Fuzzy statistical tests were then applied to determine thedegree of membership that v0 belonged to A For the con-struction project at the XWS the appropriate project logs overn 179days (715 segment rings for left and right tunnels) wereselected e appropriate logs excluded abnormal engineeringsituations (restrictive condition S) such as TBM launchingTBM arrival and abnormal downtime during which theformation was reinforced and the excavation speed could notbe considered normal In this way the boundaries for the dailyldquonormal excavation speedrdquo could be determined for the left andright tunnels of the XWS (Table 3 Figure 3)

Table 4 shows the membership frequency that v0 23mmmin belonged to the normal excavation speed as was de-termined by the statistical tests Figure 4 shows that themembership frequency f that v0 23mmmin falls within theldquonormal excavation speedrdquo of the TBM stabilized around 066Hence A(v0) A(23) 066 e membership frequency f ofother excavation speeds could also be obtained similarlye data from the construction logs recorded a mini-mum and maximum excavation speed of 2mmmin and96mmmin respectively Hence we divided the domain V

into 96 intervals each spanning 1mmmin starting from15mmmin and ending at 965mmmin e mean of eachinterval was used to calculate the membership frequencyand the results are shown in Table 5 A program was de-veloped in MATLAB to reduce the computational com-plexity and save time

Figure 5 plots the histogram of membership frequencybased on the data in Table 5 e fitted curve of themembership function A(v) was then drawn accordinglyefitted curve conformed to the Cauchy distribution and couldbe expressed as follows

1113957A(v) v A(v) ∣ A(v) 1 +vminus 3212

1113874 11138752

1113888 1113889

minus1

v isin N⎧⎨

⎩

⎫⎬

⎭

(3)

(1) Determination of the Standard Excavation Speed In thefuzzy set theory [31] the element with the membershipfrequency A(v) 1 is designated as the kernel of the fuzzy setA and written as ldquokerArdquo Figure 5 shows that kerA 32 iev0 32mmmin was the kernel of the fuzzy set of ldquonormalexcavation speedrdquo erefore v0 32mmmin was consid-ered as the standard excavation speed in the ensuing PSAanalysis

ConvertingFTA to BN

Fuzzystatistical test

theory

ldquoNormalexcavation

phaserdquo

Preparingbow-tiediagram

ConvertingETA to BN

ConstructingBN-bow-tie

diagram

Confirmingoccurrenceprobability

TBMfacilitiesfailure

Operationalerror and

failure

TBMparameterdatabase

Triangularnumbers

Trapezoidalnumbers

Expertjudgment

Aggregation

Occurrenceprobability

Calculatingoccurrenceprobability

Calculatingimportancemeasures

BM

RAW

FV

Identifyingkey nodes

System ofTBM phases

Providingsafety

measures

Figure 2 Flowchart of the proposed methodology

Advances in Civil Engineering 5

(2) Determination of the Range of Excavation Speed In thefuzzy set theory all elements whose membership frequencyA(v)gt 0 constitute a support of the fuzzy setA and is writtenas ldquosupp Ardquo and all elements whose membership frequencyA(v)gt α is designated as the α cut set of the fuzzy set A andwritten as Aα Figure 5 shows that the excavation speed

fluctuated around the kernel (32mmmin) during shieldtunnel excavation In order to express the range of normalexcavation speed the confidence level α 05 was selectedand the excavation speed whose membership frequencysatisfied A(v)gt 05 was considered to constitute the in-terval of normal excavation speed (ie the 05 cut set of A)

Table 3 Partial construction log of the ldquonormal excavation speedrdquo in the XWS

n 1ndash10 n 11ndash20 n 21ndash30 n 31ndash40 n 41ndash50 n 51ndash60 n 61ndash70 n 71ndash80 n 81ndash90 n 91ndash100303ndash506 25ndash32 276ndash424 78ndash425 25ndash35 18ndash39 27ndash43 20ndash41 30ndash47 20ndash54324ndash388 26ndash34 232ndash476 83ndash417 28ndash46 20ndash35 24ndash40 10ndash40 30ndash61 32ndash63284ndash396 27ndash42 233ndash445 202ndash476 17ndash35 15ndash42 27ndash47 20ndash35 20ndash61 32ndash58303ndash388 23ndash36 205ndash427 242ndash425 28ndash37 27ndash41 20ndash33 17ndash32 30ndash60 20ndash37303ndash363 123ndash348 282ndash456 287ndash526 17ndash36 21ndash37 22ndash34 8ndash40 14ndash58 24ndash4032ndash44 178ndash325 182ndash426 19ndash32 20ndash37 31ndash41 27ndash48 8ndash40 27ndash74 25ndash4831ndash42 198ndash374 137ndash375 22ndash45 20ndash35 30ndash40 30ndash42 20ndash50 15ndash55 24ndash5131ndash39 135ndash326 156ndash326 21ndash44 21ndash37 30ndash35 25ndash43 20ndash50 25ndash45 32ndash4630ndash42 134ndash326 20ndash37 19ndash42 20ndash35 20ndash40 28ndash36 20ndash46 28ndash52 25ndash4031ndash38 156ndash364 15ndash40 20ndash41 20ndash37 25ndash40 225ndash37 31ndash42 31ndash47 20ndash35

Rang

e of a

dvan

ce sp

eed

(mm

min

)

v-lower limitv-upper limit

0102030405060708090

100

100 200 300 400 500 600 700 8000Segment number

Figure 3 Distribution of the ldquonormal excavation speedrdquo

Table 4 Membership frequency of 23mmmin belonging to the ldquonormal excavation speedrdquo

Description Number and membershipNumber of rings 50 100 150 200 250 300 350Membership counts 28 51 60 97 128 153 178Membership frequency 056 051 04 049 051 051 051Number of rings 400 450 500 550 600 650 715Membership count 202 252 302 342 382 427 470Membership frequency 051 056 061 062 064 066 066

066

v = 23mmmin

001020304050607

Cov

erag

e fre

quen

cy f

100 600300 700500200 8000 400Segment number

Figure 4 Membership frequency of 23mmmin belonging to the ldquonormal excavation speedrdquo

6 Advances in Civil Engineering

e set of normal excavation speed in Zadehrsquos form wasordered as shown in equations (4) and (5) usv0 20ndash44mmmin was considered as the range of normalexcavation speed in the ensuing PSA analysis

1113957A(v) 05020

+05421

+05922

+06423

+06924

+07525

+08026

+08527

+09028

+09429

+09730

+09931

+132

+09933

+09734

+09435

+09036

+08537

+08038

+07539

+06940

+06441

+05942

+05443

+05044

(4)

supp 1113957A(v) 111386420 21 22 23 24 25 26 27 28 29 30 31 32

33 34 35 36 37 38 39 40 41 42 43 441113865

(5)

Table 5 Membership frequency of the ldquonormal excavation speedrdquo

No Group Count Frequency1 15ndash25 1 00012 25ndash35 2 00033 35ndash45 2 00034 45ndash55 2 00035 55ndash65 5 00076 65ndash75 6 00087 75ndash85 17 00248 85ndash95 21 00299 95ndash105 31 004310 105ndash115 34 004811 115ndash125 46 006412 125ndash135 60 008413 135ndash145 66 009214 145ndash155 100 01415 155ndash165 132 018516 165ndash175 168 023517 175ndash185 217 030318 185ndash195 240 033619 195ndash205 366 051220 205ndash215 396 055421 215ndash225 425 059422 225ndash235 470 065723 235ndash245 500 069924 245ndash255 535 074825 255ndash265 563 078726 265ndash275 588 082227 275ndash285 609 085228 285ndash295 619 086629 295ndash305 668 093430 305ndash315 686 095931 315ndash325 715 132 325ndash335 698 097633 335ndash345 685 095834 345ndash355 670 093735 355ndash365 643 089936 365ndash375 623 087137 375ndash385 586 08238 385ndash395 562 078639 395ndash405 536 07540 405ndash415 495 069241 415ndash425 456 063842 425ndash435 406 056843 435ndash445 358 050144 445ndash455 332 046445 455ndash465 290 040646 465ndash475 246 034447 475ndash485 201 028148 485ndash495 157 02249 495ndash505 136 01950 505ndash515 116 016251 515ndash525 101 014152 525ndash535 91 012753 535ndash545 88 012354 545ndash555 77 010855 555ndash565 69 009756 565ndash575 62 008757 575ndash585 56 007858 585ndash595 51 007159 595ndash605 45 006360 605ndash615 41 0057

Table 5 Continued

No Group Count Frequency61 615ndash625 38 005362 625ndash635 35 004963 635ndash645 32 004564 645ndash655 30 004265 665ndash675 28 003966 675ndash685 28 003967 685ndash695 25 003568 695ndash705 23 003269 705ndash715 23 003270 715ndash725 21 002971 725ndash735 20 002872 735ndash745 19 002773 745ndash755 19 002774 755ndash765 18 002575 765ndash775 18 002576 775ndash785 18 002577 785ndash795 18 002578 795ndash805 16 002279 805ndash815 16 002280 815ndash825 15 002181 825ndash835 15 002182 835ndash845 12 001783 845ndash855 11 001584 855ndash865 8 001185 865ndash875 7 00186 875ndash885 6 000887 885ndash895 5 000788 895ndash905 4 000689 905ndash915 4 000690 915ndash925 4 000691 925ndash935 4 000692 935ndash945 4 000693 945ndash955 3 000494 955ndash965 2 000395 965ndash975 2 0003

Advances in Civil Engineering 7

313 Fuzzy Statistical Tests of Excavation Parameterse excavation speed of the TBM reflects the influenceexerted by the excavation parameters (eg total thrust facepressure and cutter head torque) on the force and dis-placement of the surrounding soil erefore it is necessaryto determine the realistic and practical excavation param-eters based on the excavation speed

Formation reinforcement during TBM launching and TBMarrival can exert a strong influence on the shield tunnel ex-cavation and lead to highly discrete parameters erefore thedata from the TBM launching and TBM arrival stages werediscarded in studying the relationship between excavation speedand TBMparameters Figure 6 shows how the TBMparametersvaried with the excavation speed during the construction of the715 segments in the XWSe curves were fitted viaMATLABand the slope of the curves was highly indicative of the cor-relation between the TBMparameters and the excavation speed

In Figure 6(a) the total thrust (F) increased with risingexcavation speed is was because bentonite was used as alubricant and injected around the shield of the TBM duringexcavation to reduce friction When the amount of injectedbentonite was appropriate the friction coefficient betweenthe shield and the surrounding soil would decrease and theexcavation speed would then increase when the thrust (F)was higher In Figure 6(b) the excavation speed decreasedwhen the cutter head torque (MT) increased is wasbecause when the soil body of the tunneling face wasrelatively difficult to cut a larger torque of the cutter headwould be needed and the excavation speed would decreaseFigure 6(c) shows that during normal excavation thepressure of the tunneling face increased slightly with risingexcavation speed Besides Mair pointed out that duringsegment assembly the downtime of TBM would decreasethe soil and water pressure on the tunneling face whichcould reduce the control pressure of the tunneling face [33]e same pattern was observed in the current constructionlogs and the R2 value of the curve in Figure 6(c) was hencerelatively low Figure 6(d) shows that the grouting pressuredecreased slightly with rising excavation speed However

since the pressure of primary grouting was read off from thegrouting pressure pump the actual grouting pressureexerted on the surrounding soil was smaller and theprimary grouting pressure hence had limited impact onexcavation speed

(1) Determination of Standard TBM Parameters It wasdetermined from the fuzzy statistical tests above that thestandard excavation speed was 32mmmin e corre-sponding standard TBM parameters could be determinedaccordingly from the following equation

TBMPstandard value 1113936

Nn1TBMPnv

N v321113868111386811138681113868 (6)

where TBMP is the TBM parameter and v is the excavationspeed (mmmin)

(2) Determination of the Range of TBM Parameters It wasdetermined from the fuzzy statistical tests above that therange of excavation speed was 20ndash44mmmin e corre-sponding boundaries of TBM parameters could be de-termined from the extreme values in the monitoring records(Figure 6) via the following equation

TBMPupper limit max TBMPv 20levle4411138681113868111386811138681113966 1113967

TBMPlower limit min TBMPv 20levle4411138681113868111386811138681113966 1113967

(7)

(3) ldquoNormal Excavation Phaserdquo of TBM According to thefuzzy set theory the excavation speed in the ldquonormal ex-cavation phaserdquo fell within 20ndash44mmmin e TBM wasconsidered to be in the ldquonormal excavation phaserdquo whenthe excavation speed and the TBM parameters all fellwithin the prescribed ranges specified above and listedagain in Table 6 e standard values and ranges were usedfurther in the subsequent PSA analysis Table 6 shows thatamong the examined parameters the face pressure had adeviation interval of merely 196 and was controlled the

Advance speed v (mmmin)

Mem

bers

hip

Atilde (v

)

Cov

erag

e fre

quen

cy A

(v)

04

02

06

08

1

10090807060504030201000

04

02

06

08

1

0

Fuzzy statistical experiment methodCauchy distribution curve

Figure 5 e histogram of membership frequency and the membership function of TBM excavation speed

8 Advances in Civil Engineering

best whereas the cutter head torque had a deviation in-terval of 7401 and was controlled the worst

(4) Statistical Relationship between TBM Parameters andExcavation Speed e monitoring results in Figure 6

demonstrated that in the ldquonormal excavation phaserdquo ofthe XWS the total thrust and the face pressure were posi-tively correlated with the excavation speed In particular thetotal thrust had a stronger correlation to the excavationspeed than the face pressure In contrast the cutter head

2000400060008000

1000012000140001600018000

Tota

l thr

ust

F (k

N)

20 25 30 35 40 45 50 55 60 6515Advance speed v (mmmin)

(a)

0500

10001500200025003000350040004500

Cutte

r hea

d to

rque

MT

(kNlowast

m)

20 25 30 35 40 45 50 55 60 6515Advance speed v (mmmin)

(b)

0

50

100

150

200

250

Face

pre

ssur

eP N

(kPa

)

20 25 30 35 40 45 50 55 60 6515Advance speed v (mmmin)

(c)

Gro

utin

g pr

essu

reP G

(kPa

)

100150200250300350400450500550

20 25 30 35 40 45 50 55 60 6515Advance speed v (mmmin)

(d)

Figure 6 Variations in the TBM parameters at different excavation speeds (data from XW section) (a) total thrust versus excavationspeed (b) cutter head torque versus excavation speed (c) face pressure versus excavation speed (d) grouting pressure versus excavationspeed

Table 6 Standard values and ranges of excavation speed and TBMPs

Factors v (mmmin) F (kN) P N (kPa) M T (kNmiddotm) P G (kPa)Parameter range [20 44] [8300 13100] [117 143] [1294 2974] [197 302]Standard value 32 9700 1326 2270 302Deviation range () [minus375 375] [minus1443 3505] [minus1176 784] [minus430 3101] [minus3477 0]

Advances in Civil Engineering 9

torque and the primary grouting pressure were negativelycorrelated with the excavation speed

32 Bow-Tie-Bayesian Network Analysis e bow-tie anal-ysis combines FTand ETanalysese FTanalysis in bow-tiecalculates the occurrence probability of the loss event (LE) aswell as the top event (TE) e occurrence probability of theTE can also be obtained from the occurrence probability ofthe basic event (BE) e events could be evaluated by theirlogical relationship and their occurrence probability in theBN Mapping the bow-tie analysis to BN involves convertingboth FT and ET analyses Figure 7(a) provides a brief de-scription of calculation steps

ree importance measures described in the followingBorst and Schoonakker [30] were introduced in the newmethodology according to the Bayes theorem Figure 7(b)gives a brief description of their calculation In the proposedmethodology the critical nodes that could more easilytrigger accidents were obtained by calculating these im-portance measures

33 Confirming Failure Occurrence Probability e BT-BNanalysis requires knowing the occurrence probability of eachbasic event (BE) e basic events fall into four categoriesenvironmental failure operational error multiple failuresand facility failures e occurrence rate of facility failureswas obtained from the construction log of the XWS for thetunneling project that spanned 179 days (715 segments intotal) and was converted into occurrence probability via thefollowing equation

F 1minus eminusλt

(8)

where F denotes the occurrence probability of the failure andλ denotes the occurrence rate of the failure

e occurrence probability of environmental failureoperational error and multiple failures cannot be readilyderived from existing data and was thus estimated via expertopinione fuzzymethod combines the opinions of differentexperts in a weighted manner to calculate the fuzzy fault rate(FFR) from the triangular fuzzy numbers or trapezoidal fuzzynumbers proposed by the experts e occurrence probabilityof environmental failure operational error and multiplefailures was then determined from the FFR [34] e generalprocedure of the fuzzy method is as follows

(1) Determine the weight of the opinion of each expertbased on the age education background work ex-perience and position of the consulted expert (Ta-ble 7) e crude weight score of each expert iscalculated via the following equation

Sn Sna+ Snb

+ Snc+ Snd

(9)

where Sn represents the total weight score of theexpert e relative weight score of each expert iscalculated via the following equation

Wn Sn

1113936mn1Sn

(10)

where m represents the number of experts(2) e occurrence probability is divided into the

following categories nonoccurrence absolute lowvery low low fairly low medium fairly high highvery high absolute high or occurrence e rankvalue of the categories escalates from 0 for non-occurrence to 1 for the occurrence (Table 8) eoccurrence probability of the event is then evalu-ated based on the corresponding triangular numberor trapezoidal number given by the experts

(3) Aggregation of the fuzzy numbers When the fuzzynumbers are all triangular number or trapezoidalnumber the aggregated fuzzy numbers of an event iscalculated via equation (11) [35] e aggregatedfuzzy number considering the expert weight isshown in equation (12)

1113957Aaggregated 1113944m

n1Wn otimes 1113957An (11)

where 1113957Aaggregated represents the aggregated fuzzifiednumber given by expert m and Wn represents theweight of the expertrsquos opinion

1113957AW 1113874W1a11 + W2a21 W1a12 + W2a22 W1a12

+W2a23 W1a13 + W2a241113875

(12)

(4) After the aggregated fuzzy numbers are determinedthe centroid index method (equation (13)) is used tohandle the fuzzy numbers and obtain the fuzzyprobability score (FPS) [36]

X 1113938g(x)x dx

1113938g(x)dx (13)

where X is the defuzzified output g(x) is themembership function and x is the output variableAssume 1113957An (an1 an2 an3) a triangular number and1113957An (an1 an2 an3) a trapezoidal number e FPS iscalculated via equation (14) when a fuzzy number is atriangular number and via equation (15) when thefuzzy number is a trapezoidal number

FPS 13

an1 + an2 + an3( 1113857 (14)

FPS 13

an3 + an4( 11138572 minus an3an4 minus an1 + an2( 1113857

2+ an1an2

an3 + an4 minus an1 minus an2( 1113857

(15)

10 Advances in Civil Engineering

(5) Finally the FPS is converted to FFR via equation(16) [37] and the FFR is further converted tothe occurrence probability of environmentalfailure operational error and multiple failures(equation (8))

FFR

110k

FPSne 0

0 FPS 0

k 2301 times(1minus FPS)

FPS1113890 1113891

13

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(16)

4 Results

41 Analysis of Excessive Surface Settlement inNormal TunnelExcavation Figure 8 shows that the normal excavation

(1) If the logical relationship is AND between events the TE occurs when all events occur The probability of TE can be calculated from the following equation

(A)

(2) If the logical relationship is OR between events the TE occurs when any of the event occurs The probability of TE can be calculated from the following equation

(B)

(3) By definition in the FT analysis the probability of TE is the same as that of LE Similarly the probability of the initial event (IE) in the ET analysis is the same as that of LE The probability of OE in ET analysis can be calculated from the following equation

(C)

(4) The BN an inference method based on the Bayes theorem combines both graph theory and probability theory

(D)

FTE = i=1

nFBEi

FTE = 1 ndashi=1

n(1 ndash FBEi)

FOEn = FIE middot i=1

nP (Ei = 0) middot

j=1

nP (Ej = 1)

P(B | A) = P(A | B) middot P(B)

P(A)

(a)

(1) The Birnbaum measure (BM) whichdetermines the increment of the occurrenceprobability of TE when BE occurs is shownin the following equation

(E)

where P(TE | BE = 1) denotes the occurrence probability of TE when BE occurs and P(TE | BE = 0) denotes the occurrence probability of TE when BE does not occur

(2) Risk achievement worth (RAW) evaluatesthe impact of BE on TE when the probabilityof BE is considered The RAW is adjustedby the probability of TE and BE as shown inthe following equation

(F)

where P(BE) denotes the occurrence probability of BE and P(TE) denotes the occurrence probability of TE under all circumstances

(3) The FussellndashVesely (FV) importance which describes the contribution of BE to system fault is shown in the following equation

IBBE

M = P(TE | BE = 1) ndash P(TE | BE = 0)

IRB

AE

W = IBBE

M middot P(BE)P(TE)

(G)

P(TE) ndash P(TE | BE = 0)P(TE)

IFB

VE =

(b)

Figure 7 Bow-tie-Bayesian network analysis Calculation of (a) event probability and (b) importance measures

Table 7 Weight scores for experts

Factor Category Score

Age (a)

lt30 130ndash39 240ndash49 3ge50 4

Education (b)

High school 1College 2Bachelor 3Master 4PhD 5

Work experience (c)

lt5 years 15ndash10 years 211ndash20 years 321ndash30 years 4ge30 years 5

Position (d)

Worker 1Technician 2

Junior scholarengineer 3Senior scholarengineer 4

Table 8 Rank value of each category

Classified occurrence probability Rank valueNonoccurrence 0Absolute low 01Very low 02Low 03Fairly low 04Medium 05Fairly high 06High 07Very high 08Absolute high 09Occurrence 10

Advances in Civil Engineering 11

phase involves the environment TBM operation supervi-sion management and emergency handling Risk analysis ofthe ldquonormal excavation phaserdquo in soft soil engineering basedon the XWS allows the identification of potential risk factorsthat may trigger surface settlement and consequently lead toaccidents Eskesen et al have described three principles forrisk analysis as follows (1) eliminate risk factors that are easyto detect and can be controlled timely and effectively (2)eliminate risk factors with low occurrence probability andno catastrophic consequences and (3) combine risk factorswith similar loss consequences [38] Accordingly the riskfactors during shield tunneling were organized into three

basic categories improper control of excavation parameters(eg poor control of face pressure) catastrophic geology (egground cavity or flow sand) and unforeseeable factors (egsegment damage) Figure 9 shows the bow-tie model builtfrom the categorized factors for the risk of surface collapsecaused by excessive surface settlement during shield tun-neling OEs of various degrees were successfully predictedbased on the CEs (Figure 9) Many risk factors exist in anygiven surface collapse In this section based on the previouscalculation results in Section 31 we selected the manageableshield excavation parameters (shield total thrust groutingpressure cutter head torque soil pressure etc) in the ldquonormal

Synchronousgrouting

ExcavationSegment

installationAttitudecontrol Tail sealing

Excavationcycle

Quality controlacceptance

Dangeroussituation exists Yes

Prepareemergencymeasures

Emergencymeasures

Execution of emergencymeasures

Acceptance ofexcavationprocedures

Excavationacceptance

report

Monitoring measurements

Monitored dataof excavationenvironment

Formation geologyTBM parametersExcavation axis

Segment installationSynchronous grouting

TBM construction parameter

No

TBM parametersv (mmmm) F (kN) PN (kPa)

MT (kNmiddotm) PG (kNmiddotm)TBM attitude TBM position TBM fault information

Soil bodyparameters

Soil evolutionmodel

Confined waterObstacles

Ground cavity orquicksand

Metro tunnel excavation

Emergencyhandling

Supervision

TBMoperation

TBM

Environment

Management

Figure 8 System diagram of the ldquonormal excavation phaserdquo

12 Advances in Civil Engineering

excavation phaserdquo as the base events assigning their weightsaccording to Section 33 and then performed PSA analysis

As mentioned earlier the ldquonormal excavation phaserdquo isunder the influence of excavation parameters catastrophicgeology and unforeseeable factors Surface settlement canoccur once the condition deteriorates Here we set excessivesurface settlement as the TE in the FT analysis Meanwhilethe tunneling system has a built-in emergency managementsystem Upon excessive surface settlement the emergencymanagement system will start to shut down the TBM timelyHence in the ETanalysis the excessive surface settlement isset as the IE and TBM shutdown is set as the CE OEs ofvarious degrees are obtained based on the considered CEFinally the surface settlement is set as the LE to connect theFT and the ET and furnish the BTmodel (Figure 9 Table 9)Eight OEs of various degrees were predicted based on theCEs including surface collapse events OE3 OE4 OE6 OE7and OE8 (Figure 9 Table 10) e TBM shuts down if CE1occurs and continues to operate if otherwise

e BN-BT model for excessive surface settlement isconstructed by mapping the FT and ET analyses in the BT(Figure 9) model to BN (Figure 10) All the nodes of BN havepreviously been described in the BT except the node OEwhich is the consequence node OE is added to accommodatethe outcomes of BT By connecting the node of excessivesurface settlement to OE another state also called the safe

state is added to the state set It includes consequences OE1 toOE8 to account for the nonoccurrence of the top event iewhen excessive surface settlement controlled To show thedependence among the safety barriers and the top eventcausal arcs are also drawn between TBM shutdown andgrouting in the settlement area and bentonite injection to soilchamber and TBM shield It is worth noting that since variouscombinations of the failure and success of the sequentialsafety barriers result in different consequences in the BT allthe safety nodes of BN are connected to node OE

42 Determination of Event Occurrence Probability emaximum surface settlement that resulted from the aber-ration of the ith TBM parameter is denoted as δmaxi eprobability of safety accident becomes higher when δmaxiapproaches the permitted surface settlement δi Whenδmaxi δi the accident will occur as soon as the TBM pa-rameter gives rise to a surface settlement of δmaxi eprobability of equipment fault for the normal excavationsystem was calculated via equation (8) from the engineeringlog data of the XWS over 179 days of construction (715segments rings in total) e construction of all 715 rings fellwithin the ldquonormal excavation phaserdquo as was defined by thefuzzy statistical test (v 20ndash44mmmin) Table 11 lists thecalculation results

X3X2X1

OR

M1

X7X6X5X4

OR

M2

X10X9 X11 X13X12

M3

OR

Excessive surface

settlement

X8

Caus

esLE

CE1

CE2

CE3

Con

sequ

ence

sSt

op

TBM

Gro

utin

g in

settl

emen

tar

ea

Bent

onite

inje

ctio

n

OE 1

OE 2

OE 3

OE 4

OE 5

OE 6

OE 7

OE 8

Success Failure

AND

Figure 9 Diagram of bow-tie analysis for excessive surface settlement

Advances in Civil Engineering 13

To address the uncertainty regarding the events ofenvironmental failure operational error and multiplefailure six domain experts who participated in the con-struction of the Wuhan metro system including two seniorengineers one senior academic professor one technicalconsultant one junior engineer and one worker wereinvited to evaluate the occurrence probability of events thatcannot be readily derived from existing data (Table 12)eweights of their opinion were then calculated by usingequations (9) and (10) and the distribution of each opinionweight is shown in Figure 11

In addition Table 13 lists the expert opinions regardingthe events of environmental failure operational error andmultiple failures in the form of fuzzy numbers based onTable 8 e fuzzy numbers were aggregated via equations(12) and converted to FPS and FFR via equations (13)ndash(16)(Table 14) e occurrence probabilities were finally derivedfrom FFR (Table 14) Generally the expert knowledge isconsidered as a scarce resource which cannot provide

universal consultation or real-time guidance us there ismuch room to improve the data use efficiency

43 Update in Occurrence Probability of LE and OE eoccurrence probability of basic events is calculated as de-scribed in Section 42 including the occurrence probabilityof facility failure from the engineering log data of the XWS aswell as that of environmental failure operational error andmultiple failures derived from expert opinion e occur-rence probability of excessive surface settlement (LE) isdetermined via equations (A) and (B) by considering thelogical relationship between events in Figure 7 Finally theoccurrence probability of OEs including surface collapse canbe calculated via equation (C) in the figure by mapping theFT and ET analyses in the BTmodel to BN Figure 12 showsthe occurrence probabilities of the LE (ie excessive surfacesettlement) and that of the OEs

e above analysis shows that the occurrence probabilityof excessive surface settlement within one year is 08299(Figure 12) is occurrence probability of surface collapse(OE3 OE4 OE6 OE7 and OE8) may be decreased whenemergency measures are put in place including grouting insettlement area and bentonite injection to soil chamber andTBM shield However these measures cannot help to reduceminor accidents since the occurrence probability remains athigh levels for OE1 OE2 and OE5 Admittedly grouting andbentonite injection are necessary measures and they candecrease the effects of excessive surface settlement duringshield tunneling However the key point of avoiding outcomeevents including surface collapse to ensure project safety is toprevent the excessive surface settlement from occurring in thefirst place Hence we sought to determine the key nodesleading to excessive surface settlement via BT-BN analysis andpropose the corresponding preventive measures

Table 10 Analysis of event occurrence

Symbol EventOE1 Excessive surface settlement

OE2Grouted cutter head and shield excessive surface

settlement and minor property damageOE3 Minor surface collapse and property damage

OE4Moderate surface collapse major property damage

and minor casualtiesOE5 Excessive surface settlement

OE6Grouted cutter head and shield moderate surface

collapse and minor property damage

OE7Moderate surface collapse and major property

damage

OE8Severe surface collapse major property damage and

major casualties

Table 9 Details of bow-tie components in Figure 9

Event Symbol Logic link type Failure modelGround settlement Excessive surface settlement OR gate mdashCatastrophic geology M1 OR gate mdashUnforeseeable factors M2 OR gate mdashExcavation parameters M3 AND gate mdashConfined water X1 mdash Environmental failureGround cavity or flow sand X2 mdash Environmental failureObstacles X3 mdash Environmental failureSegment damage X4 mdash Operational errorAbnormal TBM shutdown X5 mdash Multiple failureSeal failure at shield tail X6 mdash Multiple failureExcessive deviation from axis X7 mdash Operational errorEquipment failure X8 mdash Multiple failureUntimely grouting X9 mdash Facility failureExcessive cutter head torque X10 mdash Facility failureImproper control of face pressure X11 mdash Facility failureExcessive thrust X12 mdash Facility failureImproper control of excavation speed X13 mdash Facility failureTBM shutdown CE1 mdash Multiple failureGrouting in settlement area CE2 mdash Multiple failureBentonite injection to soil chamber and TBM shield CE3 mdash Multiple failure

14 Advances in Civil Engineering

Table 11 Probability of equipment fault

Event Surface settlementδmaxi (mm)

Permitted surfacesettlement δi (mm)

Value of TBMparameter

Occurrence rate(dminus1)

Occurrence probability(in 1 year)

X9 89 15 302 kPa 10675eminus 04 382eminus 02X10 84 10 2974 kNmiddotM 17792eminus 04 629eminus 02X11 86 15 143 kPa 71167eminus 05 256eminus 02X12 98 15 13100 kN 14233eminus 04 506eminus 02X13 120 15 41mmmin 28467eminus 04 987eminus 02All data were obtained from the operation log of the XWS

Table 12 Characteristics of experts participated in the occurrence probability evaluation

Expert Age Education Service (years) Professional position1 56 High school 25 Worker2 35 Master 10 Technician3 41 Master 15 Junior engineer4 47 Bachelor 20 Senior engineer5 50 PhD 18 Senior academic6 59 PhD 30 Senior engineer

0125 0125

01625 01625

020225

AgeEducationService

Professional positionWeighting

2 3 4 5 61Expert

0

005

01

015

02

025

Wei

ghtin

g

0

1

2

3

4

5

6

Wei

ghtin

g sc

ore

Figure 11 Distribution of each expert opinion weight

X1 X2 X3

M1

X5 X6 X7 X8

M2

X9 X11

M3

Excessive surface

settlement

X10 X12 X13X4

CE1 CE2 CE3

OE

Caus

esLE

CEC

onse

quen

ces

Figure 10 Bow-tie chart of excessive surface settlement

Advances in Civil Engineering 15

44 Identify Key Nodes and Provide Safety Measures Inorder to find the key nodes leading to excessive surfacesettlement the importance measure of each event was cal-culated via equations (E)ndash(G) in Figure 7 as shown inTable 15 Assume the number of events as ldquonrdquo e nor-malized weight Rlowast could be calculated from the importancemeasure Ii via the following equation

Rlowast

Ii

1113936ni1Ii

times 100 (17)

After the normalized weight Rlowast is calculated for eachimportance measure the total weight Rlowast could be calculatedvia equation (18) e total weight Rlowast of events was finally

ranked in descending order to find the key nodes as shownin Table 16

Rlowast R

lowastBM + R

lowastRAW + R

lowastFV (18)

It can be seen that X6 (seal failure at shield tail) X1(confined water) X2 (ground cavity or flow sand) X5 (ab-normal TBM shutdown) and X7 (excessive deviation fromaxis) have far higher weight than other events and are thusthe key nodes to accidents related to excessive surface set-tlement Measures can be taken to particularly ensure safetyat these nodes e occurrence probability of excessivesurface settlement can be reduced by 66 when X6 X1 X2X5 and X7 are ensured safe (Figure 13)

Table 13 Expert opinion on environmental failure operational error and multiple failures

Event Fuzzy numbers proposed by each expert

X1

Expert 1 Expert 2 Expert 3(02 03 04 05) (01 02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 02 03 05)

X2

Expert 1 Expert 2 Expert 3(01 02 03 05) (02 03 04) (01 02 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (02 03 05) (01 02 03 05)

X3

Expert 1 Expert 2 Expert 3(01 02 04 05) (01 02 03 05) (01 03 04)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03) (01 02 03)

X4

Expert 1 Expert 2 Expert 3(02 03 04 05) (01 02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(02 03 04) (02 03 05) (01 02 03 05)

X5

Expert 1 Expert 2 Expert 3(01 03 04) (01 02 03 05) (02 03 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (02 03 05) (01 02 03)

X6

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 03 05) (02 03 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (02 03 05) (01 02 04 05)

X7

Expert 1 Expert 2 Expert 3(01 02 04 05) (01 02 03 05) (02 03 04)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 03 05)

X8

Expert 1 Expert 2 Expert 3(01 03 04 05) (01 02 03 04) (02 03 04)

Expert 4 Expert 5 Expert 6(02 03 04) (01 02 03 05) (01 02 03)

CE1

Expert 1 Expert 2 Expert 3(02 03 04 05) (02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 02 04 05)

CE2

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 05) (02 03 04 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (01 02 03 05) (01 03 05)

CE3

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 03 05) (03 04 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (01 02 04 05) (01 02 03 05)

16 Advances in Civil Engineering

In accordance with the predictive and diagnosticanalysis results using the established model some safetymeasures for key nodes are displayed in time to reduce theexcessive surface settlement risk during the tunnelexcavation

(1) e nodes X5 (abnormal TBM shutdown) and X7(excessive deviation from the axis) mostly involveoperational error Safety management and supervi-sion need to be strengthened at the construction siteto eliminate such errors and ensure that the TBM isoperated properly Besides an advanced real-time

laser locator may help to alarm in the case of largeaxial deviation

(2) e nodes X1 (confined water) and X2 (ground cavityor flow sand) belong to environmental failure Inorder to reduce the influence of environmental failurecareful geological exploration should be carried outbefore tunneling to identify the poor geological and

Table 14 Calculation of FPS FFR and the occurrence probability of environmental failure operational error and multiple failures

Event Aggregated fuzzy numbers FPS FFR (dminus1) Failure probability (in 1 year)X1 (01288 02288 03288 04838) 02951 83969eminus 04 26402eminus 1X2 (01325 02325 03163 04713) 02909 80032eminus 04 25336eminus 1X3 (01000 02163 02700 03825) 02420 42986eminus 04 14518eminus 1X4 (00450 00900 01125 01800) 01082 22492eminus 05 81803eminus 3X5 (01363 02488 02775 04263) 02747 66022eminus 04 214155eminus 1X6 (01488 02488 03225 04713) 03004 89125eminus 04 27770eminus 1X7 (01163 02388 03125 04675) 02855 75157eminus 04 24002eminus 1X8 (01450 02538 02950 03100) 02463 45643eminus 04 15338eminus 1CE1 (01413 02413 03513 04838) 03058 94598eminus 04 29202eminus 1CE2 (01288 02513 03038 04713) 02916 80679eminus 04 25496eminus 1CE3 (01450 02450 03363 04713) 03010 89722eminus 04 27937eminus 1

08299

03155

01223 010800419

01301

00504 00445 00173

Occ

urre

nce p

roba

bilit

y (in

1 y

ear)

00

01

02

03

04

05

06

07

08

09

OE1 OE2 OE3 OE4 OE5 OE6 OE7 OE8LE

Figure 12 Occurrence probability of surface settlement and otheroutcome events

Table 15 Calculation of importance measure of influential factors

SymbolImportance measure

BM RAW FVX1 2311eminus 1 7352eminus 02 7352eminus 02X2 2279eminus 1 6958eminus 02 6958eminus 02X3 1990eminus 1 3481eminus 02 3481eminus 02X4 1716eminus 1 1691eminus 03 1691eminus 03X5 2165eminus 1 5587eminus 02 5587eminus 02X6 2356eminus 1 7884eminus 02 7884eminus 02X7 2239eminus 1 6476eminus 02 6476eminus 02X8 2010eminus 1 3715eminus 02 3715eminus 02X9 1370eminus 6 6306eminus 08 6306eminus 08X10 8300eminus 7 6291eminus 08 6291eminus 08X11 2040eminus 6 6293eminus 08 6293eminus 08X12 1030eminus 6 6280eminus 08 6280eminus 08X13 5300eminus 7 6303eminus 08 6303eminus 08

Table 16 Ranking results of the key events

Rank SymbolNormalization weighting (Rlowast) Total

weighting(Rlowast)

RlowastBM RlowastRAW RlowastFV

1 X6 13805 18942 18942 516892 X1 13541 17664 17664 488693 X2 13354 16717 16717 467884 X7 13120 15559 15559 442385 X5 12686 13423 13423 395326 X8 11778 8926 89255 296297 X3 11661 8363 8363 283878 X4 10055 0406 0406 108689 X11 00002 1512eminus 05 1512eminus 05 1498eminus 0410 X9 8028eminus 05 1515eminus 05 1515eminus 05 1106eminus 0411 X12 6035eminus 05 1509eminus 05 1509eminus 05 9053eminus 0512 X10 4863eminus 05 1511eminus 05 1511eminus 05 7886eminus 0513 X13 3106eminus 05 1514eminus 05 1514eminus 05 6134eminus 05Total 100 100 100 100

02822

01073

00416 0036700142

0044200172 00151 00059

Occ

urre

nce p

roba

bilit

y (in

1 y

ear)

000

005

010

015

020

025

030

OE1 OE2 OE3 OE4 OE5 OE6 OE7 OE8LE

Figure 13 Occurrence probability when safety is ensured at keynodes

Advances in Civil Engineering 17

hydrological conditions that may be encounteredDuring excavation the advanced geological pre-diction technologymay be employed to detect adversegeological and hydrological conditions ahead of theTBM in real time including confined water groundcavity and flow sand

(3) Node X6 (seal failure at shield tail) belongs tomultiple failures e quality of the tail brush needsto be enhanced and tail brush should promptly bereplaced when it is worn

By adopting corresponding safety measures in shieldtunnel excavation the occurrence probability of variousdegrees of surface collapse (OE3 OE4 OE6 OE7 and OE8)was significantly decreased (Figure 13) Finally the TBMssuccessfully passed through the left track of DCS on March3 2017 and the right track on June 11 2017 without anysurface collapse accident demonstrating the effectiveness ofour proposed hybrid method

5 Conclusions and Future Works

In this work we first defined the ldquonormal excavation phaserdquoof shield tunneling based on the fuzzy statistical test theoryData were extracted from the construction log of the XWS inthe Wuhan metro line 7 to determine the occurrenceprobability of facility fault and expert opinions were soli-cited to determine the occurrence probability of environ-mental failure operational error and multiple failuresProbabilistic safety assessment (PSA) of the normal shieldtunnel excavation system was then performed accordingly

We employed the bow-tie analysis to evaluate the oc-currence of excessive surface settlement during normaltunnel excavation e presence of emergency measurescould reduce the occurrence probability of surface collapsecaused by excessive surface settlement (OE3 OE4 OE6 OE7and OE8) but have limited effect on the prevention of ac-cidents of OE1 OE2 and OE5 It is essential to decrease theprobability of excessive surface settlement in order to pre-vent the resulting outcome events (OEs)

By mapping the bow-tie analysis to Bayesian networks(ie BT-BN analysis) we determined the key nodes thatcould cause excessive surface settlement (LE) e key nodesincluded the following X6 (seal failure at shield tail) X1(confined water) X2 (ground cavity or flow sand) X5 (ab-normal TBM shutdown) and X7 (excessive deviation fromthe axis) Effective safety measures at these nodes couldreduce the occurrence probability of excessive surface set-tlement (LE) by 66

To ensure safety careful geological exploration shouldbe carried out before the tunneling project During thetunneling safety management and supervision should bestrengthened at the construction site Advanced geo-logical prediction technology should be used to detectpoor geological and hydrological conditions ahead of theTBM in real time Advanced laser locator should be usedto monitor and alarm excessive axial deviation equality of the tail brush should be improved and tailbrush should be replaced timely when it becomes worn

e occurrence probability of excessive surface settlementwas decreased by adopting these safety measures and theoccurrence of the resulting surface collapse was sub-sequently decreased

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

e authors thank the workers foremen and safety co-ordinators of the main contractors for their participatione authors also wish to thank the engineers Yun Zhang andPeilun Tu for assistance in gathering field data

References

[1] T Zhao W Liu and Z Ye ldquoEffects of water inrush fromtunnel excavation face on the deformation and mechanicalperformance of shield tunnel segment jointsrdquo Advances inCivil Engineering vol 2017 Article ID 5913640 9 pages 2017

[2] W Liu T Zhao W Zhou and J Tang ldquoSafety risk factors ofmetro tunnel construction in China an integrated study withEFA and SEMrdquo Safety Science vol 105 pp 98ndash113 2018

[3] K Li ldquoHangzhou metro site collapse accidentrdquo 2008 httpnewssohucom20081115n260653551shtml

[4] S Liu ldquoConstruction of Nanchang metro line 2 constructionsection pavement collapsesrdquo 2017 httpnewssohucom20160514n449414512shtml

[5] R B Peck ldquoDeep excavations and tunneling in soft groundrdquo7th International Conference on Soil Mechanics and Foun-dation Engineering vol 7 no 3 pp 225ndash290 1969

[6] P B Attewell I W Farmer and N H Glossop ldquoGrounddeformation caused by tunnelling in a silty alluvial clayrdquoGround Engineering vol 11 no 8 pp 32ndash41 1978

[7] W J Rankin ldquoGround movements resulting from urbantunnelling predictions and effectsrdquo Geological Society Lon-don Engineering Geology Special Publications vol 5 no 1pp 79ndash92 1988

[8] P B Attewell and J P Woodman ldquoPredicting the dynamicsof ground settlement and its derivatives caused by tunnelingin soilrdquo Ground Engineering vol 15 no 8 pp 13ndash20 1982

[9] M P OrsquoReilly and B M New ldquoSettlement above tunnels inthe United Kingdommdashtheir magnitude and prediction intunnelling 82 proceedings of the 3rd international sympo-sium brighton 7ndash11 June 1982 P173ndash181 Publ LondonIMM 1982rdquo International Journal of Rock Mechanics ampMining Sciences amp Geomechanics Abstracts vol 20 no 1pp 1ndash18 1983

[10] R J Mair R N Taylor and A Bracegirdle ldquoSubsurfacesettlement profiles above tunnels in claysrdquo Geotechniquevol 45 no 2 pp 361-362 1995

[11] X L Yang and J MWang ldquoGroundmovement prediction fortunnels using simplified procedurerdquo Tunnelling and Un-derground Space Technology vol 26 no 3 pp 462ndash471 2011

18 Advances in Civil Engineering

Besides long learning time is needed and the requirementon known parameters can be demanding

Overall surface settlement in shield tunneling arisesfrom various risk factors that involve geology constructionmethod environment and management In order to thor-oughly study the safety risk of surface settlement it isnecessary to analyze in real time the uncertain informationin the risk factors from multiple sources However suchuncertainty including fuzziness and stochasticity is ubiq-uitous and restricts the application of traditional method-ologies such as empirical formula simulation and analyticalmodeling Other methods based on artificial intelligencesuch as neural networks also suffer from the memory effectbecause it is difficult to update the risk factors in real timewhen new information arises

22 Bayesian Network and Bow-Tie In recent years thebow-tie (BT) model has been combined with the Bayesiannetwork (BN) to tackle various problems in which un-certainty is deeply rooted e BT-BN approach has a solidfoundation in mathematical theory and has unique ad-vantages in dealing with complex dynamic uncertainty Ithas been considered as an ideal tool for knowledge repre-sentation inference and forecasting in an uncertainenvironment

Bow-tie analysis is a quantitative model that consists offault tree (FT) analysis and event tree (ET) analysis [20] andallows investigating the causes and consequences of a givenundesirable event Cherubin et al applied BT analysis as asimple and effective quantitative risk assessment (QRA)approach for the identification and evaluation of potential

Table 1 Standards for monitoring surface settlement in shield tunnel excavation

Country US Japan France Germany China

Acceptable surface settlement (mm) 10ndash15 25ndash50 Hard rock 10ndash20Soft rock 20ndash50 50 Hard soil 10ndash40

Soft soil 15ndash45

Table 2 Classification of risk levels

Level 1 2 3 4 5Description Negligible Alarming Serious Dangerous CatastrophicSurface settlement (mm) 0ndash10 5ndash15 10ndash25 20ndash35 30ndash45

Line 1Line 2Line 3Line 4Line 5

Location of Xiaodongmen-Wuchang section (XWS)

Site picture of theconstruction of XWS

Line 6Line 7Line 8Line 11Line 21

Ordinary stationTransfer stationTerminal station

Railway stationAirport

Figure 1 Location of XWS in the Wuhan metro system

Advances in Civil Engineering 3

hazards and associated risks with the baseline risk assess-ment tool (BART) [21] Targoutzidis argued that BTanalysisis an effective tool for identifying environmental risk sourcesbecause it can clearly show the connections between thecause the loss events (LEs) the conditional events (CEs)and the outcome events (OEs) [22] e BT approach hasbeen applied in the risk assessment of hexane distillation therisk management of harbor and maritime terminals and therisk assessment of airworthiness in military aviation [23ndash25]

e focus of these BT models is to depict the entirescenario of the accident to identify and evaluate the po-tential causes and consequences but does not readily revealthe actual causes through logical connections and occur-rence probability is caveat can be remedied by mappingBT to BN For example Badreddine and Amor improvedthe BTmodel by exploiting the advantages of BN dynamicanalysis ey built the BT chart in an automated anddynamic way to implement appropriate barriers to pre-vention and protection in dynamic systems [26] Khakzadet al made a dynamic risk analysis of systems whosephysical reliability is updated periodically [27] ey madeuse of the Bayes theorem to periodically update the failureprobability of safety barriers in the BT chart and estimatedthe probability of consequences based on the enhanced BTchart It was argued that mapping BT to BN [28] couldalleviate the limitations of BT caused by static factorsAbimbola et al used BT and BN to determine the keyfactors of the integrity model In their study the posteriorprobability was obtained through the Bayes theorem andthe key factors were determined by the ratio of the posteriorprobability to the prior probability [29]

In summary mapping BT to BN allows dynamic riskanalysis and the key factors of the system can be identifiedby calculating the posterior probability through the Bayestheorem Meanwhile since the conditional probability canbe calculated via the Bayes theorem the importance measureof PSA can also be introduced [30] and BN can be fitted withthese important measures very well to calculate the im-portance measures accurately and easily erefore the BT-BN analysis can not only analyze surface collapse caused byexcessive surface settlement in shield tunneling metroconstruction but also use PSA to confirm the critical causesof accidents by adding the importance measures

3 Methodology

BT analysis is used to display the scenario of the loss event(LE) in the system In the BTmodel the FTanalysis can revealthe cause of the LE and the consequences of LE can bedetermined by the ET analysis In the proposed BT-BNmethod the FT and ETanalyses in the BTmodel are mappedto the BN such that the nodes that give rise to accidents can bemore easily determined e BT-BN method requires explicitoccurrence probability of failure Data for the failure prob-ability of the TBM were extracted from construction logduring the ldquonormal excavation phaserdquo of the XWS Whenexisting data could not provide the required informationexpert opinion in the form of the fuzzy number was used todetermine the corresponding failure probability e

consequences were then predicted by the BT-BN analysis andthe critical nodes related to the consequences were obtainedFigure 2 shows the flowchart of the proposed methodology

31 ldquoNormal Excavation Phaserdquo of TBM

311 Fuzzy Statistical Test 9eory e concept of ldquofuzzysetrdquo introduced by Zadeh is a crucial extension of the classicset theory of Cantor [31] e fuzzy set theory has maturedover the past years to a well-established research area inmathematics and has found extensive applications in manyfields e fuzzy set A on domain X is in fact a function ofX⟶ [01] e primary task of dealing with fuzziness inpractical applications is to determine the membershipfunction A(x) Just like probabilistic theory cannot giveprecise but only approximate probability due to limitedknowledge and information the fuzzy set theory can onlyestablish the approximate degree of membership and con-sequently an estimatedmembership function Fuzzy statisticaltests that demonstrate the stability of frequency can be carriedout to characterize the objectivity of degree of membershipand to derive an approximate membership function

Two-phase fuzzy statistics divides the domain X (egTBM excavation speed) into two statistical sets ie A(ldquonormalrdquo) and Ac (ldquoabnormalrdquo) at is two opposite fuzzyconcepts compete for statistics in domain X e so-calledldquotwo-phaserdquo indicates P2 A Ac [32] ie each fuzzy testwill establish a mapping e X⟶ P2 is mapping dividesthe domain X ie forallx isinX A(x) +Ac(x) 1 e two-phasefuzzy statistical test contains four elements (1) domainX (2)a fixed element x0 in X (3) a varying classical set Alowast in X (Alowastreflects the flexible boundary of the fuzzy set A and allows todetermine if the x0 in each test conforms to the fuzzy conceptdescribed by A) and (4) condition S which restricts thechanges of Alowast

In fuzzy statistical tests x0 remains fixed while Alowast isvaried In each test a decision must be made as for whetherx0 belongs to Alowast Note that the changing Alowast is always asubset of X After n tests the membership frequency of x0belonging to the fuzzy set Alowast is calculated as ln(A)(x0)

ln(A) x0( 1113857 number of times that ldquox0 isin Alowastrdquo

n (1)

It has been experimentally found that ln(A)(x0) tends tostabilize as n increases e stabilized value is referred to asthe degree of membership that x0 belongs to A

ln(A) x0( 1113857 limx⟶infin

number of times that ldquox0 isin Alowastrdquon

(2)

312 Fuzzy Statistical Test of the Excavation Speed of TBMExcavation speed is a macroscopic measure of the workingstate of the TBM erefore the normal state of the TBM ischaracterized by the normal excavation speed In our casethe normal excavation speed during tunneling was obtainedby running a fuzzy statistical test with the construction logsof the XWS

4 Advances in Civil Engineering

In this work the excavation speed of the TBM had adomain ofV [1 96] (mmmin)e fuzzy setA represents thefuzzy concept of ldquonormal excavation speedrdquo For the purpose ofillustration select an arbitrary excavation speed v0 23mmmin Fuzzy statistical tests were then applied to determine thedegree of membership that v0 belonged to A For the con-struction project at the XWS the appropriate project logs overn 179days (715 segment rings for left and right tunnels) wereselected e appropriate logs excluded abnormal engineeringsituations (restrictive condition S) such as TBM launchingTBM arrival and abnormal downtime during which theformation was reinforced and the excavation speed could notbe considered normal In this way the boundaries for the dailyldquonormal excavation speedrdquo could be determined for the left andright tunnels of the XWS (Table 3 Figure 3)

Table 4 shows the membership frequency that v0 23mmmin belonged to the normal excavation speed as was de-termined by the statistical tests Figure 4 shows that themembership frequency f that v0 23mmmin falls within theldquonormal excavation speedrdquo of the TBM stabilized around 066Hence A(v0) A(23) 066 e membership frequency f ofother excavation speeds could also be obtained similarlye data from the construction logs recorded a mini-mum and maximum excavation speed of 2mmmin and96mmmin respectively Hence we divided the domain V

into 96 intervals each spanning 1mmmin starting from15mmmin and ending at 965mmmin e mean of eachinterval was used to calculate the membership frequencyand the results are shown in Table 5 A program was de-veloped in MATLAB to reduce the computational com-plexity and save time

Figure 5 plots the histogram of membership frequencybased on the data in Table 5 e fitted curve of themembership function A(v) was then drawn accordinglyefitted curve conformed to the Cauchy distribution and couldbe expressed as follows

1113957A(v) v A(v) ∣ A(v) 1 +vminus 3212

1113874 11138752

1113888 1113889

minus1

v isin N⎧⎨

⎩

⎫⎬

⎭

(3)

(1) Determination of the Standard Excavation Speed In thefuzzy set theory [31] the element with the membershipfrequency A(v) 1 is designated as the kernel of the fuzzy setA and written as ldquokerArdquo Figure 5 shows that kerA 32 iev0 32mmmin was the kernel of the fuzzy set of ldquonormalexcavation speedrdquo erefore v0 32mmmin was consid-ered as the standard excavation speed in the ensuing PSAanalysis

ConvertingFTA to BN

Fuzzystatistical test

theory

ldquoNormalexcavation

phaserdquo

Preparingbow-tiediagram

ConvertingETA to BN

ConstructingBN-bow-tie

diagram

Confirmingoccurrenceprobability

TBMfacilitiesfailure

Operationalerror and

failure

TBMparameterdatabase

Triangularnumbers

Trapezoidalnumbers

Expertjudgment

Aggregation

Occurrenceprobability

Calculatingoccurrenceprobability

Calculatingimportancemeasures

BM

RAW

FV

Identifyingkey nodes

System ofTBM phases

Providingsafety

measures

Figure 2 Flowchart of the proposed methodology

Advances in Civil Engineering 5

(2) Determination of the Range of Excavation Speed In thefuzzy set theory all elements whose membership frequencyA(v)gt 0 constitute a support of the fuzzy setA and is writtenas ldquosupp Ardquo and all elements whose membership frequencyA(v)gt α is designated as the α cut set of the fuzzy set A andwritten as Aα Figure 5 shows that the excavation speed

fluctuated around the kernel (32mmmin) during shieldtunnel excavation In order to express the range of normalexcavation speed the confidence level α 05 was selectedand the excavation speed whose membership frequencysatisfied A(v)gt 05 was considered to constitute the in-terval of normal excavation speed (ie the 05 cut set of A)

Table 3 Partial construction log of the ldquonormal excavation speedrdquo in the XWS

n 1ndash10 n 11ndash20 n 21ndash30 n 31ndash40 n 41ndash50 n 51ndash60 n 61ndash70 n 71ndash80 n 81ndash90 n 91ndash100303ndash506 25ndash32 276ndash424 78ndash425 25ndash35 18ndash39 27ndash43 20ndash41 30ndash47 20ndash54324ndash388 26ndash34 232ndash476 83ndash417 28ndash46 20ndash35 24ndash40 10ndash40 30ndash61 32ndash63284ndash396 27ndash42 233ndash445 202ndash476 17ndash35 15ndash42 27ndash47 20ndash35 20ndash61 32ndash58303ndash388 23ndash36 205ndash427 242ndash425 28ndash37 27ndash41 20ndash33 17ndash32 30ndash60 20ndash37303ndash363 123ndash348 282ndash456 287ndash526 17ndash36 21ndash37 22ndash34 8ndash40 14ndash58 24ndash4032ndash44 178ndash325 182ndash426 19ndash32 20ndash37 31ndash41 27ndash48 8ndash40 27ndash74 25ndash4831ndash42 198ndash374 137ndash375 22ndash45 20ndash35 30ndash40 30ndash42 20ndash50 15ndash55 24ndash5131ndash39 135ndash326 156ndash326 21ndash44 21ndash37 30ndash35 25ndash43 20ndash50 25ndash45 32ndash4630ndash42 134ndash326 20ndash37 19ndash42 20ndash35 20ndash40 28ndash36 20ndash46 28ndash52 25ndash4031ndash38 156ndash364 15ndash40 20ndash41 20ndash37 25ndash40 225ndash37 31ndash42 31ndash47 20ndash35

Rang

e of a

dvan

ce sp

eed

(mm

min

)

v-lower limitv-upper limit

0102030405060708090

100

100 200 300 400 500 600 700 8000Segment number

Figure 3 Distribution of the ldquonormal excavation speedrdquo

Table 4 Membership frequency of 23mmmin belonging to the ldquonormal excavation speedrdquo

Description Number and membershipNumber of rings 50 100 150 200 250 300 350Membership counts 28 51 60 97 128 153 178Membership frequency 056 051 04 049 051 051 051Number of rings 400 450 500 550 600 650 715Membership count 202 252 302 342 382 427 470Membership frequency 051 056 061 062 064 066 066

066

v = 23mmmin

001020304050607

Cov

erag

e fre

quen

cy f

100 600300 700500200 8000 400Segment number

Figure 4 Membership frequency of 23mmmin belonging to the ldquonormal excavation speedrdquo

6 Advances in Civil Engineering

e set of normal excavation speed in Zadehrsquos form wasordered as shown in equations (4) and (5) usv0 20ndash44mmmin was considered as the range of normalexcavation speed in the ensuing PSA analysis

1113957A(v) 05020

+05421

+05922

+06423

+06924

+07525

+08026

+08527

+09028

+09429

+09730

+09931

+132

+09933

+09734

+09435

+09036

+08537

+08038

+07539

+06940

+06441

+05942

+05443

+05044

(4)

supp 1113957A(v) 111386420 21 22 23 24 25 26 27 28 29 30 31 32

33 34 35 36 37 38 39 40 41 42 43 441113865

(5)

Table 5 Membership frequency of the ldquonormal excavation speedrdquo

No Group Count Frequency1 15ndash25 1 00012 25ndash35 2 00033 35ndash45 2 00034 45ndash55 2 00035 55ndash65 5 00076 65ndash75 6 00087 75ndash85 17 00248 85ndash95 21 00299 95ndash105 31 004310 105ndash115 34 004811 115ndash125 46 006412 125ndash135 60 008413 135ndash145 66 009214 145ndash155 100 01415 155ndash165 132 018516 165ndash175 168 023517 175ndash185 217 030318 185ndash195 240 033619 195ndash205 366 051220 205ndash215 396 055421 215ndash225 425 059422 225ndash235 470 065723 235ndash245 500 069924 245ndash255 535 074825 255ndash265 563 078726 265ndash275 588 082227 275ndash285 609 085228 285ndash295 619 086629 295ndash305 668 093430 305ndash315 686 095931 315ndash325 715 132 325ndash335 698 097633 335ndash345 685 095834 345ndash355 670 093735 355ndash365 643 089936 365ndash375 623 087137 375ndash385 586 08238 385ndash395 562 078639 395ndash405 536 07540 405ndash415 495 069241 415ndash425 456 063842 425ndash435 406 056843 435ndash445 358 050144 445ndash455 332 046445 455ndash465 290 040646 465ndash475 246 034447 475ndash485 201 028148 485ndash495 157 02249 495ndash505 136 01950 505ndash515 116 016251 515ndash525 101 014152 525ndash535 91 012753 535ndash545 88 012354 545ndash555 77 010855 555ndash565 69 009756 565ndash575 62 008757 575ndash585 56 007858 585ndash595 51 007159 595ndash605 45 006360 605ndash615 41 0057

Table 5 Continued

No Group Count Frequency61 615ndash625 38 005362 625ndash635 35 004963 635ndash645 32 004564 645ndash655 30 004265 665ndash675 28 003966 675ndash685 28 003967 685ndash695 25 003568 695ndash705 23 003269 705ndash715 23 003270 715ndash725 21 002971 725ndash735 20 002872 735ndash745 19 002773 745ndash755 19 002774 755ndash765 18 002575 765ndash775 18 002576 775ndash785 18 002577 785ndash795 18 002578 795ndash805 16 002279 805ndash815 16 002280 815ndash825 15 002181 825ndash835 15 002182 835ndash845 12 001783 845ndash855 11 001584 855ndash865 8 001185 865ndash875 7 00186 875ndash885 6 000887 885ndash895 5 000788 895ndash905 4 000689 905ndash915 4 000690 915ndash925 4 000691 925ndash935 4 000692 935ndash945 4 000693 945ndash955 3 000494 955ndash965 2 000395 965ndash975 2 0003

Advances in Civil Engineering 7

313 Fuzzy Statistical Tests of Excavation Parameterse excavation speed of the TBM reflects the influenceexerted by the excavation parameters (eg total thrust facepressure and cutter head torque) on the force and dis-placement of the surrounding soil erefore it is necessaryto determine the realistic and practical excavation param-eters based on the excavation speed

Formation reinforcement during TBM launching and TBMarrival can exert a strong influence on the shield tunnel ex-cavation and lead to highly discrete parameters erefore thedata from the TBM launching and TBM arrival stages werediscarded in studying the relationship between excavation speedand TBMparameters Figure 6 shows how the TBMparametersvaried with the excavation speed during the construction of the715 segments in the XWSe curves were fitted viaMATLABand the slope of the curves was highly indicative of the cor-relation between the TBMparameters and the excavation speed

In Figure 6(a) the total thrust (F) increased with risingexcavation speed is was because bentonite was used as alubricant and injected around the shield of the TBM duringexcavation to reduce friction When the amount of injectedbentonite was appropriate the friction coefficient betweenthe shield and the surrounding soil would decrease and theexcavation speed would then increase when the thrust (F)was higher In Figure 6(b) the excavation speed decreasedwhen the cutter head torque (MT) increased is wasbecause when the soil body of the tunneling face wasrelatively difficult to cut a larger torque of the cutter headwould be needed and the excavation speed would decreaseFigure 6(c) shows that during normal excavation thepressure of the tunneling face increased slightly with risingexcavation speed Besides Mair pointed out that duringsegment assembly the downtime of TBM would decreasethe soil and water pressure on the tunneling face whichcould reduce the control pressure of the tunneling face [33]e same pattern was observed in the current constructionlogs and the R2 value of the curve in Figure 6(c) was hencerelatively low Figure 6(d) shows that the grouting pressuredecreased slightly with rising excavation speed However

since the pressure of primary grouting was read off from thegrouting pressure pump the actual grouting pressureexerted on the surrounding soil was smaller and theprimary grouting pressure hence had limited impact onexcavation speed

(1) Determination of Standard TBM Parameters It wasdetermined from the fuzzy statistical tests above that thestandard excavation speed was 32mmmin e corre-sponding standard TBM parameters could be determinedaccordingly from the following equation

TBMPstandard value 1113936

Nn1TBMPnv

N v321113868111386811138681113868 (6)

where TBMP is the TBM parameter and v is the excavationspeed (mmmin)

(2) Determination of the Range of TBM Parameters It wasdetermined from the fuzzy statistical tests above that therange of excavation speed was 20ndash44mmmin e corre-sponding boundaries of TBM parameters could be de-termined from the extreme values in the monitoring records(Figure 6) via the following equation

TBMPupper limit max TBMPv 20levle4411138681113868111386811138681113966 1113967

TBMPlower limit min TBMPv 20levle4411138681113868111386811138681113966 1113967

(7)

(3) ldquoNormal Excavation Phaserdquo of TBM According to thefuzzy set theory the excavation speed in the ldquonormal ex-cavation phaserdquo fell within 20ndash44mmmin e TBM wasconsidered to be in the ldquonormal excavation phaserdquo whenthe excavation speed and the TBM parameters all fellwithin the prescribed ranges specified above and listedagain in Table 6 e standard values and ranges were usedfurther in the subsequent PSA analysis Table 6 shows thatamong the examined parameters the face pressure had adeviation interval of merely 196 and was controlled the

Advance speed v (mmmin)

Mem

bers

hip

Atilde (v

)

Cov

erag

e fre

quen

cy A

(v)

04

02

06

08

1

10090807060504030201000

04

02

06

08

1

0

Fuzzy statistical experiment methodCauchy distribution curve

Figure 5 e histogram of membership frequency and the membership function of TBM excavation speed

8 Advances in Civil Engineering

best whereas the cutter head torque had a deviation in-terval of 7401 and was controlled the worst

(4) Statistical Relationship between TBM Parameters andExcavation Speed e monitoring results in Figure 6

demonstrated that in the ldquonormal excavation phaserdquo ofthe XWS the total thrust and the face pressure were posi-tively correlated with the excavation speed In particular thetotal thrust had a stronger correlation to the excavationspeed than the face pressure In contrast the cutter head

2000400060008000

1000012000140001600018000

Tota

l thr

ust

F (k

N)

20 25 30 35 40 45 50 55 60 6515Advance speed v (mmmin)

(a)

0500

10001500200025003000350040004500

Cutte

r hea

d to

rque

MT

(kNlowast

m)

20 25 30 35 40 45 50 55 60 6515Advance speed v (mmmin)

(b)

0

50

100

150

200

250

Face

pre

ssur

eP N

(kPa

)

20 25 30 35 40 45 50 55 60 6515Advance speed v (mmmin)

(c)

Gro

utin

g pr

essu

reP G

(kPa

)

100150200250300350400450500550

20 25 30 35 40 45 50 55 60 6515Advance speed v (mmmin)

(d)

Figure 6 Variations in the TBM parameters at different excavation speeds (data from XW section) (a) total thrust versus excavationspeed (b) cutter head torque versus excavation speed (c) face pressure versus excavation speed (d) grouting pressure versus excavationspeed

Table 6 Standard values and ranges of excavation speed and TBMPs

Factors v (mmmin) F (kN) P N (kPa) M T (kNmiddotm) P G (kPa)Parameter range [20 44] [8300 13100] [117 143] [1294 2974] [197 302]Standard value 32 9700 1326 2270 302Deviation range () [minus375 375] [minus1443 3505] [minus1176 784] [minus430 3101] [minus3477 0]

Advances in Civil Engineering 9

torque and the primary grouting pressure were negativelycorrelated with the excavation speed

32 Bow-Tie-Bayesian Network Analysis e bow-tie anal-ysis combines FTand ETanalysese FTanalysis in bow-tiecalculates the occurrence probability of the loss event (LE) aswell as the top event (TE) e occurrence probability of theTE can also be obtained from the occurrence probability ofthe basic event (BE) e events could be evaluated by theirlogical relationship and their occurrence probability in theBN Mapping the bow-tie analysis to BN involves convertingboth FT and ET analyses Figure 7(a) provides a brief de-scription of calculation steps

ree importance measures described in the followingBorst and Schoonakker [30] were introduced in the newmethodology according to the Bayes theorem Figure 7(b)gives a brief description of their calculation In the proposedmethodology the critical nodes that could more easilytrigger accidents were obtained by calculating these im-portance measures

33 Confirming Failure Occurrence Probability e BT-BNanalysis requires knowing the occurrence probability of eachbasic event (BE) e basic events fall into four categoriesenvironmental failure operational error multiple failuresand facility failures e occurrence rate of facility failureswas obtained from the construction log of the XWS for thetunneling project that spanned 179 days (715 segments intotal) and was converted into occurrence probability via thefollowing equation

F 1minus eminusλt

(8)

where F denotes the occurrence probability of the failure andλ denotes the occurrence rate of the failure

e occurrence probability of environmental failureoperational error and multiple failures cannot be readilyderived from existing data and was thus estimated via expertopinione fuzzymethod combines the opinions of differentexperts in a weighted manner to calculate the fuzzy fault rate(FFR) from the triangular fuzzy numbers or trapezoidal fuzzynumbers proposed by the experts e occurrence probabilityof environmental failure operational error and multiplefailures was then determined from the FFR [34] e generalprocedure of the fuzzy method is as follows

(1) Determine the weight of the opinion of each expertbased on the age education background work ex-perience and position of the consulted expert (Ta-ble 7) e crude weight score of each expert iscalculated via the following equation

Sn Sna+ Snb

+ Snc+ Snd

(9)

where Sn represents the total weight score of theexpert e relative weight score of each expert iscalculated via the following equation

Wn Sn

1113936mn1Sn

(10)

where m represents the number of experts(2) e occurrence probability is divided into the

following categories nonoccurrence absolute lowvery low low fairly low medium fairly high highvery high absolute high or occurrence e rankvalue of the categories escalates from 0 for non-occurrence to 1 for the occurrence (Table 8) eoccurrence probability of the event is then evalu-ated based on the corresponding triangular numberor trapezoidal number given by the experts

(3) Aggregation of the fuzzy numbers When the fuzzynumbers are all triangular number or trapezoidalnumber the aggregated fuzzy numbers of an event iscalculated via equation (11) [35] e aggregatedfuzzy number considering the expert weight isshown in equation (12)

1113957Aaggregated 1113944m

n1Wn otimes 1113957An (11)

where 1113957Aaggregated represents the aggregated fuzzifiednumber given by expert m and Wn represents theweight of the expertrsquos opinion

1113957AW 1113874W1a11 + W2a21 W1a12 + W2a22 W1a12

+W2a23 W1a13 + W2a241113875

(12)

(4) After the aggregated fuzzy numbers are determinedthe centroid index method (equation (13)) is used tohandle the fuzzy numbers and obtain the fuzzyprobability score (FPS) [36]

X 1113938g(x)x dx

1113938g(x)dx (13)

where X is the defuzzified output g(x) is themembership function and x is the output variableAssume 1113957An (an1 an2 an3) a triangular number and1113957An (an1 an2 an3) a trapezoidal number e FPS iscalculated via equation (14) when a fuzzy number is atriangular number and via equation (15) when thefuzzy number is a trapezoidal number

FPS 13

an1 + an2 + an3( 1113857 (14)

FPS 13

an3 + an4( 11138572 minus an3an4 minus an1 + an2( 1113857

2+ an1an2

an3 + an4 minus an1 minus an2( 1113857

(15)

10 Advances in Civil Engineering

(5) Finally the FPS is converted to FFR via equation(16) [37] and the FFR is further converted tothe occurrence probability of environmentalfailure operational error and multiple failures(equation (8))

FFR

110k

FPSne 0

0 FPS 0

k 2301 times(1minus FPS)

FPS1113890 1113891

13

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(16)

4 Results

41 Analysis of Excessive Surface Settlement inNormal TunnelExcavation Figure 8 shows that the normal excavation

(1) If the logical relationship is AND between events the TE occurs when all events occur The probability of TE can be calculated from the following equation

(A)

(2) If the logical relationship is OR between events the TE occurs when any of the event occurs The probability of TE can be calculated from the following equation

(B)

(3) By definition in the FT analysis the probability of TE is the same as that of LE Similarly the probability of the initial event (IE) in the ET analysis is the same as that of LE The probability of OE in ET analysis can be calculated from the following equation

(C)

(4) The BN an inference method based on the Bayes theorem combines both graph theory and probability theory

(D)

FTE = i=1

nFBEi

FTE = 1 ndashi=1

n(1 ndash FBEi)

FOEn = FIE middot i=1

nP (Ei = 0) middot

j=1

nP (Ej = 1)

P(B | A) = P(A | B) middot P(B)

P(A)

(a)

(1) The Birnbaum measure (BM) whichdetermines the increment of the occurrenceprobability of TE when BE occurs is shownin the following equation

(E)

where P(TE | BE = 1) denotes the occurrence probability of TE when BE occurs and P(TE | BE = 0) denotes the occurrence probability of TE when BE does not occur

(2) Risk achievement worth (RAW) evaluatesthe impact of BE on TE when the probabilityof BE is considered The RAW is adjustedby the probability of TE and BE as shown inthe following equation

(F)

where P(BE) denotes the occurrence probability of BE and P(TE) denotes the occurrence probability of TE under all circumstances

(3) The FussellndashVesely (FV) importance which describes the contribution of BE to system fault is shown in the following equation

IBBE

M = P(TE | BE = 1) ndash P(TE | BE = 0)

IRB

AE

W = IBBE

M middot P(BE)P(TE)

(G)

P(TE) ndash P(TE | BE = 0)P(TE)

IFB

VE =

(b)

Figure 7 Bow-tie-Bayesian network analysis Calculation of (a) event probability and (b) importance measures

Table 7 Weight scores for experts

Factor Category Score

Age (a)

lt30 130ndash39 240ndash49 3ge50 4

Education (b)

High school 1College 2Bachelor 3Master 4PhD 5

Work experience (c)

lt5 years 15ndash10 years 211ndash20 years 321ndash30 years 4ge30 years 5

Position (d)

Worker 1Technician 2

Junior scholarengineer 3Senior scholarengineer 4

Table 8 Rank value of each category

Classified occurrence probability Rank valueNonoccurrence 0Absolute low 01Very low 02Low 03Fairly low 04Medium 05Fairly high 06High 07Very high 08Absolute high 09Occurrence 10

Advances in Civil Engineering 11

phase involves the environment TBM operation supervi-sion management and emergency handling Risk analysis ofthe ldquonormal excavation phaserdquo in soft soil engineering basedon the XWS allows the identification of potential risk factorsthat may trigger surface settlement and consequently lead toaccidents Eskesen et al have described three principles forrisk analysis as follows (1) eliminate risk factors that are easyto detect and can be controlled timely and effectively (2)eliminate risk factors with low occurrence probability andno catastrophic consequences and (3) combine risk factorswith similar loss consequences [38] Accordingly the riskfactors during shield tunneling were organized into three

basic categories improper control of excavation parameters(eg poor control of face pressure) catastrophic geology (egground cavity or flow sand) and unforeseeable factors (egsegment damage) Figure 9 shows the bow-tie model builtfrom the categorized factors for the risk of surface collapsecaused by excessive surface settlement during shield tun-neling OEs of various degrees were successfully predictedbased on the CEs (Figure 9) Many risk factors exist in anygiven surface collapse In this section based on the previouscalculation results in Section 31 we selected the manageableshield excavation parameters (shield total thrust groutingpressure cutter head torque soil pressure etc) in the ldquonormal

Synchronousgrouting

ExcavationSegment

installationAttitudecontrol Tail sealing

Excavationcycle

Quality controlacceptance

Dangeroussituation exists Yes

Prepareemergencymeasures

Emergencymeasures

Execution of emergencymeasures

Acceptance ofexcavationprocedures

Excavationacceptance

report

Monitoring measurements

Monitored dataof excavationenvironment

Formation geologyTBM parametersExcavation axis

Segment installationSynchronous grouting

TBM construction parameter

No

TBM parametersv (mmmm) F (kN) PN (kPa)

MT (kNmiddotm) PG (kNmiddotm)TBM attitude TBM position TBM fault information

Soil bodyparameters

Soil evolutionmodel

Confined waterObstacles

Ground cavity orquicksand

Metro tunnel excavation

Emergencyhandling

Supervision

TBMoperation

TBM

Environment

Management

Figure 8 System diagram of the ldquonormal excavation phaserdquo

12 Advances in Civil Engineering

excavation phaserdquo as the base events assigning their weightsaccording to Section 33 and then performed PSA analysis

As mentioned earlier the ldquonormal excavation phaserdquo isunder the influence of excavation parameters catastrophicgeology and unforeseeable factors Surface settlement canoccur once the condition deteriorates Here we set excessivesurface settlement as the TE in the FT analysis Meanwhilethe tunneling system has a built-in emergency managementsystem Upon excessive surface settlement the emergencymanagement system will start to shut down the TBM timelyHence in the ETanalysis the excessive surface settlement isset as the IE and TBM shutdown is set as the CE OEs ofvarious degrees are obtained based on the considered CEFinally the surface settlement is set as the LE to connect theFT and the ET and furnish the BTmodel (Figure 9 Table 9)Eight OEs of various degrees were predicted based on theCEs including surface collapse events OE3 OE4 OE6 OE7and OE8 (Figure 9 Table 10) e TBM shuts down if CE1occurs and continues to operate if otherwise

e BN-BT model for excessive surface settlement isconstructed by mapping the FT and ET analyses in the BT(Figure 9) model to BN (Figure 10) All the nodes of BN havepreviously been described in the BT except the node OEwhich is the consequence node OE is added to accommodatethe outcomes of BT By connecting the node of excessivesurface settlement to OE another state also called the safe

state is added to the state set It includes consequences OE1 toOE8 to account for the nonoccurrence of the top event iewhen excessive surface settlement controlled To show thedependence among the safety barriers and the top eventcausal arcs are also drawn between TBM shutdown andgrouting in the settlement area and bentonite injection to soilchamber and TBM shield It is worth noting that since variouscombinations of the failure and success of the sequentialsafety barriers result in different consequences in the BT allthe safety nodes of BN are connected to node OE

42 Determination of Event Occurrence Probability emaximum surface settlement that resulted from the aber-ration of the ith TBM parameter is denoted as δmaxi eprobability of safety accident becomes higher when δmaxiapproaches the permitted surface settlement δi Whenδmaxi δi the accident will occur as soon as the TBM pa-rameter gives rise to a surface settlement of δmaxi eprobability of equipment fault for the normal excavationsystem was calculated via equation (8) from the engineeringlog data of the XWS over 179 days of construction (715segments rings in total) e construction of all 715 rings fellwithin the ldquonormal excavation phaserdquo as was defined by thefuzzy statistical test (v 20ndash44mmmin) Table 11 lists thecalculation results

X3X2X1

OR

M1

X7X6X5X4

OR

M2

X10X9 X11 X13X12

M3

OR

Excessive surface

settlement

X8

Caus

esLE

CE1

CE2

CE3

Con

sequ

ence

sSt

op

TBM

Gro

utin

g in

settl

emen

tar

ea

Bent

onite

inje

ctio

n

OE 1

OE 2

OE 3

OE 4

OE 5

OE 6

OE 7

OE 8

Success Failure

AND

Figure 9 Diagram of bow-tie analysis for excessive surface settlement

Advances in Civil Engineering 13

To address the uncertainty regarding the events ofenvironmental failure operational error and multiplefailure six domain experts who participated in the con-struction of the Wuhan metro system including two seniorengineers one senior academic professor one technicalconsultant one junior engineer and one worker wereinvited to evaluate the occurrence probability of events thatcannot be readily derived from existing data (Table 12)eweights of their opinion were then calculated by usingequations (9) and (10) and the distribution of each opinionweight is shown in Figure 11

In addition Table 13 lists the expert opinions regardingthe events of environmental failure operational error andmultiple failures in the form of fuzzy numbers based onTable 8 e fuzzy numbers were aggregated via equations(12) and converted to FPS and FFR via equations (13)ndash(16)(Table 14) e occurrence probabilities were finally derivedfrom FFR (Table 14) Generally the expert knowledge isconsidered as a scarce resource which cannot provide

universal consultation or real-time guidance us there ismuch room to improve the data use efficiency

43 Update in Occurrence Probability of LE and OE eoccurrence probability of basic events is calculated as de-scribed in Section 42 including the occurrence probabilityof facility failure from the engineering log data of the XWS aswell as that of environmental failure operational error andmultiple failures derived from expert opinion e occur-rence probability of excessive surface settlement (LE) isdetermined via equations (A) and (B) by considering thelogical relationship between events in Figure 7 Finally theoccurrence probability of OEs including surface collapse canbe calculated via equation (C) in the figure by mapping theFT and ET analyses in the BTmodel to BN Figure 12 showsthe occurrence probabilities of the LE (ie excessive surfacesettlement) and that of the OEs

e above analysis shows that the occurrence probabilityof excessive surface settlement within one year is 08299(Figure 12) is occurrence probability of surface collapse(OE3 OE4 OE6 OE7 and OE8) may be decreased whenemergency measures are put in place including grouting insettlement area and bentonite injection to soil chamber andTBM shield However these measures cannot help to reduceminor accidents since the occurrence probability remains athigh levels for OE1 OE2 and OE5 Admittedly grouting andbentonite injection are necessary measures and they candecrease the effects of excessive surface settlement duringshield tunneling However the key point of avoiding outcomeevents including surface collapse to ensure project safety is toprevent the excessive surface settlement from occurring in thefirst place Hence we sought to determine the key nodesleading to excessive surface settlement via BT-BN analysis andpropose the corresponding preventive measures

Table 10 Analysis of event occurrence

Symbol EventOE1 Excessive surface settlement

OE2Grouted cutter head and shield excessive surface

settlement and minor property damageOE3 Minor surface collapse and property damage

OE4Moderate surface collapse major property damage

and minor casualtiesOE5 Excessive surface settlement

OE6Grouted cutter head and shield moderate surface

collapse and minor property damage

OE7Moderate surface collapse and major property

damage

OE8Severe surface collapse major property damage and

major casualties

Table 9 Details of bow-tie components in Figure 9

Event Symbol Logic link type Failure modelGround settlement Excessive surface settlement OR gate mdashCatastrophic geology M1 OR gate mdashUnforeseeable factors M2 OR gate mdashExcavation parameters M3 AND gate mdashConfined water X1 mdash Environmental failureGround cavity or flow sand X2 mdash Environmental failureObstacles X3 mdash Environmental failureSegment damage X4 mdash Operational errorAbnormal TBM shutdown X5 mdash Multiple failureSeal failure at shield tail X6 mdash Multiple failureExcessive deviation from axis X7 mdash Operational errorEquipment failure X8 mdash Multiple failureUntimely grouting X9 mdash Facility failureExcessive cutter head torque X10 mdash Facility failureImproper control of face pressure X11 mdash Facility failureExcessive thrust X12 mdash Facility failureImproper control of excavation speed X13 mdash Facility failureTBM shutdown CE1 mdash Multiple failureGrouting in settlement area CE2 mdash Multiple failureBentonite injection to soil chamber and TBM shield CE3 mdash Multiple failure

14 Advances in Civil Engineering

Table 11 Probability of equipment fault

Event Surface settlementδmaxi (mm)

Permitted surfacesettlement δi (mm)

Value of TBMparameter

Occurrence rate(dminus1)

Occurrence probability(in 1 year)

X9 89 15 302 kPa 10675eminus 04 382eminus 02X10 84 10 2974 kNmiddotM 17792eminus 04 629eminus 02X11 86 15 143 kPa 71167eminus 05 256eminus 02X12 98 15 13100 kN 14233eminus 04 506eminus 02X13 120 15 41mmmin 28467eminus 04 987eminus 02All data were obtained from the operation log of the XWS

Table 12 Characteristics of experts participated in the occurrence probability evaluation

Expert Age Education Service (years) Professional position1 56 High school 25 Worker2 35 Master 10 Technician3 41 Master 15 Junior engineer4 47 Bachelor 20 Senior engineer5 50 PhD 18 Senior academic6 59 PhD 30 Senior engineer

0125 0125

01625 01625

020225

AgeEducationService

Professional positionWeighting

2 3 4 5 61Expert

0

005

01

015

02

025

Wei

ghtin

g

0

1

2

3

4

5

6

Wei

ghtin

g sc

ore

Figure 11 Distribution of each expert opinion weight

X1 X2 X3

M1

X5 X6 X7 X8

M2

X9 X11

M3

Excessive surface

settlement

X10 X12 X13X4

CE1 CE2 CE3

OE

Caus

esLE

CEC

onse

quen

ces

Figure 10 Bow-tie chart of excessive surface settlement

Advances in Civil Engineering 15

44 Identify Key Nodes and Provide Safety Measures Inorder to find the key nodes leading to excessive surfacesettlement the importance measure of each event was cal-culated via equations (E)ndash(G) in Figure 7 as shown inTable 15 Assume the number of events as ldquonrdquo e nor-malized weight Rlowast could be calculated from the importancemeasure Ii via the following equation

Rlowast

Ii

1113936ni1Ii

times 100 (17)

After the normalized weight Rlowast is calculated for eachimportance measure the total weight Rlowast could be calculatedvia equation (18) e total weight Rlowast of events was finally

ranked in descending order to find the key nodes as shownin Table 16

Rlowast R

lowastBM + R

lowastRAW + R

lowastFV (18)

It can be seen that X6 (seal failure at shield tail) X1(confined water) X2 (ground cavity or flow sand) X5 (ab-normal TBM shutdown) and X7 (excessive deviation fromaxis) have far higher weight than other events and are thusthe key nodes to accidents related to excessive surface set-tlement Measures can be taken to particularly ensure safetyat these nodes e occurrence probability of excessivesurface settlement can be reduced by 66 when X6 X1 X2X5 and X7 are ensured safe (Figure 13)

Table 13 Expert opinion on environmental failure operational error and multiple failures

Event Fuzzy numbers proposed by each expert

X1

Expert 1 Expert 2 Expert 3(02 03 04 05) (01 02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 02 03 05)

X2

Expert 1 Expert 2 Expert 3(01 02 03 05) (02 03 04) (01 02 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (02 03 05) (01 02 03 05)

X3

Expert 1 Expert 2 Expert 3(01 02 04 05) (01 02 03 05) (01 03 04)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03) (01 02 03)

X4

Expert 1 Expert 2 Expert 3(02 03 04 05) (01 02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(02 03 04) (02 03 05) (01 02 03 05)

X5

Expert 1 Expert 2 Expert 3(01 03 04) (01 02 03 05) (02 03 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (02 03 05) (01 02 03)

X6

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 03 05) (02 03 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (02 03 05) (01 02 04 05)

X7

Expert 1 Expert 2 Expert 3(01 02 04 05) (01 02 03 05) (02 03 04)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 03 05)

X8

Expert 1 Expert 2 Expert 3(01 03 04 05) (01 02 03 04) (02 03 04)

Expert 4 Expert 5 Expert 6(02 03 04) (01 02 03 05) (01 02 03)

CE1

Expert 1 Expert 2 Expert 3(02 03 04 05) (02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 02 04 05)

CE2

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 05) (02 03 04 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (01 02 03 05) (01 03 05)

CE3

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 03 05) (03 04 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (01 02 04 05) (01 02 03 05)

16 Advances in Civil Engineering

In accordance with the predictive and diagnosticanalysis results using the established model some safetymeasures for key nodes are displayed in time to reduce theexcessive surface settlement risk during the tunnelexcavation

(1) e nodes X5 (abnormal TBM shutdown) and X7(excessive deviation from the axis) mostly involveoperational error Safety management and supervi-sion need to be strengthened at the construction siteto eliminate such errors and ensure that the TBM isoperated properly Besides an advanced real-time

laser locator may help to alarm in the case of largeaxial deviation

(2) e nodes X1 (confined water) and X2 (ground cavityor flow sand) belong to environmental failure Inorder to reduce the influence of environmental failurecareful geological exploration should be carried outbefore tunneling to identify the poor geological and

Table 14 Calculation of FPS FFR and the occurrence probability of environmental failure operational error and multiple failures

Event Aggregated fuzzy numbers FPS FFR (dminus1) Failure probability (in 1 year)X1 (01288 02288 03288 04838) 02951 83969eminus 04 26402eminus 1X2 (01325 02325 03163 04713) 02909 80032eminus 04 25336eminus 1X3 (01000 02163 02700 03825) 02420 42986eminus 04 14518eminus 1X4 (00450 00900 01125 01800) 01082 22492eminus 05 81803eminus 3X5 (01363 02488 02775 04263) 02747 66022eminus 04 214155eminus 1X6 (01488 02488 03225 04713) 03004 89125eminus 04 27770eminus 1X7 (01163 02388 03125 04675) 02855 75157eminus 04 24002eminus 1X8 (01450 02538 02950 03100) 02463 45643eminus 04 15338eminus 1CE1 (01413 02413 03513 04838) 03058 94598eminus 04 29202eminus 1CE2 (01288 02513 03038 04713) 02916 80679eminus 04 25496eminus 1CE3 (01450 02450 03363 04713) 03010 89722eminus 04 27937eminus 1

08299

03155

01223 010800419

01301

00504 00445 00173

Occ

urre

nce p

roba

bilit

y (in

1 y

ear)

00

01

02

03

04

05

06

07

08

09

OE1 OE2 OE3 OE4 OE5 OE6 OE7 OE8LE

Figure 12 Occurrence probability of surface settlement and otheroutcome events

Table 15 Calculation of importance measure of influential factors

SymbolImportance measure

BM RAW FVX1 2311eminus 1 7352eminus 02 7352eminus 02X2 2279eminus 1 6958eminus 02 6958eminus 02X3 1990eminus 1 3481eminus 02 3481eminus 02X4 1716eminus 1 1691eminus 03 1691eminus 03X5 2165eminus 1 5587eminus 02 5587eminus 02X6 2356eminus 1 7884eminus 02 7884eminus 02X7 2239eminus 1 6476eminus 02 6476eminus 02X8 2010eminus 1 3715eminus 02 3715eminus 02X9 1370eminus 6 6306eminus 08 6306eminus 08X10 8300eminus 7 6291eminus 08 6291eminus 08X11 2040eminus 6 6293eminus 08 6293eminus 08X12 1030eminus 6 6280eminus 08 6280eminus 08X13 5300eminus 7 6303eminus 08 6303eminus 08

Table 16 Ranking results of the key events

Rank SymbolNormalization weighting (Rlowast) Total

weighting(Rlowast)

RlowastBM RlowastRAW RlowastFV

1 X6 13805 18942 18942 516892 X1 13541 17664 17664 488693 X2 13354 16717 16717 467884 X7 13120 15559 15559 442385 X5 12686 13423 13423 395326 X8 11778 8926 89255 296297 X3 11661 8363 8363 283878 X4 10055 0406 0406 108689 X11 00002 1512eminus 05 1512eminus 05 1498eminus 0410 X9 8028eminus 05 1515eminus 05 1515eminus 05 1106eminus 0411 X12 6035eminus 05 1509eminus 05 1509eminus 05 9053eminus 0512 X10 4863eminus 05 1511eminus 05 1511eminus 05 7886eminus 0513 X13 3106eminus 05 1514eminus 05 1514eminus 05 6134eminus 05Total 100 100 100 100

02822

01073

00416 0036700142

0044200172 00151 00059

Occ

urre

nce p

roba

bilit

y (in

1 y

ear)

000

005

010

015

020

025

030

OE1 OE2 OE3 OE4 OE5 OE6 OE7 OE8LE

Figure 13 Occurrence probability when safety is ensured at keynodes

Advances in Civil Engineering 17

hydrological conditions that may be encounteredDuring excavation the advanced geological pre-diction technologymay be employed to detect adversegeological and hydrological conditions ahead of theTBM in real time including confined water groundcavity and flow sand

(3) Node X6 (seal failure at shield tail) belongs tomultiple failures e quality of the tail brush needsto be enhanced and tail brush should promptly bereplaced when it is worn

By adopting corresponding safety measures in shieldtunnel excavation the occurrence probability of variousdegrees of surface collapse (OE3 OE4 OE6 OE7 and OE8)was significantly decreased (Figure 13) Finally the TBMssuccessfully passed through the left track of DCS on March3 2017 and the right track on June 11 2017 without anysurface collapse accident demonstrating the effectiveness ofour proposed hybrid method

5 Conclusions and Future Works

In this work we first defined the ldquonormal excavation phaserdquoof shield tunneling based on the fuzzy statistical test theoryData were extracted from the construction log of the XWS inthe Wuhan metro line 7 to determine the occurrenceprobability of facility fault and expert opinions were soli-cited to determine the occurrence probability of environ-mental failure operational error and multiple failuresProbabilistic safety assessment (PSA) of the normal shieldtunnel excavation system was then performed accordingly

We employed the bow-tie analysis to evaluate the oc-currence of excessive surface settlement during normaltunnel excavation e presence of emergency measurescould reduce the occurrence probability of surface collapsecaused by excessive surface settlement (OE3 OE4 OE6 OE7and OE8) but have limited effect on the prevention of ac-cidents of OE1 OE2 and OE5 It is essential to decrease theprobability of excessive surface settlement in order to pre-vent the resulting outcome events (OEs)

By mapping the bow-tie analysis to Bayesian networks(ie BT-BN analysis) we determined the key nodes thatcould cause excessive surface settlement (LE) e key nodesincluded the following X6 (seal failure at shield tail) X1(confined water) X2 (ground cavity or flow sand) X5 (ab-normal TBM shutdown) and X7 (excessive deviation fromthe axis) Effective safety measures at these nodes couldreduce the occurrence probability of excessive surface set-tlement (LE) by 66

To ensure safety careful geological exploration shouldbe carried out before the tunneling project During thetunneling safety management and supervision should bestrengthened at the construction site Advanced geo-logical prediction technology should be used to detectpoor geological and hydrological conditions ahead of theTBM in real time Advanced laser locator should be usedto monitor and alarm excessive axial deviation equality of the tail brush should be improved and tailbrush should be replaced timely when it becomes worn

e occurrence probability of excessive surface settlementwas decreased by adopting these safety measures and theoccurrence of the resulting surface collapse was sub-sequently decreased

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

e authors thank the workers foremen and safety co-ordinators of the main contractors for their participatione authors also wish to thank the engineers Yun Zhang andPeilun Tu for assistance in gathering field data

References

[1] T Zhao W Liu and Z Ye ldquoEffects of water inrush fromtunnel excavation face on the deformation and mechanicalperformance of shield tunnel segment jointsrdquo Advances inCivil Engineering vol 2017 Article ID 5913640 9 pages 2017

[2] W Liu T Zhao W Zhou and J Tang ldquoSafety risk factors ofmetro tunnel construction in China an integrated study withEFA and SEMrdquo Safety Science vol 105 pp 98ndash113 2018

[3] K Li ldquoHangzhou metro site collapse accidentrdquo 2008 httpnewssohucom20081115n260653551shtml

[4] S Liu ldquoConstruction of Nanchang metro line 2 constructionsection pavement collapsesrdquo 2017 httpnewssohucom20160514n449414512shtml

[5] R B Peck ldquoDeep excavations and tunneling in soft groundrdquo7th International Conference on Soil Mechanics and Foun-dation Engineering vol 7 no 3 pp 225ndash290 1969

[6] P B Attewell I W Farmer and N H Glossop ldquoGrounddeformation caused by tunnelling in a silty alluvial clayrdquoGround Engineering vol 11 no 8 pp 32ndash41 1978

[7] W J Rankin ldquoGround movements resulting from urbantunnelling predictions and effectsrdquo Geological Society Lon-don Engineering Geology Special Publications vol 5 no 1pp 79ndash92 1988

[8] P B Attewell and J P Woodman ldquoPredicting the dynamicsof ground settlement and its derivatives caused by tunnelingin soilrdquo Ground Engineering vol 15 no 8 pp 13ndash20 1982

[9] M P OrsquoReilly and B M New ldquoSettlement above tunnels inthe United Kingdommdashtheir magnitude and prediction intunnelling 82 proceedings of the 3rd international sympo-sium brighton 7ndash11 June 1982 P173ndash181 Publ LondonIMM 1982rdquo International Journal of Rock Mechanics ampMining Sciences amp Geomechanics Abstracts vol 20 no 1pp 1ndash18 1983

[10] R J Mair R N Taylor and A Bracegirdle ldquoSubsurfacesettlement profiles above tunnels in claysrdquo Geotechniquevol 45 no 2 pp 361-362 1995

[11] X L Yang and J MWang ldquoGroundmovement prediction fortunnels using simplified procedurerdquo Tunnelling and Un-derground Space Technology vol 26 no 3 pp 462ndash471 2011

18 Advances in Civil Engineering

hazards and associated risks with the baseline risk assess-ment tool (BART) [21] Targoutzidis argued that BTanalysisis an effective tool for identifying environmental risk sourcesbecause it can clearly show the connections between thecause the loss events (LEs) the conditional events (CEs)and the outcome events (OEs) [22] e BT approach hasbeen applied in the risk assessment of hexane distillation therisk management of harbor and maritime terminals and therisk assessment of airworthiness in military aviation [23ndash25]

e focus of these BT models is to depict the entirescenario of the accident to identify and evaluate the po-tential causes and consequences but does not readily revealthe actual causes through logical connections and occur-rence probability is caveat can be remedied by mappingBT to BN For example Badreddine and Amor improvedthe BTmodel by exploiting the advantages of BN dynamicanalysis ey built the BT chart in an automated anddynamic way to implement appropriate barriers to pre-vention and protection in dynamic systems [26] Khakzadet al made a dynamic risk analysis of systems whosephysical reliability is updated periodically [27] ey madeuse of the Bayes theorem to periodically update the failureprobability of safety barriers in the BT chart and estimatedthe probability of consequences based on the enhanced BTchart It was argued that mapping BT to BN [28] couldalleviate the limitations of BT caused by static factorsAbimbola et al used BT and BN to determine the keyfactors of the integrity model In their study the posteriorprobability was obtained through the Bayes theorem andthe key factors were determined by the ratio of the posteriorprobability to the prior probability [29]

In summary mapping BT to BN allows dynamic riskanalysis and the key factors of the system can be identifiedby calculating the posterior probability through the Bayestheorem Meanwhile since the conditional probability canbe calculated via the Bayes theorem the importance measureof PSA can also be introduced [30] and BN can be fitted withthese important measures very well to calculate the im-portance measures accurately and easily erefore the BT-BN analysis can not only analyze surface collapse caused byexcessive surface settlement in shield tunneling metroconstruction but also use PSA to confirm the critical causesof accidents by adding the importance measures

3 Methodology

BT analysis is used to display the scenario of the loss event(LE) in the system In the BTmodel the FTanalysis can revealthe cause of the LE and the consequences of LE can bedetermined by the ET analysis In the proposed BT-BNmethod the FT and ETanalyses in the BTmodel are mappedto the BN such that the nodes that give rise to accidents can bemore easily determined e BT-BN method requires explicitoccurrence probability of failure Data for the failure prob-ability of the TBM were extracted from construction logduring the ldquonormal excavation phaserdquo of the XWS Whenexisting data could not provide the required informationexpert opinion in the form of the fuzzy number was used todetermine the corresponding failure probability e

consequences were then predicted by the BT-BN analysis andthe critical nodes related to the consequences were obtainedFigure 2 shows the flowchart of the proposed methodology

31 ldquoNormal Excavation Phaserdquo of TBM

311 Fuzzy Statistical Test 9eory e concept of ldquofuzzysetrdquo introduced by Zadeh is a crucial extension of the classicset theory of Cantor [31] e fuzzy set theory has maturedover the past years to a well-established research area inmathematics and has found extensive applications in manyfields e fuzzy set A on domain X is in fact a function ofX⟶ [01] e primary task of dealing with fuzziness inpractical applications is to determine the membershipfunction A(x) Just like probabilistic theory cannot giveprecise but only approximate probability due to limitedknowledge and information the fuzzy set theory can onlyestablish the approximate degree of membership and con-sequently an estimatedmembership function Fuzzy statisticaltests that demonstrate the stability of frequency can be carriedout to characterize the objectivity of degree of membershipand to derive an approximate membership function

Two-phase fuzzy statistics divides the domain X (egTBM excavation speed) into two statistical sets ie A(ldquonormalrdquo) and Ac (ldquoabnormalrdquo) at is two opposite fuzzyconcepts compete for statistics in domain X e so-calledldquotwo-phaserdquo indicates P2 A Ac [32] ie each fuzzy testwill establish a mapping e X⟶ P2 is mapping dividesthe domain X ie forallx isinX A(x) +Ac(x) 1 e two-phasefuzzy statistical test contains four elements (1) domainX (2)a fixed element x0 in X (3) a varying classical set Alowast in X (Alowastreflects the flexible boundary of the fuzzy set A and allows todetermine if the x0 in each test conforms to the fuzzy conceptdescribed by A) and (4) condition S which restricts thechanges of Alowast

In fuzzy statistical tests x0 remains fixed while Alowast isvaried In each test a decision must be made as for whetherx0 belongs to Alowast Note that the changing Alowast is always asubset of X After n tests the membership frequency of x0belonging to the fuzzy set Alowast is calculated as ln(A)(x0)

ln(A) x0( 1113857 number of times that ldquox0 isin Alowastrdquo

n (1)

It has been experimentally found that ln(A)(x0) tends tostabilize as n increases e stabilized value is referred to asthe degree of membership that x0 belongs to A

ln(A) x0( 1113857 limx⟶infin

number of times that ldquox0 isin Alowastrdquon

(2)

312 Fuzzy Statistical Test of the Excavation Speed of TBMExcavation speed is a macroscopic measure of the workingstate of the TBM erefore the normal state of the TBM ischaracterized by the normal excavation speed In our casethe normal excavation speed during tunneling was obtainedby running a fuzzy statistical test with the construction logsof the XWS

4 Advances in Civil Engineering

In this work the excavation speed of the TBM had adomain ofV [1 96] (mmmin)e fuzzy setA represents thefuzzy concept of ldquonormal excavation speedrdquo For the purpose ofillustration select an arbitrary excavation speed v0 23mmmin Fuzzy statistical tests were then applied to determine thedegree of membership that v0 belonged to A For the con-struction project at the XWS the appropriate project logs overn 179days (715 segment rings for left and right tunnels) wereselected e appropriate logs excluded abnormal engineeringsituations (restrictive condition S) such as TBM launchingTBM arrival and abnormal downtime during which theformation was reinforced and the excavation speed could notbe considered normal In this way the boundaries for the dailyldquonormal excavation speedrdquo could be determined for the left andright tunnels of the XWS (Table 3 Figure 3)

Table 4 shows the membership frequency that v0 23mmmin belonged to the normal excavation speed as was de-termined by the statistical tests Figure 4 shows that themembership frequency f that v0 23mmmin falls within theldquonormal excavation speedrdquo of the TBM stabilized around 066Hence A(v0) A(23) 066 e membership frequency f ofother excavation speeds could also be obtained similarlye data from the construction logs recorded a mini-mum and maximum excavation speed of 2mmmin and96mmmin respectively Hence we divided the domain V

into 96 intervals each spanning 1mmmin starting from15mmmin and ending at 965mmmin e mean of eachinterval was used to calculate the membership frequencyand the results are shown in Table 5 A program was de-veloped in MATLAB to reduce the computational com-plexity and save time

Figure 5 plots the histogram of membership frequencybased on the data in Table 5 e fitted curve of themembership function A(v) was then drawn accordinglyefitted curve conformed to the Cauchy distribution and couldbe expressed as follows

1113957A(v) v A(v) ∣ A(v) 1 +vminus 3212

1113874 11138752

1113888 1113889

minus1

v isin N⎧⎨

⎩

⎫⎬

⎭

(3)

(1) Determination of the Standard Excavation Speed In thefuzzy set theory [31] the element with the membershipfrequency A(v) 1 is designated as the kernel of the fuzzy setA and written as ldquokerArdquo Figure 5 shows that kerA 32 iev0 32mmmin was the kernel of the fuzzy set of ldquonormalexcavation speedrdquo erefore v0 32mmmin was consid-ered as the standard excavation speed in the ensuing PSAanalysis

ConvertingFTA to BN

Fuzzystatistical test

theory

ldquoNormalexcavation

phaserdquo

Preparingbow-tiediagram

ConvertingETA to BN

ConstructingBN-bow-tie

diagram

Confirmingoccurrenceprobability

TBMfacilitiesfailure

Operationalerror and

failure

TBMparameterdatabase

Triangularnumbers

Trapezoidalnumbers

Expertjudgment

Aggregation

Occurrenceprobability

Calculatingoccurrenceprobability

Calculatingimportancemeasures

BM

RAW

FV

Identifyingkey nodes

System ofTBM phases

Providingsafety

measures

Figure 2 Flowchart of the proposed methodology

Advances in Civil Engineering 5

(2) Determination of the Range of Excavation Speed In thefuzzy set theory all elements whose membership frequencyA(v)gt 0 constitute a support of the fuzzy setA and is writtenas ldquosupp Ardquo and all elements whose membership frequencyA(v)gt α is designated as the α cut set of the fuzzy set A andwritten as Aα Figure 5 shows that the excavation speed

fluctuated around the kernel (32mmmin) during shieldtunnel excavation In order to express the range of normalexcavation speed the confidence level α 05 was selectedand the excavation speed whose membership frequencysatisfied A(v)gt 05 was considered to constitute the in-terval of normal excavation speed (ie the 05 cut set of A)

Table 3 Partial construction log of the ldquonormal excavation speedrdquo in the XWS

n 1ndash10 n 11ndash20 n 21ndash30 n 31ndash40 n 41ndash50 n 51ndash60 n 61ndash70 n 71ndash80 n 81ndash90 n 91ndash100303ndash506 25ndash32 276ndash424 78ndash425 25ndash35 18ndash39 27ndash43 20ndash41 30ndash47 20ndash54324ndash388 26ndash34 232ndash476 83ndash417 28ndash46 20ndash35 24ndash40 10ndash40 30ndash61 32ndash63284ndash396 27ndash42 233ndash445 202ndash476 17ndash35 15ndash42 27ndash47 20ndash35 20ndash61 32ndash58303ndash388 23ndash36 205ndash427 242ndash425 28ndash37 27ndash41 20ndash33 17ndash32 30ndash60 20ndash37303ndash363 123ndash348 282ndash456 287ndash526 17ndash36 21ndash37 22ndash34 8ndash40 14ndash58 24ndash4032ndash44 178ndash325 182ndash426 19ndash32 20ndash37 31ndash41 27ndash48 8ndash40 27ndash74 25ndash4831ndash42 198ndash374 137ndash375 22ndash45 20ndash35 30ndash40 30ndash42 20ndash50 15ndash55 24ndash5131ndash39 135ndash326 156ndash326 21ndash44 21ndash37 30ndash35 25ndash43 20ndash50 25ndash45 32ndash4630ndash42 134ndash326 20ndash37 19ndash42 20ndash35 20ndash40 28ndash36 20ndash46 28ndash52 25ndash4031ndash38 156ndash364 15ndash40 20ndash41 20ndash37 25ndash40 225ndash37 31ndash42 31ndash47 20ndash35

Rang

e of a

dvan

ce sp

eed

(mm

min

)

v-lower limitv-upper limit

0102030405060708090

100

100 200 300 400 500 600 700 8000Segment number

Figure 3 Distribution of the ldquonormal excavation speedrdquo

Table 4 Membership frequency of 23mmmin belonging to the ldquonormal excavation speedrdquo

Description Number and membershipNumber of rings 50 100 150 200 250 300 350Membership counts 28 51 60 97 128 153 178Membership frequency 056 051 04 049 051 051 051Number of rings 400 450 500 550 600 650 715Membership count 202 252 302 342 382 427 470Membership frequency 051 056 061 062 064 066 066

066

v = 23mmmin

001020304050607

Cov

erag

e fre

quen

cy f

100 600300 700500200 8000 400Segment number

Figure 4 Membership frequency of 23mmmin belonging to the ldquonormal excavation speedrdquo

6 Advances in Civil Engineering

e set of normal excavation speed in Zadehrsquos form wasordered as shown in equations (4) and (5) usv0 20ndash44mmmin was considered as the range of normalexcavation speed in the ensuing PSA analysis

1113957A(v) 05020

+05421

+05922

+06423

+06924

+07525

+08026

+08527

+09028

+09429

+09730

+09931

+132

+09933

+09734

+09435

+09036

+08537

+08038

+07539

+06940

+06441

+05942

+05443

+05044

(4)

supp 1113957A(v) 111386420 21 22 23 24 25 26 27 28 29 30 31 32

33 34 35 36 37 38 39 40 41 42 43 441113865

(5)

Table 5 Membership frequency of the ldquonormal excavation speedrdquo

No Group Count Frequency1 15ndash25 1 00012 25ndash35 2 00033 35ndash45 2 00034 45ndash55 2 00035 55ndash65 5 00076 65ndash75 6 00087 75ndash85 17 00248 85ndash95 21 00299 95ndash105 31 004310 105ndash115 34 004811 115ndash125 46 006412 125ndash135 60 008413 135ndash145 66 009214 145ndash155 100 01415 155ndash165 132 018516 165ndash175 168 023517 175ndash185 217 030318 185ndash195 240 033619 195ndash205 366 051220 205ndash215 396 055421 215ndash225 425 059422 225ndash235 470 065723 235ndash245 500 069924 245ndash255 535 074825 255ndash265 563 078726 265ndash275 588 082227 275ndash285 609 085228 285ndash295 619 086629 295ndash305 668 093430 305ndash315 686 095931 315ndash325 715 132 325ndash335 698 097633 335ndash345 685 095834 345ndash355 670 093735 355ndash365 643 089936 365ndash375 623 087137 375ndash385 586 08238 385ndash395 562 078639 395ndash405 536 07540 405ndash415 495 069241 415ndash425 456 063842 425ndash435 406 056843 435ndash445 358 050144 445ndash455 332 046445 455ndash465 290 040646 465ndash475 246 034447 475ndash485 201 028148 485ndash495 157 02249 495ndash505 136 01950 505ndash515 116 016251 515ndash525 101 014152 525ndash535 91 012753 535ndash545 88 012354 545ndash555 77 010855 555ndash565 69 009756 565ndash575 62 008757 575ndash585 56 007858 585ndash595 51 007159 595ndash605 45 006360 605ndash615 41 0057

Table 5 Continued

No Group Count Frequency61 615ndash625 38 005362 625ndash635 35 004963 635ndash645 32 004564 645ndash655 30 004265 665ndash675 28 003966 675ndash685 28 003967 685ndash695 25 003568 695ndash705 23 003269 705ndash715 23 003270 715ndash725 21 002971 725ndash735 20 002872 735ndash745 19 002773 745ndash755 19 002774 755ndash765 18 002575 765ndash775 18 002576 775ndash785 18 002577 785ndash795 18 002578 795ndash805 16 002279 805ndash815 16 002280 815ndash825 15 002181 825ndash835 15 002182 835ndash845 12 001783 845ndash855 11 001584 855ndash865 8 001185 865ndash875 7 00186 875ndash885 6 000887 885ndash895 5 000788 895ndash905 4 000689 905ndash915 4 000690 915ndash925 4 000691 925ndash935 4 000692 935ndash945 4 000693 945ndash955 3 000494 955ndash965 2 000395 965ndash975 2 0003

Advances in Civil Engineering 7

313 Fuzzy Statistical Tests of Excavation Parameterse excavation speed of the TBM reflects the influenceexerted by the excavation parameters (eg total thrust facepressure and cutter head torque) on the force and dis-placement of the surrounding soil erefore it is necessaryto determine the realistic and practical excavation param-eters based on the excavation speed

Formation reinforcement during TBM launching and TBMarrival can exert a strong influence on the shield tunnel ex-cavation and lead to highly discrete parameters erefore thedata from the TBM launching and TBM arrival stages werediscarded in studying the relationship between excavation speedand TBMparameters Figure 6 shows how the TBMparametersvaried with the excavation speed during the construction of the715 segments in the XWSe curves were fitted viaMATLABand the slope of the curves was highly indicative of the cor-relation between the TBMparameters and the excavation speed

In Figure 6(a) the total thrust (F) increased with risingexcavation speed is was because bentonite was used as alubricant and injected around the shield of the TBM duringexcavation to reduce friction When the amount of injectedbentonite was appropriate the friction coefficient betweenthe shield and the surrounding soil would decrease and theexcavation speed would then increase when the thrust (F)was higher In Figure 6(b) the excavation speed decreasedwhen the cutter head torque (MT) increased is wasbecause when the soil body of the tunneling face wasrelatively difficult to cut a larger torque of the cutter headwould be needed and the excavation speed would decreaseFigure 6(c) shows that during normal excavation thepressure of the tunneling face increased slightly with risingexcavation speed Besides Mair pointed out that duringsegment assembly the downtime of TBM would decreasethe soil and water pressure on the tunneling face whichcould reduce the control pressure of the tunneling face [33]e same pattern was observed in the current constructionlogs and the R2 value of the curve in Figure 6(c) was hencerelatively low Figure 6(d) shows that the grouting pressuredecreased slightly with rising excavation speed However

since the pressure of primary grouting was read off from thegrouting pressure pump the actual grouting pressureexerted on the surrounding soil was smaller and theprimary grouting pressure hence had limited impact onexcavation speed

(1) Determination of Standard TBM Parameters It wasdetermined from the fuzzy statistical tests above that thestandard excavation speed was 32mmmin e corre-sponding standard TBM parameters could be determinedaccordingly from the following equation

TBMPstandard value 1113936

Nn1TBMPnv

N v321113868111386811138681113868 (6)

where TBMP is the TBM parameter and v is the excavationspeed (mmmin)

(2) Determination of the Range of TBM Parameters It wasdetermined from the fuzzy statistical tests above that therange of excavation speed was 20ndash44mmmin e corre-sponding boundaries of TBM parameters could be de-termined from the extreme values in the monitoring records(Figure 6) via the following equation

TBMPupper limit max TBMPv 20levle4411138681113868111386811138681113966 1113967

TBMPlower limit min TBMPv 20levle4411138681113868111386811138681113966 1113967

(7)

(3) ldquoNormal Excavation Phaserdquo of TBM According to thefuzzy set theory the excavation speed in the ldquonormal ex-cavation phaserdquo fell within 20ndash44mmmin e TBM wasconsidered to be in the ldquonormal excavation phaserdquo whenthe excavation speed and the TBM parameters all fellwithin the prescribed ranges specified above and listedagain in Table 6 e standard values and ranges were usedfurther in the subsequent PSA analysis Table 6 shows thatamong the examined parameters the face pressure had adeviation interval of merely 196 and was controlled the

Advance speed v (mmmin)

Mem

bers

hip

Atilde (v

)

Cov

erag

e fre

quen

cy A

(v)

04

02

06

08

1

10090807060504030201000

04

02

06

08

1

0

Fuzzy statistical experiment methodCauchy distribution curve

Figure 5 e histogram of membership frequency and the membership function of TBM excavation speed

8 Advances in Civil Engineering

best whereas the cutter head torque had a deviation in-terval of 7401 and was controlled the worst

(4) Statistical Relationship between TBM Parameters andExcavation Speed e monitoring results in Figure 6

demonstrated that in the ldquonormal excavation phaserdquo ofthe XWS the total thrust and the face pressure were posi-tively correlated with the excavation speed In particular thetotal thrust had a stronger correlation to the excavationspeed than the face pressure In contrast the cutter head

2000400060008000

1000012000140001600018000

Tota

l thr

ust

F (k

N)

20 25 30 35 40 45 50 55 60 6515Advance speed v (mmmin)

(a)

0500

10001500200025003000350040004500

Cutte

r hea

d to

rque

MT

(kNlowast

m)

20 25 30 35 40 45 50 55 60 6515Advance speed v (mmmin)

(b)

0

50

100

150

200

250

Face

pre

ssur

eP N

(kPa

)

20 25 30 35 40 45 50 55 60 6515Advance speed v (mmmin)

(c)

Gro

utin

g pr

essu

reP G

(kPa

)

100150200250300350400450500550

20 25 30 35 40 45 50 55 60 6515Advance speed v (mmmin)

(d)

Figure 6 Variations in the TBM parameters at different excavation speeds (data from XW section) (a) total thrust versus excavationspeed (b) cutter head torque versus excavation speed (c) face pressure versus excavation speed (d) grouting pressure versus excavationspeed

Table 6 Standard values and ranges of excavation speed and TBMPs

Factors v (mmmin) F (kN) P N (kPa) M T (kNmiddotm) P G (kPa)Parameter range [20 44] [8300 13100] [117 143] [1294 2974] [197 302]Standard value 32 9700 1326 2270 302Deviation range () [minus375 375] [minus1443 3505] [minus1176 784] [minus430 3101] [minus3477 0]

Advances in Civil Engineering 9

torque and the primary grouting pressure were negativelycorrelated with the excavation speed

32 Bow-Tie-Bayesian Network Analysis e bow-tie anal-ysis combines FTand ETanalysese FTanalysis in bow-tiecalculates the occurrence probability of the loss event (LE) aswell as the top event (TE) e occurrence probability of theTE can also be obtained from the occurrence probability ofthe basic event (BE) e events could be evaluated by theirlogical relationship and their occurrence probability in theBN Mapping the bow-tie analysis to BN involves convertingboth FT and ET analyses Figure 7(a) provides a brief de-scription of calculation steps

ree importance measures described in the followingBorst and Schoonakker [30] were introduced in the newmethodology according to the Bayes theorem Figure 7(b)gives a brief description of their calculation In the proposedmethodology the critical nodes that could more easilytrigger accidents were obtained by calculating these im-portance measures

33 Confirming Failure Occurrence Probability e BT-BNanalysis requires knowing the occurrence probability of eachbasic event (BE) e basic events fall into four categoriesenvironmental failure operational error multiple failuresand facility failures e occurrence rate of facility failureswas obtained from the construction log of the XWS for thetunneling project that spanned 179 days (715 segments intotal) and was converted into occurrence probability via thefollowing equation

F 1minus eminusλt

(8)

where F denotes the occurrence probability of the failure andλ denotes the occurrence rate of the failure

e occurrence probability of environmental failureoperational error and multiple failures cannot be readilyderived from existing data and was thus estimated via expertopinione fuzzymethod combines the opinions of differentexperts in a weighted manner to calculate the fuzzy fault rate(FFR) from the triangular fuzzy numbers or trapezoidal fuzzynumbers proposed by the experts e occurrence probabilityof environmental failure operational error and multiplefailures was then determined from the FFR [34] e generalprocedure of the fuzzy method is as follows

(1) Determine the weight of the opinion of each expertbased on the age education background work ex-perience and position of the consulted expert (Ta-ble 7) e crude weight score of each expert iscalculated via the following equation

Sn Sna+ Snb

+ Snc+ Snd

(9)

where Sn represents the total weight score of theexpert e relative weight score of each expert iscalculated via the following equation

Wn Sn

1113936mn1Sn

(10)

where m represents the number of experts(2) e occurrence probability is divided into the

following categories nonoccurrence absolute lowvery low low fairly low medium fairly high highvery high absolute high or occurrence e rankvalue of the categories escalates from 0 for non-occurrence to 1 for the occurrence (Table 8) eoccurrence probability of the event is then evalu-ated based on the corresponding triangular numberor trapezoidal number given by the experts

(3) Aggregation of the fuzzy numbers When the fuzzynumbers are all triangular number or trapezoidalnumber the aggregated fuzzy numbers of an event iscalculated via equation (11) [35] e aggregatedfuzzy number considering the expert weight isshown in equation (12)

1113957Aaggregated 1113944m

n1Wn otimes 1113957An (11)

where 1113957Aaggregated represents the aggregated fuzzifiednumber given by expert m and Wn represents theweight of the expertrsquos opinion

1113957AW 1113874W1a11 + W2a21 W1a12 + W2a22 W1a12

+W2a23 W1a13 + W2a241113875

(12)

(4) After the aggregated fuzzy numbers are determinedthe centroid index method (equation (13)) is used tohandle the fuzzy numbers and obtain the fuzzyprobability score (FPS) [36]

X 1113938g(x)x dx

1113938g(x)dx (13)

where X is the defuzzified output g(x) is themembership function and x is the output variableAssume 1113957An (an1 an2 an3) a triangular number and1113957An (an1 an2 an3) a trapezoidal number e FPS iscalculated via equation (14) when a fuzzy number is atriangular number and via equation (15) when thefuzzy number is a trapezoidal number

FPS 13

an1 + an2 + an3( 1113857 (14)

FPS 13

an3 + an4( 11138572 minus an3an4 minus an1 + an2( 1113857

2+ an1an2

an3 + an4 minus an1 minus an2( 1113857

(15)

10 Advances in Civil Engineering

(5) Finally the FPS is converted to FFR via equation(16) [37] and the FFR is further converted tothe occurrence probability of environmentalfailure operational error and multiple failures(equation (8))

FFR

110k

FPSne 0

0 FPS 0

k 2301 times(1minus FPS)

FPS1113890 1113891

13

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(16)

4 Results

41 Analysis of Excessive Surface Settlement inNormal TunnelExcavation Figure 8 shows that the normal excavation

(1) If the logical relationship is AND between events the TE occurs when all events occur The probability of TE can be calculated from the following equation

(A)

(2) If the logical relationship is OR between events the TE occurs when any of the event occurs The probability of TE can be calculated from the following equation

(B)

(3) By definition in the FT analysis the probability of TE is the same as that of LE Similarly the probability of the initial event (IE) in the ET analysis is the same as that of LE The probability of OE in ET analysis can be calculated from the following equation

(C)

(4) The BN an inference method based on the Bayes theorem combines both graph theory and probability theory

(D)

FTE = i=1

nFBEi

FTE = 1 ndashi=1

n(1 ndash FBEi)

FOEn = FIE middot i=1

nP (Ei = 0) middot

j=1

nP (Ej = 1)

P(B | A) = P(A | B) middot P(B)

P(A)

(a)

(1) The Birnbaum measure (BM) whichdetermines the increment of the occurrenceprobability of TE when BE occurs is shownin the following equation

(E)

where P(TE | BE = 1) denotes the occurrence probability of TE when BE occurs and P(TE | BE = 0) denotes the occurrence probability of TE when BE does not occur

(2) Risk achievement worth (RAW) evaluatesthe impact of BE on TE when the probabilityof BE is considered The RAW is adjustedby the probability of TE and BE as shown inthe following equation

(F)

where P(BE) denotes the occurrence probability of BE and P(TE) denotes the occurrence probability of TE under all circumstances

(3) The FussellndashVesely (FV) importance which describes the contribution of BE to system fault is shown in the following equation

IBBE

M = P(TE | BE = 1) ndash P(TE | BE = 0)

IRB

AE

W = IBBE

M middot P(BE)P(TE)

(G)

P(TE) ndash P(TE | BE = 0)P(TE)

IFB

VE =

(b)

Figure 7 Bow-tie-Bayesian network analysis Calculation of (a) event probability and (b) importance measures

Table 7 Weight scores for experts

Factor Category Score

Age (a)

lt30 130ndash39 240ndash49 3ge50 4

Education (b)

High school 1College 2Bachelor 3Master 4PhD 5

Work experience (c)

lt5 years 15ndash10 years 211ndash20 years 321ndash30 years 4ge30 years 5

Position (d)

Worker 1Technician 2

Junior scholarengineer 3Senior scholarengineer 4

Table 8 Rank value of each category

Classified occurrence probability Rank valueNonoccurrence 0Absolute low 01Very low 02Low 03Fairly low 04Medium 05Fairly high 06High 07Very high 08Absolute high 09Occurrence 10

Advances in Civil Engineering 11

phase involves the environment TBM operation supervi-sion management and emergency handling Risk analysis ofthe ldquonormal excavation phaserdquo in soft soil engineering basedon the XWS allows the identification of potential risk factorsthat may trigger surface settlement and consequently lead toaccidents Eskesen et al have described three principles forrisk analysis as follows (1) eliminate risk factors that are easyto detect and can be controlled timely and effectively (2)eliminate risk factors with low occurrence probability andno catastrophic consequences and (3) combine risk factorswith similar loss consequences [38] Accordingly the riskfactors during shield tunneling were organized into three

basic categories improper control of excavation parameters(eg poor control of face pressure) catastrophic geology (egground cavity or flow sand) and unforeseeable factors (egsegment damage) Figure 9 shows the bow-tie model builtfrom the categorized factors for the risk of surface collapsecaused by excessive surface settlement during shield tun-neling OEs of various degrees were successfully predictedbased on the CEs (Figure 9) Many risk factors exist in anygiven surface collapse In this section based on the previouscalculation results in Section 31 we selected the manageableshield excavation parameters (shield total thrust groutingpressure cutter head torque soil pressure etc) in the ldquonormal

Synchronousgrouting

ExcavationSegment

installationAttitudecontrol Tail sealing

Excavationcycle

Quality controlacceptance

Dangeroussituation exists Yes

Prepareemergencymeasures

Emergencymeasures

Execution of emergencymeasures

Acceptance ofexcavationprocedures

Excavationacceptance

report

Monitoring measurements

Monitored dataof excavationenvironment

Formation geologyTBM parametersExcavation axis

Segment installationSynchronous grouting

TBM construction parameter

No

TBM parametersv (mmmm) F (kN) PN (kPa)

MT (kNmiddotm) PG (kNmiddotm)TBM attitude TBM position TBM fault information

Soil bodyparameters

Soil evolutionmodel

Confined waterObstacles

Ground cavity orquicksand

Metro tunnel excavation

Emergencyhandling

Supervision

TBMoperation

TBM

Environment

Management

Figure 8 System diagram of the ldquonormal excavation phaserdquo

12 Advances in Civil Engineering

excavation phaserdquo as the base events assigning their weightsaccording to Section 33 and then performed PSA analysis

As mentioned earlier the ldquonormal excavation phaserdquo isunder the influence of excavation parameters catastrophicgeology and unforeseeable factors Surface settlement canoccur once the condition deteriorates Here we set excessivesurface settlement as the TE in the FT analysis Meanwhilethe tunneling system has a built-in emergency managementsystem Upon excessive surface settlement the emergencymanagement system will start to shut down the TBM timelyHence in the ETanalysis the excessive surface settlement isset as the IE and TBM shutdown is set as the CE OEs ofvarious degrees are obtained based on the considered CEFinally the surface settlement is set as the LE to connect theFT and the ET and furnish the BTmodel (Figure 9 Table 9)Eight OEs of various degrees were predicted based on theCEs including surface collapse events OE3 OE4 OE6 OE7and OE8 (Figure 9 Table 10) e TBM shuts down if CE1occurs and continues to operate if otherwise

e BN-BT model for excessive surface settlement isconstructed by mapping the FT and ET analyses in the BT(Figure 9) model to BN (Figure 10) All the nodes of BN havepreviously been described in the BT except the node OEwhich is the consequence node OE is added to accommodatethe outcomes of BT By connecting the node of excessivesurface settlement to OE another state also called the safe

state is added to the state set It includes consequences OE1 toOE8 to account for the nonoccurrence of the top event iewhen excessive surface settlement controlled To show thedependence among the safety barriers and the top eventcausal arcs are also drawn between TBM shutdown andgrouting in the settlement area and bentonite injection to soilchamber and TBM shield It is worth noting that since variouscombinations of the failure and success of the sequentialsafety barriers result in different consequences in the BT allthe safety nodes of BN are connected to node OE

42 Determination of Event Occurrence Probability emaximum surface settlement that resulted from the aber-ration of the ith TBM parameter is denoted as δmaxi eprobability of safety accident becomes higher when δmaxiapproaches the permitted surface settlement δi Whenδmaxi δi the accident will occur as soon as the TBM pa-rameter gives rise to a surface settlement of δmaxi eprobability of equipment fault for the normal excavationsystem was calculated via equation (8) from the engineeringlog data of the XWS over 179 days of construction (715segments rings in total) e construction of all 715 rings fellwithin the ldquonormal excavation phaserdquo as was defined by thefuzzy statistical test (v 20ndash44mmmin) Table 11 lists thecalculation results

X3X2X1

OR

M1

X7X6X5X4

OR

M2

X10X9 X11 X13X12

M3

OR

Excessive surface

settlement

X8

Caus

esLE

CE1

CE2

CE3

Con

sequ

ence

sSt

op

TBM

Gro

utin

g in

settl

emen

tar

ea

Bent

onite

inje

ctio

n

OE 1

OE 2

OE 3

OE 4

OE 5

OE 6

OE 7

OE 8

Success Failure

AND

Figure 9 Diagram of bow-tie analysis for excessive surface settlement

Advances in Civil Engineering 13

To address the uncertainty regarding the events ofenvironmental failure operational error and multiplefailure six domain experts who participated in the con-struction of the Wuhan metro system including two seniorengineers one senior academic professor one technicalconsultant one junior engineer and one worker wereinvited to evaluate the occurrence probability of events thatcannot be readily derived from existing data (Table 12)eweights of their opinion were then calculated by usingequations (9) and (10) and the distribution of each opinionweight is shown in Figure 11

In addition Table 13 lists the expert opinions regardingthe events of environmental failure operational error andmultiple failures in the form of fuzzy numbers based onTable 8 e fuzzy numbers were aggregated via equations(12) and converted to FPS and FFR via equations (13)ndash(16)(Table 14) e occurrence probabilities were finally derivedfrom FFR (Table 14) Generally the expert knowledge isconsidered as a scarce resource which cannot provide

universal consultation or real-time guidance us there ismuch room to improve the data use efficiency

43 Update in Occurrence Probability of LE and OE eoccurrence probability of basic events is calculated as de-scribed in Section 42 including the occurrence probabilityof facility failure from the engineering log data of the XWS aswell as that of environmental failure operational error andmultiple failures derived from expert opinion e occur-rence probability of excessive surface settlement (LE) isdetermined via equations (A) and (B) by considering thelogical relationship between events in Figure 7 Finally theoccurrence probability of OEs including surface collapse canbe calculated via equation (C) in the figure by mapping theFT and ET analyses in the BTmodel to BN Figure 12 showsthe occurrence probabilities of the LE (ie excessive surfacesettlement) and that of the OEs

e above analysis shows that the occurrence probabilityof excessive surface settlement within one year is 08299(Figure 12) is occurrence probability of surface collapse(OE3 OE4 OE6 OE7 and OE8) may be decreased whenemergency measures are put in place including grouting insettlement area and bentonite injection to soil chamber andTBM shield However these measures cannot help to reduceminor accidents since the occurrence probability remains athigh levels for OE1 OE2 and OE5 Admittedly grouting andbentonite injection are necessary measures and they candecrease the effects of excessive surface settlement duringshield tunneling However the key point of avoiding outcomeevents including surface collapse to ensure project safety is toprevent the excessive surface settlement from occurring in thefirst place Hence we sought to determine the key nodesleading to excessive surface settlement via BT-BN analysis andpropose the corresponding preventive measures

Table 10 Analysis of event occurrence

Symbol EventOE1 Excessive surface settlement

OE2Grouted cutter head and shield excessive surface

settlement and minor property damageOE3 Minor surface collapse and property damage

OE4Moderate surface collapse major property damage

and minor casualtiesOE5 Excessive surface settlement

OE6Grouted cutter head and shield moderate surface

collapse and minor property damage

OE7Moderate surface collapse and major property

damage

OE8Severe surface collapse major property damage and

major casualties

Table 9 Details of bow-tie components in Figure 9

Event Symbol Logic link type Failure modelGround settlement Excessive surface settlement OR gate mdashCatastrophic geology M1 OR gate mdashUnforeseeable factors M2 OR gate mdashExcavation parameters M3 AND gate mdashConfined water X1 mdash Environmental failureGround cavity or flow sand X2 mdash Environmental failureObstacles X3 mdash Environmental failureSegment damage X4 mdash Operational errorAbnormal TBM shutdown X5 mdash Multiple failureSeal failure at shield tail X6 mdash Multiple failureExcessive deviation from axis X7 mdash Operational errorEquipment failure X8 mdash Multiple failureUntimely grouting X9 mdash Facility failureExcessive cutter head torque X10 mdash Facility failureImproper control of face pressure X11 mdash Facility failureExcessive thrust X12 mdash Facility failureImproper control of excavation speed X13 mdash Facility failureTBM shutdown CE1 mdash Multiple failureGrouting in settlement area CE2 mdash Multiple failureBentonite injection to soil chamber and TBM shield CE3 mdash Multiple failure

14 Advances in Civil Engineering

Table 11 Probability of equipment fault

Event Surface settlementδmaxi (mm)

Permitted surfacesettlement δi (mm)

Value of TBMparameter

Occurrence rate(dminus1)

Occurrence probability(in 1 year)

X9 89 15 302 kPa 10675eminus 04 382eminus 02X10 84 10 2974 kNmiddotM 17792eminus 04 629eminus 02X11 86 15 143 kPa 71167eminus 05 256eminus 02X12 98 15 13100 kN 14233eminus 04 506eminus 02X13 120 15 41mmmin 28467eminus 04 987eminus 02All data were obtained from the operation log of the XWS

Table 12 Characteristics of experts participated in the occurrence probability evaluation

Expert Age Education Service (years) Professional position1 56 High school 25 Worker2 35 Master 10 Technician3 41 Master 15 Junior engineer4 47 Bachelor 20 Senior engineer5 50 PhD 18 Senior academic6 59 PhD 30 Senior engineer

0125 0125

01625 01625

020225

AgeEducationService

Professional positionWeighting

2 3 4 5 61Expert

0

005

01

015

02

025

Wei

ghtin

g

0

1

2

3

4

5

6

Wei

ghtin

g sc

ore

Figure 11 Distribution of each expert opinion weight

X1 X2 X3

M1

X5 X6 X7 X8

M2

X9 X11

M3

Excessive surface

settlement

X10 X12 X13X4

CE1 CE2 CE3

OE

Caus

esLE

CEC

onse

quen

ces

Figure 10 Bow-tie chart of excessive surface settlement

Advances in Civil Engineering 15

44 Identify Key Nodes and Provide Safety Measures Inorder to find the key nodes leading to excessive surfacesettlement the importance measure of each event was cal-culated via equations (E)ndash(G) in Figure 7 as shown inTable 15 Assume the number of events as ldquonrdquo e nor-malized weight Rlowast could be calculated from the importancemeasure Ii via the following equation

Rlowast

Ii

1113936ni1Ii

times 100 (17)

After the normalized weight Rlowast is calculated for eachimportance measure the total weight Rlowast could be calculatedvia equation (18) e total weight Rlowast of events was finally

ranked in descending order to find the key nodes as shownin Table 16

Rlowast R

lowastBM + R

lowastRAW + R

lowastFV (18)

It can be seen that X6 (seal failure at shield tail) X1(confined water) X2 (ground cavity or flow sand) X5 (ab-normal TBM shutdown) and X7 (excessive deviation fromaxis) have far higher weight than other events and are thusthe key nodes to accidents related to excessive surface set-tlement Measures can be taken to particularly ensure safetyat these nodes e occurrence probability of excessivesurface settlement can be reduced by 66 when X6 X1 X2X5 and X7 are ensured safe (Figure 13)

Table 13 Expert opinion on environmental failure operational error and multiple failures

Event Fuzzy numbers proposed by each expert

X1

Expert 1 Expert 2 Expert 3(02 03 04 05) (01 02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 02 03 05)

X2

Expert 1 Expert 2 Expert 3(01 02 03 05) (02 03 04) (01 02 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (02 03 05) (01 02 03 05)

X3

Expert 1 Expert 2 Expert 3(01 02 04 05) (01 02 03 05) (01 03 04)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03) (01 02 03)

X4

Expert 1 Expert 2 Expert 3(02 03 04 05) (01 02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(02 03 04) (02 03 05) (01 02 03 05)

X5

Expert 1 Expert 2 Expert 3(01 03 04) (01 02 03 05) (02 03 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (02 03 05) (01 02 03)

X6

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 03 05) (02 03 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (02 03 05) (01 02 04 05)

X7

Expert 1 Expert 2 Expert 3(01 02 04 05) (01 02 03 05) (02 03 04)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 03 05)

X8

Expert 1 Expert 2 Expert 3(01 03 04 05) (01 02 03 04) (02 03 04)

Expert 4 Expert 5 Expert 6(02 03 04) (01 02 03 05) (01 02 03)

CE1

Expert 1 Expert 2 Expert 3(02 03 04 05) (02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 02 04 05)

CE2

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 05) (02 03 04 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (01 02 03 05) (01 03 05)

CE3

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 03 05) (03 04 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (01 02 04 05) (01 02 03 05)

16 Advances in Civil Engineering

In accordance with the predictive and diagnosticanalysis results using the established model some safetymeasures for key nodes are displayed in time to reduce theexcessive surface settlement risk during the tunnelexcavation

(1) e nodes X5 (abnormal TBM shutdown) and X7(excessive deviation from the axis) mostly involveoperational error Safety management and supervi-sion need to be strengthened at the construction siteto eliminate such errors and ensure that the TBM isoperated properly Besides an advanced real-time

laser locator may help to alarm in the case of largeaxial deviation

(2) e nodes X1 (confined water) and X2 (ground cavityor flow sand) belong to environmental failure Inorder to reduce the influence of environmental failurecareful geological exploration should be carried outbefore tunneling to identify the poor geological and

Table 14 Calculation of FPS FFR and the occurrence probability of environmental failure operational error and multiple failures

Event Aggregated fuzzy numbers FPS FFR (dminus1) Failure probability (in 1 year)X1 (01288 02288 03288 04838) 02951 83969eminus 04 26402eminus 1X2 (01325 02325 03163 04713) 02909 80032eminus 04 25336eminus 1X3 (01000 02163 02700 03825) 02420 42986eminus 04 14518eminus 1X4 (00450 00900 01125 01800) 01082 22492eminus 05 81803eminus 3X5 (01363 02488 02775 04263) 02747 66022eminus 04 214155eminus 1X6 (01488 02488 03225 04713) 03004 89125eminus 04 27770eminus 1X7 (01163 02388 03125 04675) 02855 75157eminus 04 24002eminus 1X8 (01450 02538 02950 03100) 02463 45643eminus 04 15338eminus 1CE1 (01413 02413 03513 04838) 03058 94598eminus 04 29202eminus 1CE2 (01288 02513 03038 04713) 02916 80679eminus 04 25496eminus 1CE3 (01450 02450 03363 04713) 03010 89722eminus 04 27937eminus 1

08299

03155

01223 010800419

01301

00504 00445 00173

Occ

urre

nce p

roba

bilit

y (in

1 y

ear)

00

01

02

03

04

05

06

07

08

09

OE1 OE2 OE3 OE4 OE5 OE6 OE7 OE8LE

Figure 12 Occurrence probability of surface settlement and otheroutcome events

Table 15 Calculation of importance measure of influential factors

SymbolImportance measure

BM RAW FVX1 2311eminus 1 7352eminus 02 7352eminus 02X2 2279eminus 1 6958eminus 02 6958eminus 02X3 1990eminus 1 3481eminus 02 3481eminus 02X4 1716eminus 1 1691eminus 03 1691eminus 03X5 2165eminus 1 5587eminus 02 5587eminus 02X6 2356eminus 1 7884eminus 02 7884eminus 02X7 2239eminus 1 6476eminus 02 6476eminus 02X8 2010eminus 1 3715eminus 02 3715eminus 02X9 1370eminus 6 6306eminus 08 6306eminus 08X10 8300eminus 7 6291eminus 08 6291eminus 08X11 2040eminus 6 6293eminus 08 6293eminus 08X12 1030eminus 6 6280eminus 08 6280eminus 08X13 5300eminus 7 6303eminus 08 6303eminus 08

Table 16 Ranking results of the key events

Rank SymbolNormalization weighting (Rlowast) Total

weighting(Rlowast)

RlowastBM RlowastRAW RlowastFV

1 X6 13805 18942 18942 516892 X1 13541 17664 17664 488693 X2 13354 16717 16717 467884 X7 13120 15559 15559 442385 X5 12686 13423 13423 395326 X8 11778 8926 89255 296297 X3 11661 8363 8363 283878 X4 10055 0406 0406 108689 X11 00002 1512eminus 05 1512eminus 05 1498eminus 0410 X9 8028eminus 05 1515eminus 05 1515eminus 05 1106eminus 0411 X12 6035eminus 05 1509eminus 05 1509eminus 05 9053eminus 0512 X10 4863eminus 05 1511eminus 05 1511eminus 05 7886eminus 0513 X13 3106eminus 05 1514eminus 05 1514eminus 05 6134eminus 05Total 100 100 100 100

02822

01073

00416 0036700142

0044200172 00151 00059

Occ

urre

nce p

roba

bilit

y (in

1 y

ear)

000

005

010

015

020

025

030

OE1 OE2 OE3 OE4 OE5 OE6 OE7 OE8LE

Figure 13 Occurrence probability when safety is ensured at keynodes

Advances in Civil Engineering 17

hydrological conditions that may be encounteredDuring excavation the advanced geological pre-diction technologymay be employed to detect adversegeological and hydrological conditions ahead of theTBM in real time including confined water groundcavity and flow sand

(3) Node X6 (seal failure at shield tail) belongs tomultiple failures e quality of the tail brush needsto be enhanced and tail brush should promptly bereplaced when it is worn

By adopting corresponding safety measures in shieldtunnel excavation the occurrence probability of variousdegrees of surface collapse (OE3 OE4 OE6 OE7 and OE8)was significantly decreased (Figure 13) Finally the TBMssuccessfully passed through the left track of DCS on March3 2017 and the right track on June 11 2017 without anysurface collapse accident demonstrating the effectiveness ofour proposed hybrid method

5 Conclusions and Future Works

In this work we first defined the ldquonormal excavation phaserdquoof shield tunneling based on the fuzzy statistical test theoryData were extracted from the construction log of the XWS inthe Wuhan metro line 7 to determine the occurrenceprobability of facility fault and expert opinions were soli-cited to determine the occurrence probability of environ-mental failure operational error and multiple failuresProbabilistic safety assessment (PSA) of the normal shieldtunnel excavation system was then performed accordingly

We employed the bow-tie analysis to evaluate the oc-currence of excessive surface settlement during normaltunnel excavation e presence of emergency measurescould reduce the occurrence probability of surface collapsecaused by excessive surface settlement (OE3 OE4 OE6 OE7and OE8) but have limited effect on the prevention of ac-cidents of OE1 OE2 and OE5 It is essential to decrease theprobability of excessive surface settlement in order to pre-vent the resulting outcome events (OEs)

By mapping the bow-tie analysis to Bayesian networks(ie BT-BN analysis) we determined the key nodes thatcould cause excessive surface settlement (LE) e key nodesincluded the following X6 (seal failure at shield tail) X1(confined water) X2 (ground cavity or flow sand) X5 (ab-normal TBM shutdown) and X7 (excessive deviation fromthe axis) Effective safety measures at these nodes couldreduce the occurrence probability of excessive surface set-tlement (LE) by 66

To ensure safety careful geological exploration shouldbe carried out before the tunneling project During thetunneling safety management and supervision should bestrengthened at the construction site Advanced geo-logical prediction technology should be used to detectpoor geological and hydrological conditions ahead of theTBM in real time Advanced laser locator should be usedto monitor and alarm excessive axial deviation equality of the tail brush should be improved and tailbrush should be replaced timely when it becomes worn

e occurrence probability of excessive surface settlementwas decreased by adopting these safety measures and theoccurrence of the resulting surface collapse was sub-sequently decreased

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

e authors thank the workers foremen and safety co-ordinators of the main contractors for their participatione authors also wish to thank the engineers Yun Zhang andPeilun Tu for assistance in gathering field data

References

[1] T Zhao W Liu and Z Ye ldquoEffects of water inrush fromtunnel excavation face on the deformation and mechanicalperformance of shield tunnel segment jointsrdquo Advances inCivil Engineering vol 2017 Article ID 5913640 9 pages 2017

[2] W Liu T Zhao W Zhou and J Tang ldquoSafety risk factors ofmetro tunnel construction in China an integrated study withEFA and SEMrdquo Safety Science vol 105 pp 98ndash113 2018

[3] K Li ldquoHangzhou metro site collapse accidentrdquo 2008 httpnewssohucom20081115n260653551shtml

[4] S Liu ldquoConstruction of Nanchang metro line 2 constructionsection pavement collapsesrdquo 2017 httpnewssohucom20160514n449414512shtml

[5] R B Peck ldquoDeep excavations and tunneling in soft groundrdquo7th International Conference on Soil Mechanics and Foun-dation Engineering vol 7 no 3 pp 225ndash290 1969

[6] P B Attewell I W Farmer and N H Glossop ldquoGrounddeformation caused by tunnelling in a silty alluvial clayrdquoGround Engineering vol 11 no 8 pp 32ndash41 1978

[7] W J Rankin ldquoGround movements resulting from urbantunnelling predictions and effectsrdquo Geological Society Lon-don Engineering Geology Special Publications vol 5 no 1pp 79ndash92 1988

[8] P B Attewell and J P Woodman ldquoPredicting the dynamicsof ground settlement and its derivatives caused by tunnelingin soilrdquo Ground Engineering vol 15 no 8 pp 13ndash20 1982

[9] M P OrsquoReilly and B M New ldquoSettlement above tunnels inthe United Kingdommdashtheir magnitude and prediction intunnelling 82 proceedings of the 3rd international sympo-sium brighton 7ndash11 June 1982 P173ndash181 Publ LondonIMM 1982rdquo International Journal of Rock Mechanics ampMining Sciences amp Geomechanics Abstracts vol 20 no 1pp 1ndash18 1983

[10] R J Mair R N Taylor and A Bracegirdle ldquoSubsurfacesettlement profiles above tunnels in claysrdquo Geotechniquevol 45 no 2 pp 361-362 1995

[11] X L Yang and J MWang ldquoGroundmovement prediction fortunnels using simplified procedurerdquo Tunnelling and Un-derground Space Technology vol 26 no 3 pp 462ndash471 2011

18 Advances in Civil Engineering

In this work the excavation speed of the TBM had adomain ofV [1 96] (mmmin)e fuzzy setA represents thefuzzy concept of ldquonormal excavation speedrdquo For the purpose ofillustration select an arbitrary excavation speed v0 23mmmin Fuzzy statistical tests were then applied to determine thedegree of membership that v0 belonged to A For the con-struction project at the XWS the appropriate project logs overn 179days (715 segment rings for left and right tunnels) wereselected e appropriate logs excluded abnormal engineeringsituations (restrictive condition S) such as TBM launchingTBM arrival and abnormal downtime during which theformation was reinforced and the excavation speed could notbe considered normal In this way the boundaries for the dailyldquonormal excavation speedrdquo could be determined for the left andright tunnels of the XWS (Table 3 Figure 3)

Table 4 shows the membership frequency that v0 23mmmin belonged to the normal excavation speed as was de-termined by the statistical tests Figure 4 shows that themembership frequency f that v0 23mmmin falls within theldquonormal excavation speedrdquo of the TBM stabilized around 066Hence A(v0) A(23) 066 e membership frequency f ofother excavation speeds could also be obtained similarlye data from the construction logs recorded a mini-mum and maximum excavation speed of 2mmmin and96mmmin respectively Hence we divided the domain V

into 96 intervals each spanning 1mmmin starting from15mmmin and ending at 965mmmin e mean of eachinterval was used to calculate the membership frequencyand the results are shown in Table 5 A program was de-veloped in MATLAB to reduce the computational com-plexity and save time

Figure 5 plots the histogram of membership frequencybased on the data in Table 5 e fitted curve of themembership function A(v) was then drawn accordinglyefitted curve conformed to the Cauchy distribution and couldbe expressed as follows

1113957A(v) v A(v) ∣ A(v) 1 +vminus 3212

1113874 11138752

1113888 1113889

minus1

v isin N⎧⎨

⎩

⎫⎬

⎭

(3)

(1) Determination of the Standard Excavation Speed In thefuzzy set theory [31] the element with the membershipfrequency A(v) 1 is designated as the kernel of the fuzzy setA and written as ldquokerArdquo Figure 5 shows that kerA 32 iev0 32mmmin was the kernel of the fuzzy set of ldquonormalexcavation speedrdquo erefore v0 32mmmin was consid-ered as the standard excavation speed in the ensuing PSAanalysis

ConvertingFTA to BN

Fuzzystatistical test

theory

ldquoNormalexcavation

phaserdquo

Preparingbow-tiediagram

ConvertingETA to BN

ConstructingBN-bow-tie

diagram

Confirmingoccurrenceprobability

TBMfacilitiesfailure

Operationalerror and

failure

TBMparameterdatabase

Triangularnumbers

Trapezoidalnumbers

Expertjudgment

Aggregation

Occurrenceprobability

Calculatingoccurrenceprobability

Calculatingimportancemeasures

BM

RAW

FV

Identifyingkey nodes

System ofTBM phases

Providingsafety

measures

Figure 2 Flowchart of the proposed methodology

Advances in Civil Engineering 5

(2) Determination of the Range of Excavation Speed In thefuzzy set theory all elements whose membership frequencyA(v)gt 0 constitute a support of the fuzzy setA and is writtenas ldquosupp Ardquo and all elements whose membership frequencyA(v)gt α is designated as the α cut set of the fuzzy set A andwritten as Aα Figure 5 shows that the excavation speed

fluctuated around the kernel (32mmmin) during shieldtunnel excavation In order to express the range of normalexcavation speed the confidence level α 05 was selectedand the excavation speed whose membership frequencysatisfied A(v)gt 05 was considered to constitute the in-terval of normal excavation speed (ie the 05 cut set of A)

Table 3 Partial construction log of the ldquonormal excavation speedrdquo in the XWS

n 1ndash10 n 11ndash20 n 21ndash30 n 31ndash40 n 41ndash50 n 51ndash60 n 61ndash70 n 71ndash80 n 81ndash90 n 91ndash100303ndash506 25ndash32 276ndash424 78ndash425 25ndash35 18ndash39 27ndash43 20ndash41 30ndash47 20ndash54324ndash388 26ndash34 232ndash476 83ndash417 28ndash46 20ndash35 24ndash40 10ndash40 30ndash61 32ndash63284ndash396 27ndash42 233ndash445 202ndash476 17ndash35 15ndash42 27ndash47 20ndash35 20ndash61 32ndash58303ndash388 23ndash36 205ndash427 242ndash425 28ndash37 27ndash41 20ndash33 17ndash32 30ndash60 20ndash37303ndash363 123ndash348 282ndash456 287ndash526 17ndash36 21ndash37 22ndash34 8ndash40 14ndash58 24ndash4032ndash44 178ndash325 182ndash426 19ndash32 20ndash37 31ndash41 27ndash48 8ndash40 27ndash74 25ndash4831ndash42 198ndash374 137ndash375 22ndash45 20ndash35 30ndash40 30ndash42 20ndash50 15ndash55 24ndash5131ndash39 135ndash326 156ndash326 21ndash44 21ndash37 30ndash35 25ndash43 20ndash50 25ndash45 32ndash4630ndash42 134ndash326 20ndash37 19ndash42 20ndash35 20ndash40 28ndash36 20ndash46 28ndash52 25ndash4031ndash38 156ndash364 15ndash40 20ndash41 20ndash37 25ndash40 225ndash37 31ndash42 31ndash47 20ndash35

Rang

e of a

dvan

ce sp

eed

(mm

min

)

v-lower limitv-upper limit

0102030405060708090

100

100 200 300 400 500 600 700 8000Segment number

Figure 3 Distribution of the ldquonormal excavation speedrdquo

Table 4 Membership frequency of 23mmmin belonging to the ldquonormal excavation speedrdquo

Description Number and membershipNumber of rings 50 100 150 200 250 300 350Membership counts 28 51 60 97 128 153 178Membership frequency 056 051 04 049 051 051 051Number of rings 400 450 500 550 600 650 715Membership count 202 252 302 342 382 427 470Membership frequency 051 056 061 062 064 066 066

066

v = 23mmmin

001020304050607

Cov

erag

e fre

quen

cy f

100 600300 700500200 8000 400Segment number

Figure 4 Membership frequency of 23mmmin belonging to the ldquonormal excavation speedrdquo

6 Advances in Civil Engineering

e set of normal excavation speed in Zadehrsquos form wasordered as shown in equations (4) and (5) usv0 20ndash44mmmin was considered as the range of normalexcavation speed in the ensuing PSA analysis

1113957A(v) 05020

+05421

+05922

+06423

+06924

+07525

+08026

+08527

+09028

+09429

+09730

+09931

+132

+09933

+09734

+09435

+09036

+08537

+08038

+07539

+06940

+06441

+05942

+05443

+05044

(4)

supp 1113957A(v) 111386420 21 22 23 24 25 26 27 28 29 30 31 32

33 34 35 36 37 38 39 40 41 42 43 441113865

(5)

Table 5 Membership frequency of the ldquonormal excavation speedrdquo

No Group Count Frequency1 15ndash25 1 00012 25ndash35 2 00033 35ndash45 2 00034 45ndash55 2 00035 55ndash65 5 00076 65ndash75 6 00087 75ndash85 17 00248 85ndash95 21 00299 95ndash105 31 004310 105ndash115 34 004811 115ndash125 46 006412 125ndash135 60 008413 135ndash145 66 009214 145ndash155 100 01415 155ndash165 132 018516 165ndash175 168 023517 175ndash185 217 030318 185ndash195 240 033619 195ndash205 366 051220 205ndash215 396 055421 215ndash225 425 059422 225ndash235 470 065723 235ndash245 500 069924 245ndash255 535 074825 255ndash265 563 078726 265ndash275 588 082227 275ndash285 609 085228 285ndash295 619 086629 295ndash305 668 093430 305ndash315 686 095931 315ndash325 715 132 325ndash335 698 097633 335ndash345 685 095834 345ndash355 670 093735 355ndash365 643 089936 365ndash375 623 087137 375ndash385 586 08238 385ndash395 562 078639 395ndash405 536 07540 405ndash415 495 069241 415ndash425 456 063842 425ndash435 406 056843 435ndash445 358 050144 445ndash455 332 046445 455ndash465 290 040646 465ndash475 246 034447 475ndash485 201 028148 485ndash495 157 02249 495ndash505 136 01950 505ndash515 116 016251 515ndash525 101 014152 525ndash535 91 012753 535ndash545 88 012354 545ndash555 77 010855 555ndash565 69 009756 565ndash575 62 008757 575ndash585 56 007858 585ndash595 51 007159 595ndash605 45 006360 605ndash615 41 0057

Table 5 Continued

No Group Count Frequency61 615ndash625 38 005362 625ndash635 35 004963 635ndash645 32 004564 645ndash655 30 004265 665ndash675 28 003966 675ndash685 28 003967 685ndash695 25 003568 695ndash705 23 003269 705ndash715 23 003270 715ndash725 21 002971 725ndash735 20 002872 735ndash745 19 002773 745ndash755 19 002774 755ndash765 18 002575 765ndash775 18 002576 775ndash785 18 002577 785ndash795 18 002578 795ndash805 16 002279 805ndash815 16 002280 815ndash825 15 002181 825ndash835 15 002182 835ndash845 12 001783 845ndash855 11 001584 855ndash865 8 001185 865ndash875 7 00186 875ndash885 6 000887 885ndash895 5 000788 895ndash905 4 000689 905ndash915 4 000690 915ndash925 4 000691 925ndash935 4 000692 935ndash945 4 000693 945ndash955 3 000494 955ndash965 2 000395 965ndash975 2 0003

Advances in Civil Engineering 7

313 Fuzzy Statistical Tests of Excavation Parameterse excavation speed of the TBM reflects the influenceexerted by the excavation parameters (eg total thrust facepressure and cutter head torque) on the force and dis-placement of the surrounding soil erefore it is necessaryto determine the realistic and practical excavation param-eters based on the excavation speed

Formation reinforcement during TBM launching and TBMarrival can exert a strong influence on the shield tunnel ex-cavation and lead to highly discrete parameters erefore thedata from the TBM launching and TBM arrival stages werediscarded in studying the relationship between excavation speedand TBMparameters Figure 6 shows how the TBMparametersvaried with the excavation speed during the construction of the715 segments in the XWSe curves were fitted viaMATLABand the slope of the curves was highly indicative of the cor-relation between the TBMparameters and the excavation speed

In Figure 6(a) the total thrust (F) increased with risingexcavation speed is was because bentonite was used as alubricant and injected around the shield of the TBM duringexcavation to reduce friction When the amount of injectedbentonite was appropriate the friction coefficient betweenthe shield and the surrounding soil would decrease and theexcavation speed would then increase when the thrust (F)was higher In Figure 6(b) the excavation speed decreasedwhen the cutter head torque (MT) increased is wasbecause when the soil body of the tunneling face wasrelatively difficult to cut a larger torque of the cutter headwould be needed and the excavation speed would decreaseFigure 6(c) shows that during normal excavation thepressure of the tunneling face increased slightly with risingexcavation speed Besides Mair pointed out that duringsegment assembly the downtime of TBM would decreasethe soil and water pressure on the tunneling face whichcould reduce the control pressure of the tunneling face [33]e same pattern was observed in the current constructionlogs and the R2 value of the curve in Figure 6(c) was hencerelatively low Figure 6(d) shows that the grouting pressuredecreased slightly with rising excavation speed However

since the pressure of primary grouting was read off from thegrouting pressure pump the actual grouting pressureexerted on the surrounding soil was smaller and theprimary grouting pressure hence had limited impact onexcavation speed

(1) Determination of Standard TBM Parameters It wasdetermined from the fuzzy statistical tests above that thestandard excavation speed was 32mmmin e corre-sponding standard TBM parameters could be determinedaccordingly from the following equation

TBMPstandard value 1113936

Nn1TBMPnv

N v321113868111386811138681113868 (6)

where TBMP is the TBM parameter and v is the excavationspeed (mmmin)

(2) Determination of the Range of TBM Parameters It wasdetermined from the fuzzy statistical tests above that therange of excavation speed was 20ndash44mmmin e corre-sponding boundaries of TBM parameters could be de-termined from the extreme values in the monitoring records(Figure 6) via the following equation

TBMPupper limit max TBMPv 20levle4411138681113868111386811138681113966 1113967

TBMPlower limit min TBMPv 20levle4411138681113868111386811138681113966 1113967

(7)

(3) ldquoNormal Excavation Phaserdquo of TBM According to thefuzzy set theory the excavation speed in the ldquonormal ex-cavation phaserdquo fell within 20ndash44mmmin e TBM wasconsidered to be in the ldquonormal excavation phaserdquo whenthe excavation speed and the TBM parameters all fellwithin the prescribed ranges specified above and listedagain in Table 6 e standard values and ranges were usedfurther in the subsequent PSA analysis Table 6 shows thatamong the examined parameters the face pressure had adeviation interval of merely 196 and was controlled the

Advance speed v (mmmin)

Mem

bers

hip

Atilde (v

)

Cov

erag

e fre

quen

cy A

(v)

04

02

06

08

1

10090807060504030201000

04

02

06

08

1

0

Fuzzy statistical experiment methodCauchy distribution curve

Figure 5 e histogram of membership frequency and the membership function of TBM excavation speed

8 Advances in Civil Engineering

best whereas the cutter head torque had a deviation in-terval of 7401 and was controlled the worst

(4) Statistical Relationship between TBM Parameters andExcavation Speed e monitoring results in Figure 6

demonstrated that in the ldquonormal excavation phaserdquo ofthe XWS the total thrust and the face pressure were posi-tively correlated with the excavation speed In particular thetotal thrust had a stronger correlation to the excavationspeed than the face pressure In contrast the cutter head

2000400060008000

1000012000140001600018000

Tota

l thr

ust

F (k

N)

20 25 30 35 40 45 50 55 60 6515Advance speed v (mmmin)

(a)

0500

10001500200025003000350040004500

Cutte

r hea

d to

rque

MT

(kNlowast

m)

20 25 30 35 40 45 50 55 60 6515Advance speed v (mmmin)

(b)

0

50

100

150

200

250

Face

pre

ssur

eP N

(kPa

)

20 25 30 35 40 45 50 55 60 6515Advance speed v (mmmin)

(c)

Gro

utin

g pr

essu

reP G

(kPa

)

100150200250300350400450500550

20 25 30 35 40 45 50 55 60 6515Advance speed v (mmmin)

(d)

Figure 6 Variations in the TBM parameters at different excavation speeds (data from XW section) (a) total thrust versus excavationspeed (b) cutter head torque versus excavation speed (c) face pressure versus excavation speed (d) grouting pressure versus excavationspeed

Table 6 Standard values and ranges of excavation speed and TBMPs

Factors v (mmmin) F (kN) P N (kPa) M T (kNmiddotm) P G (kPa)Parameter range [20 44] [8300 13100] [117 143] [1294 2974] [197 302]Standard value 32 9700 1326 2270 302Deviation range () [minus375 375] [minus1443 3505] [minus1176 784] [minus430 3101] [minus3477 0]

Advances in Civil Engineering 9

torque and the primary grouting pressure were negativelycorrelated with the excavation speed

32 Bow-Tie-Bayesian Network Analysis e bow-tie anal-ysis combines FTand ETanalysese FTanalysis in bow-tiecalculates the occurrence probability of the loss event (LE) aswell as the top event (TE) e occurrence probability of theTE can also be obtained from the occurrence probability ofthe basic event (BE) e events could be evaluated by theirlogical relationship and their occurrence probability in theBN Mapping the bow-tie analysis to BN involves convertingboth FT and ET analyses Figure 7(a) provides a brief de-scription of calculation steps

ree importance measures described in the followingBorst and Schoonakker [30] were introduced in the newmethodology according to the Bayes theorem Figure 7(b)gives a brief description of their calculation In the proposedmethodology the critical nodes that could more easilytrigger accidents were obtained by calculating these im-portance measures

33 Confirming Failure Occurrence Probability e BT-BNanalysis requires knowing the occurrence probability of eachbasic event (BE) e basic events fall into four categoriesenvironmental failure operational error multiple failuresand facility failures e occurrence rate of facility failureswas obtained from the construction log of the XWS for thetunneling project that spanned 179 days (715 segments intotal) and was converted into occurrence probability via thefollowing equation

F 1minus eminusλt

(8)

where F denotes the occurrence probability of the failure andλ denotes the occurrence rate of the failure

e occurrence probability of environmental failureoperational error and multiple failures cannot be readilyderived from existing data and was thus estimated via expertopinione fuzzymethod combines the opinions of differentexperts in a weighted manner to calculate the fuzzy fault rate(FFR) from the triangular fuzzy numbers or trapezoidal fuzzynumbers proposed by the experts e occurrence probabilityof environmental failure operational error and multiplefailures was then determined from the FFR [34] e generalprocedure of the fuzzy method is as follows

(1) Determine the weight of the opinion of each expertbased on the age education background work ex-perience and position of the consulted expert (Ta-ble 7) e crude weight score of each expert iscalculated via the following equation

Sn Sna+ Snb

+ Snc+ Snd

(9)

where Sn represents the total weight score of theexpert e relative weight score of each expert iscalculated via the following equation

Wn Sn

1113936mn1Sn

(10)

where m represents the number of experts(2) e occurrence probability is divided into the

following categories nonoccurrence absolute lowvery low low fairly low medium fairly high highvery high absolute high or occurrence e rankvalue of the categories escalates from 0 for non-occurrence to 1 for the occurrence (Table 8) eoccurrence probability of the event is then evalu-ated based on the corresponding triangular numberor trapezoidal number given by the experts

(3) Aggregation of the fuzzy numbers When the fuzzynumbers are all triangular number or trapezoidalnumber the aggregated fuzzy numbers of an event iscalculated via equation (11) [35] e aggregatedfuzzy number considering the expert weight isshown in equation (12)

1113957Aaggregated 1113944m

n1Wn otimes 1113957An (11)

where 1113957Aaggregated represents the aggregated fuzzifiednumber given by expert m and Wn represents theweight of the expertrsquos opinion

1113957AW 1113874W1a11 + W2a21 W1a12 + W2a22 W1a12

+W2a23 W1a13 + W2a241113875

(12)

(4) After the aggregated fuzzy numbers are determinedthe centroid index method (equation (13)) is used tohandle the fuzzy numbers and obtain the fuzzyprobability score (FPS) [36]

X 1113938g(x)x dx

1113938g(x)dx (13)

where X is the defuzzified output g(x) is themembership function and x is the output variableAssume 1113957An (an1 an2 an3) a triangular number and1113957An (an1 an2 an3) a trapezoidal number e FPS iscalculated via equation (14) when a fuzzy number is atriangular number and via equation (15) when thefuzzy number is a trapezoidal number

FPS 13

an1 + an2 + an3( 1113857 (14)

FPS 13

an3 + an4( 11138572 minus an3an4 minus an1 + an2( 1113857

2+ an1an2

an3 + an4 minus an1 minus an2( 1113857

(15)

10 Advances in Civil Engineering

(5) Finally the FPS is converted to FFR via equation(16) [37] and the FFR is further converted tothe occurrence probability of environmentalfailure operational error and multiple failures(equation (8))

FFR

110k

FPSne 0

0 FPS 0

k 2301 times(1minus FPS)

FPS1113890 1113891

13

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(16)

4 Results

41 Analysis of Excessive Surface Settlement inNormal TunnelExcavation Figure 8 shows that the normal excavation

(1) If the logical relationship is AND between events the TE occurs when all events occur The probability of TE can be calculated from the following equation

(A)

(2) If the logical relationship is OR between events the TE occurs when any of the event occurs The probability of TE can be calculated from the following equation

(B)

(3) By definition in the FT analysis the probability of TE is the same as that of LE Similarly the probability of the initial event (IE) in the ET analysis is the same as that of LE The probability of OE in ET analysis can be calculated from the following equation

(C)

(4) The BN an inference method based on the Bayes theorem combines both graph theory and probability theory

(D)

FTE = i=1

nFBEi

FTE = 1 ndashi=1

n(1 ndash FBEi)

FOEn = FIE middot i=1

nP (Ei = 0) middot

j=1

nP (Ej = 1)

P(B | A) = P(A | B) middot P(B)

P(A)

(a)

(1) The Birnbaum measure (BM) whichdetermines the increment of the occurrenceprobability of TE when BE occurs is shownin the following equation

(E)

where P(TE | BE = 1) denotes the occurrence probability of TE when BE occurs and P(TE | BE = 0) denotes the occurrence probability of TE when BE does not occur

(2) Risk achievement worth (RAW) evaluatesthe impact of BE on TE when the probabilityof BE is considered The RAW is adjustedby the probability of TE and BE as shown inthe following equation

(F)

where P(BE) denotes the occurrence probability of BE and P(TE) denotes the occurrence probability of TE under all circumstances

(3) The FussellndashVesely (FV) importance which describes the contribution of BE to system fault is shown in the following equation

IBBE

M = P(TE | BE = 1) ndash P(TE | BE = 0)

IRB

AE

W = IBBE

M middot P(BE)P(TE)

(G)

P(TE) ndash P(TE | BE = 0)P(TE)

IFB

VE =

(b)

Figure 7 Bow-tie-Bayesian network analysis Calculation of (a) event probability and (b) importance measures

Table 7 Weight scores for experts

Factor Category Score

Age (a)

lt30 130ndash39 240ndash49 3ge50 4

Education (b)

High school 1College 2Bachelor 3Master 4PhD 5

Work experience (c)

lt5 years 15ndash10 years 211ndash20 years 321ndash30 years 4ge30 years 5

Position (d)

Worker 1Technician 2

Junior scholarengineer 3Senior scholarengineer 4

Table 8 Rank value of each category

Classified occurrence probability Rank valueNonoccurrence 0Absolute low 01Very low 02Low 03Fairly low 04Medium 05Fairly high 06High 07Very high 08Absolute high 09Occurrence 10

Advances in Civil Engineering 11

phase involves the environment TBM operation supervi-sion management and emergency handling Risk analysis ofthe ldquonormal excavation phaserdquo in soft soil engineering basedon the XWS allows the identification of potential risk factorsthat may trigger surface settlement and consequently lead toaccidents Eskesen et al have described three principles forrisk analysis as follows (1) eliminate risk factors that are easyto detect and can be controlled timely and effectively (2)eliminate risk factors with low occurrence probability andno catastrophic consequences and (3) combine risk factorswith similar loss consequences [38] Accordingly the riskfactors during shield tunneling were organized into three

basic categories improper control of excavation parameters(eg poor control of face pressure) catastrophic geology (egground cavity or flow sand) and unforeseeable factors (egsegment damage) Figure 9 shows the bow-tie model builtfrom the categorized factors for the risk of surface collapsecaused by excessive surface settlement during shield tun-neling OEs of various degrees were successfully predictedbased on the CEs (Figure 9) Many risk factors exist in anygiven surface collapse In this section based on the previouscalculation results in Section 31 we selected the manageableshield excavation parameters (shield total thrust groutingpressure cutter head torque soil pressure etc) in the ldquonormal

Synchronousgrouting

ExcavationSegment

installationAttitudecontrol Tail sealing

Excavationcycle

Quality controlacceptance

Dangeroussituation exists Yes

Prepareemergencymeasures

Emergencymeasures

Execution of emergencymeasures

Acceptance ofexcavationprocedures

Excavationacceptance

report

Monitoring measurements

Monitored dataof excavationenvironment

Formation geologyTBM parametersExcavation axis

Segment installationSynchronous grouting

TBM construction parameter

No

TBM parametersv (mmmm) F (kN) PN (kPa)

MT (kNmiddotm) PG (kNmiddotm)TBM attitude TBM position TBM fault information

Soil bodyparameters

Soil evolutionmodel

Confined waterObstacles

Ground cavity orquicksand

Metro tunnel excavation

Emergencyhandling

Supervision

TBMoperation

TBM

Environment

Management

Figure 8 System diagram of the ldquonormal excavation phaserdquo

12 Advances in Civil Engineering

excavation phaserdquo as the base events assigning their weightsaccording to Section 33 and then performed PSA analysis

As mentioned earlier the ldquonormal excavation phaserdquo isunder the influence of excavation parameters catastrophicgeology and unforeseeable factors Surface settlement canoccur once the condition deteriorates Here we set excessivesurface settlement as the TE in the FT analysis Meanwhilethe tunneling system has a built-in emergency managementsystem Upon excessive surface settlement the emergencymanagement system will start to shut down the TBM timelyHence in the ETanalysis the excessive surface settlement isset as the IE and TBM shutdown is set as the CE OEs ofvarious degrees are obtained based on the considered CEFinally the surface settlement is set as the LE to connect theFT and the ET and furnish the BTmodel (Figure 9 Table 9)Eight OEs of various degrees were predicted based on theCEs including surface collapse events OE3 OE4 OE6 OE7and OE8 (Figure 9 Table 10) e TBM shuts down if CE1occurs and continues to operate if otherwise

e BN-BT model for excessive surface settlement isconstructed by mapping the FT and ET analyses in the BT(Figure 9) model to BN (Figure 10) All the nodes of BN havepreviously been described in the BT except the node OEwhich is the consequence node OE is added to accommodatethe outcomes of BT By connecting the node of excessivesurface settlement to OE another state also called the safe

state is added to the state set It includes consequences OE1 toOE8 to account for the nonoccurrence of the top event iewhen excessive surface settlement controlled To show thedependence among the safety barriers and the top eventcausal arcs are also drawn between TBM shutdown andgrouting in the settlement area and bentonite injection to soilchamber and TBM shield It is worth noting that since variouscombinations of the failure and success of the sequentialsafety barriers result in different consequences in the BT allthe safety nodes of BN are connected to node OE

42 Determination of Event Occurrence Probability emaximum surface settlement that resulted from the aber-ration of the ith TBM parameter is denoted as δmaxi eprobability of safety accident becomes higher when δmaxiapproaches the permitted surface settlement δi Whenδmaxi δi the accident will occur as soon as the TBM pa-rameter gives rise to a surface settlement of δmaxi eprobability of equipment fault for the normal excavationsystem was calculated via equation (8) from the engineeringlog data of the XWS over 179 days of construction (715segments rings in total) e construction of all 715 rings fellwithin the ldquonormal excavation phaserdquo as was defined by thefuzzy statistical test (v 20ndash44mmmin) Table 11 lists thecalculation results

X3X2X1

OR

M1

X7X6X5X4

OR

M2

X10X9 X11 X13X12

M3

OR

Excessive surface

settlement

X8

Caus

esLE

CE1

CE2

CE3

Con

sequ

ence

sSt

op

TBM

Gro

utin

g in

settl

emen

tar

ea

Bent

onite

inje

ctio

n

OE 1

OE 2

OE 3

OE 4

OE 5

OE 6

OE 7

OE 8

Success Failure

AND

Figure 9 Diagram of bow-tie analysis for excessive surface settlement

Advances in Civil Engineering 13

To address the uncertainty regarding the events ofenvironmental failure operational error and multiplefailure six domain experts who participated in the con-struction of the Wuhan metro system including two seniorengineers one senior academic professor one technicalconsultant one junior engineer and one worker wereinvited to evaluate the occurrence probability of events thatcannot be readily derived from existing data (Table 12)eweights of their opinion were then calculated by usingequations (9) and (10) and the distribution of each opinionweight is shown in Figure 11

In addition Table 13 lists the expert opinions regardingthe events of environmental failure operational error andmultiple failures in the form of fuzzy numbers based onTable 8 e fuzzy numbers were aggregated via equations(12) and converted to FPS and FFR via equations (13)ndash(16)(Table 14) e occurrence probabilities were finally derivedfrom FFR (Table 14) Generally the expert knowledge isconsidered as a scarce resource which cannot provide

universal consultation or real-time guidance us there ismuch room to improve the data use efficiency

43 Update in Occurrence Probability of LE and OE eoccurrence probability of basic events is calculated as de-scribed in Section 42 including the occurrence probabilityof facility failure from the engineering log data of the XWS aswell as that of environmental failure operational error andmultiple failures derived from expert opinion e occur-rence probability of excessive surface settlement (LE) isdetermined via equations (A) and (B) by considering thelogical relationship between events in Figure 7 Finally theoccurrence probability of OEs including surface collapse canbe calculated via equation (C) in the figure by mapping theFT and ET analyses in the BTmodel to BN Figure 12 showsthe occurrence probabilities of the LE (ie excessive surfacesettlement) and that of the OEs

e above analysis shows that the occurrence probabilityof excessive surface settlement within one year is 08299(Figure 12) is occurrence probability of surface collapse(OE3 OE4 OE6 OE7 and OE8) may be decreased whenemergency measures are put in place including grouting insettlement area and bentonite injection to soil chamber andTBM shield However these measures cannot help to reduceminor accidents since the occurrence probability remains athigh levels for OE1 OE2 and OE5 Admittedly grouting andbentonite injection are necessary measures and they candecrease the effects of excessive surface settlement duringshield tunneling However the key point of avoiding outcomeevents including surface collapse to ensure project safety is toprevent the excessive surface settlement from occurring in thefirst place Hence we sought to determine the key nodesleading to excessive surface settlement via BT-BN analysis andpropose the corresponding preventive measures

Table 10 Analysis of event occurrence

Symbol EventOE1 Excessive surface settlement

OE2Grouted cutter head and shield excessive surface

settlement and minor property damageOE3 Minor surface collapse and property damage

OE4Moderate surface collapse major property damage

and minor casualtiesOE5 Excessive surface settlement

OE6Grouted cutter head and shield moderate surface

collapse and minor property damage

OE7Moderate surface collapse and major property

damage

OE8Severe surface collapse major property damage and

major casualties

Table 9 Details of bow-tie components in Figure 9

Event Symbol Logic link type Failure modelGround settlement Excessive surface settlement OR gate mdashCatastrophic geology M1 OR gate mdashUnforeseeable factors M2 OR gate mdashExcavation parameters M3 AND gate mdashConfined water X1 mdash Environmental failureGround cavity or flow sand X2 mdash Environmental failureObstacles X3 mdash Environmental failureSegment damage X4 mdash Operational errorAbnormal TBM shutdown X5 mdash Multiple failureSeal failure at shield tail X6 mdash Multiple failureExcessive deviation from axis X7 mdash Operational errorEquipment failure X8 mdash Multiple failureUntimely grouting X9 mdash Facility failureExcessive cutter head torque X10 mdash Facility failureImproper control of face pressure X11 mdash Facility failureExcessive thrust X12 mdash Facility failureImproper control of excavation speed X13 mdash Facility failureTBM shutdown CE1 mdash Multiple failureGrouting in settlement area CE2 mdash Multiple failureBentonite injection to soil chamber and TBM shield CE3 mdash Multiple failure

14 Advances in Civil Engineering

Table 11 Probability of equipment fault

Event Surface settlementδmaxi (mm)

Permitted surfacesettlement δi (mm)

Value of TBMparameter

Occurrence rate(dminus1)

Occurrence probability(in 1 year)

X9 89 15 302 kPa 10675eminus 04 382eminus 02X10 84 10 2974 kNmiddotM 17792eminus 04 629eminus 02X11 86 15 143 kPa 71167eminus 05 256eminus 02X12 98 15 13100 kN 14233eminus 04 506eminus 02X13 120 15 41mmmin 28467eminus 04 987eminus 02All data were obtained from the operation log of the XWS

Table 12 Characteristics of experts participated in the occurrence probability evaluation

Expert Age Education Service (years) Professional position1 56 High school 25 Worker2 35 Master 10 Technician3 41 Master 15 Junior engineer4 47 Bachelor 20 Senior engineer5 50 PhD 18 Senior academic6 59 PhD 30 Senior engineer

0125 0125

01625 01625

020225

AgeEducationService

Professional positionWeighting

2 3 4 5 61Expert

0

005

01

015

02

025

Wei

ghtin

g

0

1

2

3

4

5

6

Wei

ghtin

g sc

ore

Figure 11 Distribution of each expert opinion weight

X1 X2 X3

M1

X5 X6 X7 X8

M2

X9 X11

M3

Excessive surface

settlement

X10 X12 X13X4

CE1 CE2 CE3

OE

Caus

esLE

CEC

onse

quen

ces

Figure 10 Bow-tie chart of excessive surface settlement

Advances in Civil Engineering 15

44 Identify Key Nodes and Provide Safety Measures Inorder to find the key nodes leading to excessive surfacesettlement the importance measure of each event was cal-culated via equations (E)ndash(G) in Figure 7 as shown inTable 15 Assume the number of events as ldquonrdquo e nor-malized weight Rlowast could be calculated from the importancemeasure Ii via the following equation

Rlowast

Ii

1113936ni1Ii

times 100 (17)

After the normalized weight Rlowast is calculated for eachimportance measure the total weight Rlowast could be calculatedvia equation (18) e total weight Rlowast of events was finally

ranked in descending order to find the key nodes as shownin Table 16

Rlowast R

lowastBM + R

lowastRAW + R

lowastFV (18)

It can be seen that X6 (seal failure at shield tail) X1(confined water) X2 (ground cavity or flow sand) X5 (ab-normal TBM shutdown) and X7 (excessive deviation fromaxis) have far higher weight than other events and are thusthe key nodes to accidents related to excessive surface set-tlement Measures can be taken to particularly ensure safetyat these nodes e occurrence probability of excessivesurface settlement can be reduced by 66 when X6 X1 X2X5 and X7 are ensured safe (Figure 13)

Table 13 Expert opinion on environmental failure operational error and multiple failures

Event Fuzzy numbers proposed by each expert

X1

Expert 1 Expert 2 Expert 3(02 03 04 05) (01 02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 02 03 05)

X2

Expert 1 Expert 2 Expert 3(01 02 03 05) (02 03 04) (01 02 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (02 03 05) (01 02 03 05)

X3

Expert 1 Expert 2 Expert 3(01 02 04 05) (01 02 03 05) (01 03 04)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03) (01 02 03)

X4

Expert 1 Expert 2 Expert 3(02 03 04 05) (01 02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(02 03 04) (02 03 05) (01 02 03 05)

X5

Expert 1 Expert 2 Expert 3(01 03 04) (01 02 03 05) (02 03 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (02 03 05) (01 02 03)

X6

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 03 05) (02 03 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (02 03 05) (01 02 04 05)

X7

Expert 1 Expert 2 Expert 3(01 02 04 05) (01 02 03 05) (02 03 04)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 03 05)

X8

Expert 1 Expert 2 Expert 3(01 03 04 05) (01 02 03 04) (02 03 04)

Expert 4 Expert 5 Expert 6(02 03 04) (01 02 03 05) (01 02 03)

CE1

Expert 1 Expert 2 Expert 3(02 03 04 05) (02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 02 04 05)

CE2

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 05) (02 03 04 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (01 02 03 05) (01 03 05)

CE3

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 03 05) (03 04 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (01 02 04 05) (01 02 03 05)

16 Advances in Civil Engineering

In accordance with the predictive and diagnosticanalysis results using the established model some safetymeasures for key nodes are displayed in time to reduce theexcessive surface settlement risk during the tunnelexcavation

(1) e nodes X5 (abnormal TBM shutdown) and X7(excessive deviation from the axis) mostly involveoperational error Safety management and supervi-sion need to be strengthened at the construction siteto eliminate such errors and ensure that the TBM isoperated properly Besides an advanced real-time

laser locator may help to alarm in the case of largeaxial deviation

(2) e nodes X1 (confined water) and X2 (ground cavityor flow sand) belong to environmental failure Inorder to reduce the influence of environmental failurecareful geological exploration should be carried outbefore tunneling to identify the poor geological and

Table 14 Calculation of FPS FFR and the occurrence probability of environmental failure operational error and multiple failures

Event Aggregated fuzzy numbers FPS FFR (dminus1) Failure probability (in 1 year)X1 (01288 02288 03288 04838) 02951 83969eminus 04 26402eminus 1X2 (01325 02325 03163 04713) 02909 80032eminus 04 25336eminus 1X3 (01000 02163 02700 03825) 02420 42986eminus 04 14518eminus 1X4 (00450 00900 01125 01800) 01082 22492eminus 05 81803eminus 3X5 (01363 02488 02775 04263) 02747 66022eminus 04 214155eminus 1X6 (01488 02488 03225 04713) 03004 89125eminus 04 27770eminus 1X7 (01163 02388 03125 04675) 02855 75157eminus 04 24002eminus 1X8 (01450 02538 02950 03100) 02463 45643eminus 04 15338eminus 1CE1 (01413 02413 03513 04838) 03058 94598eminus 04 29202eminus 1CE2 (01288 02513 03038 04713) 02916 80679eminus 04 25496eminus 1CE3 (01450 02450 03363 04713) 03010 89722eminus 04 27937eminus 1

08299

03155

01223 010800419

01301

00504 00445 00173

Occ

urre

nce p

roba

bilit

y (in

1 y

ear)

00

01

02

03

04

05

06

07

08

09

OE1 OE2 OE3 OE4 OE5 OE6 OE7 OE8LE

Figure 12 Occurrence probability of surface settlement and otheroutcome events

Table 15 Calculation of importance measure of influential factors

SymbolImportance measure

BM RAW FVX1 2311eminus 1 7352eminus 02 7352eminus 02X2 2279eminus 1 6958eminus 02 6958eminus 02X3 1990eminus 1 3481eminus 02 3481eminus 02X4 1716eminus 1 1691eminus 03 1691eminus 03X5 2165eminus 1 5587eminus 02 5587eminus 02X6 2356eminus 1 7884eminus 02 7884eminus 02X7 2239eminus 1 6476eminus 02 6476eminus 02X8 2010eminus 1 3715eminus 02 3715eminus 02X9 1370eminus 6 6306eminus 08 6306eminus 08X10 8300eminus 7 6291eminus 08 6291eminus 08X11 2040eminus 6 6293eminus 08 6293eminus 08X12 1030eminus 6 6280eminus 08 6280eminus 08X13 5300eminus 7 6303eminus 08 6303eminus 08

Table 16 Ranking results of the key events

Rank SymbolNormalization weighting (Rlowast) Total

weighting(Rlowast)

RlowastBM RlowastRAW RlowastFV

1 X6 13805 18942 18942 516892 X1 13541 17664 17664 488693 X2 13354 16717 16717 467884 X7 13120 15559 15559 442385 X5 12686 13423 13423 395326 X8 11778 8926 89255 296297 X3 11661 8363 8363 283878 X4 10055 0406 0406 108689 X11 00002 1512eminus 05 1512eminus 05 1498eminus 0410 X9 8028eminus 05 1515eminus 05 1515eminus 05 1106eminus 0411 X12 6035eminus 05 1509eminus 05 1509eminus 05 9053eminus 0512 X10 4863eminus 05 1511eminus 05 1511eminus 05 7886eminus 0513 X13 3106eminus 05 1514eminus 05 1514eminus 05 6134eminus 05Total 100 100 100 100

02822

01073

00416 0036700142

0044200172 00151 00059

Occ

urre

nce p

roba

bilit

y (in

1 y

ear)

000

005

010

015

020

025

030

OE1 OE2 OE3 OE4 OE5 OE6 OE7 OE8LE

Figure 13 Occurrence probability when safety is ensured at keynodes

Advances in Civil Engineering 17

hydrological conditions that may be encounteredDuring excavation the advanced geological pre-diction technologymay be employed to detect adversegeological and hydrological conditions ahead of theTBM in real time including confined water groundcavity and flow sand

(3) Node X6 (seal failure at shield tail) belongs tomultiple failures e quality of the tail brush needsto be enhanced and tail brush should promptly bereplaced when it is worn

By adopting corresponding safety measures in shieldtunnel excavation the occurrence probability of variousdegrees of surface collapse (OE3 OE4 OE6 OE7 and OE8)was significantly decreased (Figure 13) Finally the TBMssuccessfully passed through the left track of DCS on March3 2017 and the right track on June 11 2017 without anysurface collapse accident demonstrating the effectiveness ofour proposed hybrid method

5 Conclusions and Future Works

In this work we first defined the ldquonormal excavation phaserdquoof shield tunneling based on the fuzzy statistical test theoryData were extracted from the construction log of the XWS inthe Wuhan metro line 7 to determine the occurrenceprobability of facility fault and expert opinions were soli-cited to determine the occurrence probability of environ-mental failure operational error and multiple failuresProbabilistic safety assessment (PSA) of the normal shieldtunnel excavation system was then performed accordingly

We employed the bow-tie analysis to evaluate the oc-currence of excessive surface settlement during normaltunnel excavation e presence of emergency measurescould reduce the occurrence probability of surface collapsecaused by excessive surface settlement (OE3 OE4 OE6 OE7and OE8) but have limited effect on the prevention of ac-cidents of OE1 OE2 and OE5 It is essential to decrease theprobability of excessive surface settlement in order to pre-vent the resulting outcome events (OEs)

By mapping the bow-tie analysis to Bayesian networks(ie BT-BN analysis) we determined the key nodes thatcould cause excessive surface settlement (LE) e key nodesincluded the following X6 (seal failure at shield tail) X1(confined water) X2 (ground cavity or flow sand) X5 (ab-normal TBM shutdown) and X7 (excessive deviation fromthe axis) Effective safety measures at these nodes couldreduce the occurrence probability of excessive surface set-tlement (LE) by 66

To ensure safety careful geological exploration shouldbe carried out before the tunneling project During thetunneling safety management and supervision should bestrengthened at the construction site Advanced geo-logical prediction technology should be used to detectpoor geological and hydrological conditions ahead of theTBM in real time Advanced laser locator should be usedto monitor and alarm excessive axial deviation equality of the tail brush should be improved and tailbrush should be replaced timely when it becomes worn

e occurrence probability of excessive surface settlementwas decreased by adopting these safety measures and theoccurrence of the resulting surface collapse was sub-sequently decreased

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

e authors thank the workers foremen and safety co-ordinators of the main contractors for their participatione authors also wish to thank the engineers Yun Zhang andPeilun Tu for assistance in gathering field data

References

[1] T Zhao W Liu and Z Ye ldquoEffects of water inrush fromtunnel excavation face on the deformation and mechanicalperformance of shield tunnel segment jointsrdquo Advances inCivil Engineering vol 2017 Article ID 5913640 9 pages 2017

[2] W Liu T Zhao W Zhou and J Tang ldquoSafety risk factors ofmetro tunnel construction in China an integrated study withEFA and SEMrdquo Safety Science vol 105 pp 98ndash113 2018

[3] K Li ldquoHangzhou metro site collapse accidentrdquo 2008 httpnewssohucom20081115n260653551shtml

[4] S Liu ldquoConstruction of Nanchang metro line 2 constructionsection pavement collapsesrdquo 2017 httpnewssohucom20160514n449414512shtml

[5] R B Peck ldquoDeep excavations and tunneling in soft groundrdquo7th International Conference on Soil Mechanics and Foun-dation Engineering vol 7 no 3 pp 225ndash290 1969

[6] P B Attewell I W Farmer and N H Glossop ldquoGrounddeformation caused by tunnelling in a silty alluvial clayrdquoGround Engineering vol 11 no 8 pp 32ndash41 1978

[7] W J Rankin ldquoGround movements resulting from urbantunnelling predictions and effectsrdquo Geological Society Lon-don Engineering Geology Special Publications vol 5 no 1pp 79ndash92 1988

[8] P B Attewell and J P Woodman ldquoPredicting the dynamicsof ground settlement and its derivatives caused by tunnelingin soilrdquo Ground Engineering vol 15 no 8 pp 13ndash20 1982

[9] M P OrsquoReilly and B M New ldquoSettlement above tunnels inthe United Kingdommdashtheir magnitude and prediction intunnelling 82 proceedings of the 3rd international sympo-sium brighton 7ndash11 June 1982 P173ndash181 Publ LondonIMM 1982rdquo International Journal of Rock Mechanics ampMining Sciences amp Geomechanics Abstracts vol 20 no 1pp 1ndash18 1983

[10] R J Mair R N Taylor and A Bracegirdle ldquoSubsurfacesettlement profiles above tunnels in claysrdquo Geotechniquevol 45 no 2 pp 361-362 1995

[11] X L Yang and J MWang ldquoGroundmovement prediction fortunnels using simplified procedurerdquo Tunnelling and Un-derground Space Technology vol 26 no 3 pp 462ndash471 2011

18 Advances in Civil Engineering

(2) Determination of the Range of Excavation Speed In thefuzzy set theory all elements whose membership frequencyA(v)gt 0 constitute a support of the fuzzy setA and is writtenas ldquosupp Ardquo and all elements whose membership frequencyA(v)gt α is designated as the α cut set of the fuzzy set A andwritten as Aα Figure 5 shows that the excavation speed

fluctuated around the kernel (32mmmin) during shieldtunnel excavation In order to express the range of normalexcavation speed the confidence level α 05 was selectedand the excavation speed whose membership frequencysatisfied A(v)gt 05 was considered to constitute the in-terval of normal excavation speed (ie the 05 cut set of A)

Table 3 Partial construction log of the ldquonormal excavation speedrdquo in the XWS

n 1ndash10 n 11ndash20 n 21ndash30 n 31ndash40 n 41ndash50 n 51ndash60 n 61ndash70 n 71ndash80 n 81ndash90 n 91ndash100303ndash506 25ndash32 276ndash424 78ndash425 25ndash35 18ndash39 27ndash43 20ndash41 30ndash47 20ndash54324ndash388 26ndash34 232ndash476 83ndash417 28ndash46 20ndash35 24ndash40 10ndash40 30ndash61 32ndash63284ndash396 27ndash42 233ndash445 202ndash476 17ndash35 15ndash42 27ndash47 20ndash35 20ndash61 32ndash58303ndash388 23ndash36 205ndash427 242ndash425 28ndash37 27ndash41 20ndash33 17ndash32 30ndash60 20ndash37303ndash363 123ndash348 282ndash456 287ndash526 17ndash36 21ndash37 22ndash34 8ndash40 14ndash58 24ndash4032ndash44 178ndash325 182ndash426 19ndash32 20ndash37 31ndash41 27ndash48 8ndash40 27ndash74 25ndash4831ndash42 198ndash374 137ndash375 22ndash45 20ndash35 30ndash40 30ndash42 20ndash50 15ndash55 24ndash5131ndash39 135ndash326 156ndash326 21ndash44 21ndash37 30ndash35 25ndash43 20ndash50 25ndash45 32ndash4630ndash42 134ndash326 20ndash37 19ndash42 20ndash35 20ndash40 28ndash36 20ndash46 28ndash52 25ndash4031ndash38 156ndash364 15ndash40 20ndash41 20ndash37 25ndash40 225ndash37 31ndash42 31ndash47 20ndash35

Rang

e of a

dvan

ce sp

eed

(mm

min

)

v-lower limitv-upper limit

0102030405060708090

100

100 200 300 400 500 600 700 8000Segment number

Figure 3 Distribution of the ldquonormal excavation speedrdquo

Table 4 Membership frequency of 23mmmin belonging to the ldquonormal excavation speedrdquo

Description Number and membershipNumber of rings 50 100 150 200 250 300 350Membership counts 28 51 60 97 128 153 178Membership frequency 056 051 04 049 051 051 051Number of rings 400 450 500 550 600 650 715Membership count 202 252 302 342 382 427 470Membership frequency 051 056 061 062 064 066 066

066

v = 23mmmin

001020304050607

Cov

erag

e fre

quen

cy f

100 600300 700500200 8000 400Segment number

Figure 4 Membership frequency of 23mmmin belonging to the ldquonormal excavation speedrdquo

6 Advances in Civil Engineering

e set of normal excavation speed in Zadehrsquos form wasordered as shown in equations (4) and (5) usv0 20ndash44mmmin was considered as the range of normalexcavation speed in the ensuing PSA analysis

1113957A(v) 05020

+05421

+05922

+06423

+06924

+07525

+08026

+08527

+09028

+09429

+09730

+09931

+132

+09933

+09734

+09435

+09036

+08537

+08038

+07539

+06940

+06441

+05942

+05443

+05044

(4)

supp 1113957A(v) 111386420 21 22 23 24 25 26 27 28 29 30 31 32

33 34 35 36 37 38 39 40 41 42 43 441113865

(5)

Table 5 Membership frequency of the ldquonormal excavation speedrdquo

No Group Count Frequency1 15ndash25 1 00012 25ndash35 2 00033 35ndash45 2 00034 45ndash55 2 00035 55ndash65 5 00076 65ndash75 6 00087 75ndash85 17 00248 85ndash95 21 00299 95ndash105 31 004310 105ndash115 34 004811 115ndash125 46 006412 125ndash135 60 008413 135ndash145 66 009214 145ndash155 100 01415 155ndash165 132 018516 165ndash175 168 023517 175ndash185 217 030318 185ndash195 240 033619 195ndash205 366 051220 205ndash215 396 055421 215ndash225 425 059422 225ndash235 470 065723 235ndash245 500 069924 245ndash255 535 074825 255ndash265 563 078726 265ndash275 588 082227 275ndash285 609 085228 285ndash295 619 086629 295ndash305 668 093430 305ndash315 686 095931 315ndash325 715 132 325ndash335 698 097633 335ndash345 685 095834 345ndash355 670 093735 355ndash365 643 089936 365ndash375 623 087137 375ndash385 586 08238 385ndash395 562 078639 395ndash405 536 07540 405ndash415 495 069241 415ndash425 456 063842 425ndash435 406 056843 435ndash445 358 050144 445ndash455 332 046445 455ndash465 290 040646 465ndash475 246 034447 475ndash485 201 028148 485ndash495 157 02249 495ndash505 136 01950 505ndash515 116 016251 515ndash525 101 014152 525ndash535 91 012753 535ndash545 88 012354 545ndash555 77 010855 555ndash565 69 009756 565ndash575 62 008757 575ndash585 56 007858 585ndash595 51 007159 595ndash605 45 006360 605ndash615 41 0057

Table 5 Continued

No Group Count Frequency61 615ndash625 38 005362 625ndash635 35 004963 635ndash645 32 004564 645ndash655 30 004265 665ndash675 28 003966 675ndash685 28 003967 685ndash695 25 003568 695ndash705 23 003269 705ndash715 23 003270 715ndash725 21 002971 725ndash735 20 002872 735ndash745 19 002773 745ndash755 19 002774 755ndash765 18 002575 765ndash775 18 002576 775ndash785 18 002577 785ndash795 18 002578 795ndash805 16 002279 805ndash815 16 002280 815ndash825 15 002181 825ndash835 15 002182 835ndash845 12 001783 845ndash855 11 001584 855ndash865 8 001185 865ndash875 7 00186 875ndash885 6 000887 885ndash895 5 000788 895ndash905 4 000689 905ndash915 4 000690 915ndash925 4 000691 925ndash935 4 000692 935ndash945 4 000693 945ndash955 3 000494 955ndash965 2 000395 965ndash975 2 0003

Advances in Civil Engineering 7

313 Fuzzy Statistical Tests of Excavation Parameterse excavation speed of the TBM reflects the influenceexerted by the excavation parameters (eg total thrust facepressure and cutter head torque) on the force and dis-placement of the surrounding soil erefore it is necessaryto determine the realistic and practical excavation param-eters based on the excavation speed

Formation reinforcement during TBM launching and TBMarrival can exert a strong influence on the shield tunnel ex-cavation and lead to highly discrete parameters erefore thedata from the TBM launching and TBM arrival stages werediscarded in studying the relationship between excavation speedand TBMparameters Figure 6 shows how the TBMparametersvaried with the excavation speed during the construction of the715 segments in the XWSe curves were fitted viaMATLABand the slope of the curves was highly indicative of the cor-relation between the TBMparameters and the excavation speed

In Figure 6(a) the total thrust (F) increased with risingexcavation speed is was because bentonite was used as alubricant and injected around the shield of the TBM duringexcavation to reduce friction When the amount of injectedbentonite was appropriate the friction coefficient betweenthe shield and the surrounding soil would decrease and theexcavation speed would then increase when the thrust (F)was higher In Figure 6(b) the excavation speed decreasedwhen the cutter head torque (MT) increased is wasbecause when the soil body of the tunneling face wasrelatively difficult to cut a larger torque of the cutter headwould be needed and the excavation speed would decreaseFigure 6(c) shows that during normal excavation thepressure of the tunneling face increased slightly with risingexcavation speed Besides Mair pointed out that duringsegment assembly the downtime of TBM would decreasethe soil and water pressure on the tunneling face whichcould reduce the control pressure of the tunneling face [33]e same pattern was observed in the current constructionlogs and the R2 value of the curve in Figure 6(c) was hencerelatively low Figure 6(d) shows that the grouting pressuredecreased slightly with rising excavation speed However

since the pressure of primary grouting was read off from thegrouting pressure pump the actual grouting pressureexerted on the surrounding soil was smaller and theprimary grouting pressure hence had limited impact onexcavation speed

(1) Determination of Standard TBM Parameters It wasdetermined from the fuzzy statistical tests above that thestandard excavation speed was 32mmmin e corre-sponding standard TBM parameters could be determinedaccordingly from the following equation

TBMPstandard value 1113936

Nn1TBMPnv

N v321113868111386811138681113868 (6)

where TBMP is the TBM parameter and v is the excavationspeed (mmmin)

(2) Determination of the Range of TBM Parameters It wasdetermined from the fuzzy statistical tests above that therange of excavation speed was 20ndash44mmmin e corre-sponding boundaries of TBM parameters could be de-termined from the extreme values in the monitoring records(Figure 6) via the following equation

TBMPupper limit max TBMPv 20levle4411138681113868111386811138681113966 1113967

TBMPlower limit min TBMPv 20levle4411138681113868111386811138681113966 1113967

(7)

(3) ldquoNormal Excavation Phaserdquo of TBM According to thefuzzy set theory the excavation speed in the ldquonormal ex-cavation phaserdquo fell within 20ndash44mmmin e TBM wasconsidered to be in the ldquonormal excavation phaserdquo whenthe excavation speed and the TBM parameters all fellwithin the prescribed ranges specified above and listedagain in Table 6 e standard values and ranges were usedfurther in the subsequent PSA analysis Table 6 shows thatamong the examined parameters the face pressure had adeviation interval of merely 196 and was controlled the

Advance speed v (mmmin)

Mem

bers

hip

Atilde (v

)

Cov

erag

e fre

quen

cy A

(v)

04

02

06

08

1

10090807060504030201000

04

02

06

08

1

0

Fuzzy statistical experiment methodCauchy distribution curve

Figure 5 e histogram of membership frequency and the membership function of TBM excavation speed

8 Advances in Civil Engineering

best whereas the cutter head torque had a deviation in-terval of 7401 and was controlled the worst

(4) Statistical Relationship between TBM Parameters andExcavation Speed e monitoring results in Figure 6

demonstrated that in the ldquonormal excavation phaserdquo ofthe XWS the total thrust and the face pressure were posi-tively correlated with the excavation speed In particular thetotal thrust had a stronger correlation to the excavationspeed than the face pressure In contrast the cutter head

2000400060008000

1000012000140001600018000

Tota

l thr

ust

F (k

N)

20 25 30 35 40 45 50 55 60 6515Advance speed v (mmmin)

(a)

0500

10001500200025003000350040004500

Cutte

r hea

d to

rque

MT

(kNlowast

m)

20 25 30 35 40 45 50 55 60 6515Advance speed v (mmmin)

(b)

0

50

100

150

200

250

Face

pre

ssur

eP N

(kPa

)

20 25 30 35 40 45 50 55 60 6515Advance speed v (mmmin)

(c)

Gro

utin

g pr

essu

reP G

(kPa

)

100150200250300350400450500550

20 25 30 35 40 45 50 55 60 6515Advance speed v (mmmin)

(d)

Figure 6 Variations in the TBM parameters at different excavation speeds (data from XW section) (a) total thrust versus excavationspeed (b) cutter head torque versus excavation speed (c) face pressure versus excavation speed (d) grouting pressure versus excavationspeed

Table 6 Standard values and ranges of excavation speed and TBMPs

Factors v (mmmin) F (kN) P N (kPa) M T (kNmiddotm) P G (kPa)Parameter range [20 44] [8300 13100] [117 143] [1294 2974] [197 302]Standard value 32 9700 1326 2270 302Deviation range () [minus375 375] [minus1443 3505] [minus1176 784] [minus430 3101] [minus3477 0]

Advances in Civil Engineering 9

torque and the primary grouting pressure were negativelycorrelated with the excavation speed

32 Bow-Tie-Bayesian Network Analysis e bow-tie anal-ysis combines FTand ETanalysese FTanalysis in bow-tiecalculates the occurrence probability of the loss event (LE) aswell as the top event (TE) e occurrence probability of theTE can also be obtained from the occurrence probability ofthe basic event (BE) e events could be evaluated by theirlogical relationship and their occurrence probability in theBN Mapping the bow-tie analysis to BN involves convertingboth FT and ET analyses Figure 7(a) provides a brief de-scription of calculation steps

ree importance measures described in the followingBorst and Schoonakker [30] were introduced in the newmethodology according to the Bayes theorem Figure 7(b)gives a brief description of their calculation In the proposedmethodology the critical nodes that could more easilytrigger accidents were obtained by calculating these im-portance measures

33 Confirming Failure Occurrence Probability e BT-BNanalysis requires knowing the occurrence probability of eachbasic event (BE) e basic events fall into four categoriesenvironmental failure operational error multiple failuresand facility failures e occurrence rate of facility failureswas obtained from the construction log of the XWS for thetunneling project that spanned 179 days (715 segments intotal) and was converted into occurrence probability via thefollowing equation

F 1minus eminusλt

(8)

where F denotes the occurrence probability of the failure andλ denotes the occurrence rate of the failure

e occurrence probability of environmental failureoperational error and multiple failures cannot be readilyderived from existing data and was thus estimated via expertopinione fuzzymethod combines the opinions of differentexperts in a weighted manner to calculate the fuzzy fault rate(FFR) from the triangular fuzzy numbers or trapezoidal fuzzynumbers proposed by the experts e occurrence probabilityof environmental failure operational error and multiplefailures was then determined from the FFR [34] e generalprocedure of the fuzzy method is as follows

(1) Determine the weight of the opinion of each expertbased on the age education background work ex-perience and position of the consulted expert (Ta-ble 7) e crude weight score of each expert iscalculated via the following equation

Sn Sna+ Snb

+ Snc+ Snd

(9)

where Sn represents the total weight score of theexpert e relative weight score of each expert iscalculated via the following equation

Wn Sn

1113936mn1Sn

(10)

where m represents the number of experts(2) e occurrence probability is divided into the

following categories nonoccurrence absolute lowvery low low fairly low medium fairly high highvery high absolute high or occurrence e rankvalue of the categories escalates from 0 for non-occurrence to 1 for the occurrence (Table 8) eoccurrence probability of the event is then evalu-ated based on the corresponding triangular numberor trapezoidal number given by the experts

(3) Aggregation of the fuzzy numbers When the fuzzynumbers are all triangular number or trapezoidalnumber the aggregated fuzzy numbers of an event iscalculated via equation (11) [35] e aggregatedfuzzy number considering the expert weight isshown in equation (12)

1113957Aaggregated 1113944m

n1Wn otimes 1113957An (11)

where 1113957Aaggregated represents the aggregated fuzzifiednumber given by expert m and Wn represents theweight of the expertrsquos opinion

1113957AW 1113874W1a11 + W2a21 W1a12 + W2a22 W1a12

+W2a23 W1a13 + W2a241113875

(12)

(4) After the aggregated fuzzy numbers are determinedthe centroid index method (equation (13)) is used tohandle the fuzzy numbers and obtain the fuzzyprobability score (FPS) [36]

X 1113938g(x)x dx

1113938g(x)dx (13)

where X is the defuzzified output g(x) is themembership function and x is the output variableAssume 1113957An (an1 an2 an3) a triangular number and1113957An (an1 an2 an3) a trapezoidal number e FPS iscalculated via equation (14) when a fuzzy number is atriangular number and via equation (15) when thefuzzy number is a trapezoidal number

FPS 13

an1 + an2 + an3( 1113857 (14)

FPS 13

an3 + an4( 11138572 minus an3an4 minus an1 + an2( 1113857

2+ an1an2

an3 + an4 minus an1 minus an2( 1113857

(15)

10 Advances in Civil Engineering

(5) Finally the FPS is converted to FFR via equation(16) [37] and the FFR is further converted tothe occurrence probability of environmentalfailure operational error and multiple failures(equation (8))

FFR

110k

FPSne 0

0 FPS 0

k 2301 times(1minus FPS)

FPS1113890 1113891

13

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(16)

4 Results

41 Analysis of Excessive Surface Settlement inNormal TunnelExcavation Figure 8 shows that the normal excavation

(1) If the logical relationship is AND between events the TE occurs when all events occur The probability of TE can be calculated from the following equation

(A)

(2) If the logical relationship is OR between events the TE occurs when any of the event occurs The probability of TE can be calculated from the following equation

(B)

(3) By definition in the FT analysis the probability of TE is the same as that of LE Similarly the probability of the initial event (IE) in the ET analysis is the same as that of LE The probability of OE in ET analysis can be calculated from the following equation

(C)

(4) The BN an inference method based on the Bayes theorem combines both graph theory and probability theory

(D)

FTE = i=1

nFBEi

FTE = 1 ndashi=1

n(1 ndash FBEi)

FOEn = FIE middot i=1

nP (Ei = 0) middot

j=1

nP (Ej = 1)

P(B | A) = P(A | B) middot P(B)

P(A)

(a)

(1) The Birnbaum measure (BM) whichdetermines the increment of the occurrenceprobability of TE when BE occurs is shownin the following equation

(E)

where P(TE | BE = 1) denotes the occurrence probability of TE when BE occurs and P(TE | BE = 0) denotes the occurrence probability of TE when BE does not occur

(2) Risk achievement worth (RAW) evaluatesthe impact of BE on TE when the probabilityof BE is considered The RAW is adjustedby the probability of TE and BE as shown inthe following equation

(F)

where P(BE) denotes the occurrence probability of BE and P(TE) denotes the occurrence probability of TE under all circumstances

(3) The FussellndashVesely (FV) importance which describes the contribution of BE to system fault is shown in the following equation

IBBE

M = P(TE | BE = 1) ndash P(TE | BE = 0)

IRB

AE

W = IBBE

M middot P(BE)P(TE)

(G)

P(TE) ndash P(TE | BE = 0)P(TE)

IFB

VE =

(b)

Figure 7 Bow-tie-Bayesian network analysis Calculation of (a) event probability and (b) importance measures

Table 7 Weight scores for experts

Factor Category Score

Age (a)

lt30 130ndash39 240ndash49 3ge50 4

Education (b)

High school 1College 2Bachelor 3Master 4PhD 5

Work experience (c)

lt5 years 15ndash10 years 211ndash20 years 321ndash30 years 4ge30 years 5

Position (d)

Worker 1Technician 2

Junior scholarengineer 3Senior scholarengineer 4

Table 8 Rank value of each category

Classified occurrence probability Rank valueNonoccurrence 0Absolute low 01Very low 02Low 03Fairly low 04Medium 05Fairly high 06High 07Very high 08Absolute high 09Occurrence 10

Advances in Civil Engineering 11

phase involves the environment TBM operation supervi-sion management and emergency handling Risk analysis ofthe ldquonormal excavation phaserdquo in soft soil engineering basedon the XWS allows the identification of potential risk factorsthat may trigger surface settlement and consequently lead toaccidents Eskesen et al have described three principles forrisk analysis as follows (1) eliminate risk factors that are easyto detect and can be controlled timely and effectively (2)eliminate risk factors with low occurrence probability andno catastrophic consequences and (3) combine risk factorswith similar loss consequences [38] Accordingly the riskfactors during shield tunneling were organized into three

basic categories improper control of excavation parameters(eg poor control of face pressure) catastrophic geology (egground cavity or flow sand) and unforeseeable factors (egsegment damage) Figure 9 shows the bow-tie model builtfrom the categorized factors for the risk of surface collapsecaused by excessive surface settlement during shield tun-neling OEs of various degrees were successfully predictedbased on the CEs (Figure 9) Many risk factors exist in anygiven surface collapse In this section based on the previouscalculation results in Section 31 we selected the manageableshield excavation parameters (shield total thrust groutingpressure cutter head torque soil pressure etc) in the ldquonormal

Synchronousgrouting

ExcavationSegment

installationAttitudecontrol Tail sealing

Excavationcycle

Quality controlacceptance

Dangeroussituation exists Yes

Prepareemergencymeasures

Emergencymeasures

Execution of emergencymeasures

Acceptance ofexcavationprocedures

Excavationacceptance

report

Monitoring measurements

Monitored dataof excavationenvironment

Formation geologyTBM parametersExcavation axis

Segment installationSynchronous grouting

TBM construction parameter

No

TBM parametersv (mmmm) F (kN) PN (kPa)

MT (kNmiddotm) PG (kNmiddotm)TBM attitude TBM position TBM fault information

Soil bodyparameters

Soil evolutionmodel

Confined waterObstacles

Ground cavity orquicksand

Metro tunnel excavation

Emergencyhandling

Supervision

TBMoperation

TBM

Environment

Management

Figure 8 System diagram of the ldquonormal excavation phaserdquo

12 Advances in Civil Engineering

excavation phaserdquo as the base events assigning their weightsaccording to Section 33 and then performed PSA analysis

As mentioned earlier the ldquonormal excavation phaserdquo isunder the influence of excavation parameters catastrophicgeology and unforeseeable factors Surface settlement canoccur once the condition deteriorates Here we set excessivesurface settlement as the TE in the FT analysis Meanwhilethe tunneling system has a built-in emergency managementsystem Upon excessive surface settlement the emergencymanagement system will start to shut down the TBM timelyHence in the ETanalysis the excessive surface settlement isset as the IE and TBM shutdown is set as the CE OEs ofvarious degrees are obtained based on the considered CEFinally the surface settlement is set as the LE to connect theFT and the ET and furnish the BTmodel (Figure 9 Table 9)Eight OEs of various degrees were predicted based on theCEs including surface collapse events OE3 OE4 OE6 OE7and OE8 (Figure 9 Table 10) e TBM shuts down if CE1occurs and continues to operate if otherwise

e BN-BT model for excessive surface settlement isconstructed by mapping the FT and ET analyses in the BT(Figure 9) model to BN (Figure 10) All the nodes of BN havepreviously been described in the BT except the node OEwhich is the consequence node OE is added to accommodatethe outcomes of BT By connecting the node of excessivesurface settlement to OE another state also called the safe

state is added to the state set It includes consequences OE1 toOE8 to account for the nonoccurrence of the top event iewhen excessive surface settlement controlled To show thedependence among the safety barriers and the top eventcausal arcs are also drawn between TBM shutdown andgrouting in the settlement area and bentonite injection to soilchamber and TBM shield It is worth noting that since variouscombinations of the failure and success of the sequentialsafety barriers result in different consequences in the BT allthe safety nodes of BN are connected to node OE

42 Determination of Event Occurrence Probability emaximum surface settlement that resulted from the aber-ration of the ith TBM parameter is denoted as δmaxi eprobability of safety accident becomes higher when δmaxiapproaches the permitted surface settlement δi Whenδmaxi δi the accident will occur as soon as the TBM pa-rameter gives rise to a surface settlement of δmaxi eprobability of equipment fault for the normal excavationsystem was calculated via equation (8) from the engineeringlog data of the XWS over 179 days of construction (715segments rings in total) e construction of all 715 rings fellwithin the ldquonormal excavation phaserdquo as was defined by thefuzzy statistical test (v 20ndash44mmmin) Table 11 lists thecalculation results

X3X2X1

OR

M1

X7X6X5X4

OR

M2

X10X9 X11 X13X12

M3

OR

Excessive surface

settlement

X8

Caus

esLE

CE1

CE2

CE3

Con

sequ

ence

sSt

op

TBM

Gro

utin

g in

settl

emen

tar

ea

Bent

onite

inje

ctio

n

OE 1

OE 2

OE 3

OE 4

OE 5

OE 6

OE 7

OE 8

Success Failure

AND

Figure 9 Diagram of bow-tie analysis for excessive surface settlement

Advances in Civil Engineering 13

To address the uncertainty regarding the events ofenvironmental failure operational error and multiplefailure six domain experts who participated in the con-struction of the Wuhan metro system including two seniorengineers one senior academic professor one technicalconsultant one junior engineer and one worker wereinvited to evaluate the occurrence probability of events thatcannot be readily derived from existing data (Table 12)eweights of their opinion were then calculated by usingequations (9) and (10) and the distribution of each opinionweight is shown in Figure 11

In addition Table 13 lists the expert opinions regardingthe events of environmental failure operational error andmultiple failures in the form of fuzzy numbers based onTable 8 e fuzzy numbers were aggregated via equations(12) and converted to FPS and FFR via equations (13)ndash(16)(Table 14) e occurrence probabilities were finally derivedfrom FFR (Table 14) Generally the expert knowledge isconsidered as a scarce resource which cannot provide

universal consultation or real-time guidance us there ismuch room to improve the data use efficiency

43 Update in Occurrence Probability of LE and OE eoccurrence probability of basic events is calculated as de-scribed in Section 42 including the occurrence probabilityof facility failure from the engineering log data of the XWS aswell as that of environmental failure operational error andmultiple failures derived from expert opinion e occur-rence probability of excessive surface settlement (LE) isdetermined via equations (A) and (B) by considering thelogical relationship between events in Figure 7 Finally theoccurrence probability of OEs including surface collapse canbe calculated via equation (C) in the figure by mapping theFT and ET analyses in the BTmodel to BN Figure 12 showsthe occurrence probabilities of the LE (ie excessive surfacesettlement) and that of the OEs

e above analysis shows that the occurrence probabilityof excessive surface settlement within one year is 08299(Figure 12) is occurrence probability of surface collapse(OE3 OE4 OE6 OE7 and OE8) may be decreased whenemergency measures are put in place including grouting insettlement area and bentonite injection to soil chamber andTBM shield However these measures cannot help to reduceminor accidents since the occurrence probability remains athigh levels for OE1 OE2 and OE5 Admittedly grouting andbentonite injection are necessary measures and they candecrease the effects of excessive surface settlement duringshield tunneling However the key point of avoiding outcomeevents including surface collapse to ensure project safety is toprevent the excessive surface settlement from occurring in thefirst place Hence we sought to determine the key nodesleading to excessive surface settlement via BT-BN analysis andpropose the corresponding preventive measures

Table 10 Analysis of event occurrence

Symbol EventOE1 Excessive surface settlement

OE2Grouted cutter head and shield excessive surface

settlement and minor property damageOE3 Minor surface collapse and property damage

OE4Moderate surface collapse major property damage

and minor casualtiesOE5 Excessive surface settlement

OE6Grouted cutter head and shield moderate surface

collapse and minor property damage

OE7Moderate surface collapse and major property

damage

OE8Severe surface collapse major property damage and

major casualties

Table 9 Details of bow-tie components in Figure 9

Event Symbol Logic link type Failure modelGround settlement Excessive surface settlement OR gate mdashCatastrophic geology M1 OR gate mdashUnforeseeable factors M2 OR gate mdashExcavation parameters M3 AND gate mdashConfined water X1 mdash Environmental failureGround cavity or flow sand X2 mdash Environmental failureObstacles X3 mdash Environmental failureSegment damage X4 mdash Operational errorAbnormal TBM shutdown X5 mdash Multiple failureSeal failure at shield tail X6 mdash Multiple failureExcessive deviation from axis X7 mdash Operational errorEquipment failure X8 mdash Multiple failureUntimely grouting X9 mdash Facility failureExcessive cutter head torque X10 mdash Facility failureImproper control of face pressure X11 mdash Facility failureExcessive thrust X12 mdash Facility failureImproper control of excavation speed X13 mdash Facility failureTBM shutdown CE1 mdash Multiple failureGrouting in settlement area CE2 mdash Multiple failureBentonite injection to soil chamber and TBM shield CE3 mdash Multiple failure

14 Advances in Civil Engineering

Table 11 Probability of equipment fault

Event Surface settlementδmaxi (mm)

Permitted surfacesettlement δi (mm)

Value of TBMparameter

Occurrence rate(dminus1)

Occurrence probability(in 1 year)

X9 89 15 302 kPa 10675eminus 04 382eminus 02X10 84 10 2974 kNmiddotM 17792eminus 04 629eminus 02X11 86 15 143 kPa 71167eminus 05 256eminus 02X12 98 15 13100 kN 14233eminus 04 506eminus 02X13 120 15 41mmmin 28467eminus 04 987eminus 02All data were obtained from the operation log of the XWS

Table 12 Characteristics of experts participated in the occurrence probability evaluation

Expert Age Education Service (years) Professional position1 56 High school 25 Worker2 35 Master 10 Technician3 41 Master 15 Junior engineer4 47 Bachelor 20 Senior engineer5 50 PhD 18 Senior academic6 59 PhD 30 Senior engineer

0125 0125

01625 01625

020225

AgeEducationService

Professional positionWeighting

2 3 4 5 61Expert

0

005

01

015

02

025

Wei

ghtin

g

0

1

2

3

4

5

6

Wei

ghtin

g sc

ore

Figure 11 Distribution of each expert opinion weight

X1 X2 X3

M1

X5 X6 X7 X8

M2

X9 X11

M3

Excessive surface

settlement

X10 X12 X13X4

CE1 CE2 CE3

OE

Caus

esLE

CEC

onse

quen

ces

Figure 10 Bow-tie chart of excessive surface settlement

Advances in Civil Engineering 15

44 Identify Key Nodes and Provide Safety Measures Inorder to find the key nodes leading to excessive surfacesettlement the importance measure of each event was cal-culated via equations (E)ndash(G) in Figure 7 as shown inTable 15 Assume the number of events as ldquonrdquo e nor-malized weight Rlowast could be calculated from the importancemeasure Ii via the following equation

Rlowast

Ii

1113936ni1Ii

times 100 (17)

After the normalized weight Rlowast is calculated for eachimportance measure the total weight Rlowast could be calculatedvia equation (18) e total weight Rlowast of events was finally

ranked in descending order to find the key nodes as shownin Table 16

Rlowast R

lowastBM + R

lowastRAW + R

lowastFV (18)

It can be seen that X6 (seal failure at shield tail) X1(confined water) X2 (ground cavity or flow sand) X5 (ab-normal TBM shutdown) and X7 (excessive deviation fromaxis) have far higher weight than other events and are thusthe key nodes to accidents related to excessive surface set-tlement Measures can be taken to particularly ensure safetyat these nodes e occurrence probability of excessivesurface settlement can be reduced by 66 when X6 X1 X2X5 and X7 are ensured safe (Figure 13)

Table 13 Expert opinion on environmental failure operational error and multiple failures

Event Fuzzy numbers proposed by each expert

X1

Expert 1 Expert 2 Expert 3(02 03 04 05) (01 02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 02 03 05)

X2

Expert 1 Expert 2 Expert 3(01 02 03 05) (02 03 04) (01 02 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (02 03 05) (01 02 03 05)

X3

Expert 1 Expert 2 Expert 3(01 02 04 05) (01 02 03 05) (01 03 04)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03) (01 02 03)

X4

Expert 1 Expert 2 Expert 3(02 03 04 05) (01 02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(02 03 04) (02 03 05) (01 02 03 05)

X5

Expert 1 Expert 2 Expert 3(01 03 04) (01 02 03 05) (02 03 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (02 03 05) (01 02 03)

X6

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 03 05) (02 03 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (02 03 05) (01 02 04 05)

X7

Expert 1 Expert 2 Expert 3(01 02 04 05) (01 02 03 05) (02 03 04)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 03 05)

X8

Expert 1 Expert 2 Expert 3(01 03 04 05) (01 02 03 04) (02 03 04)

Expert 4 Expert 5 Expert 6(02 03 04) (01 02 03 05) (01 02 03)

CE1

Expert 1 Expert 2 Expert 3(02 03 04 05) (02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 02 04 05)

CE2

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 05) (02 03 04 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (01 02 03 05) (01 03 05)

CE3

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 03 05) (03 04 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (01 02 04 05) (01 02 03 05)

16 Advances in Civil Engineering

In accordance with the predictive and diagnosticanalysis results using the established model some safetymeasures for key nodes are displayed in time to reduce theexcessive surface settlement risk during the tunnelexcavation

(1) e nodes X5 (abnormal TBM shutdown) and X7(excessive deviation from the axis) mostly involveoperational error Safety management and supervi-sion need to be strengthened at the construction siteto eliminate such errors and ensure that the TBM isoperated properly Besides an advanced real-time

laser locator may help to alarm in the case of largeaxial deviation

(2) e nodes X1 (confined water) and X2 (ground cavityor flow sand) belong to environmental failure Inorder to reduce the influence of environmental failurecareful geological exploration should be carried outbefore tunneling to identify the poor geological and

Table 14 Calculation of FPS FFR and the occurrence probability of environmental failure operational error and multiple failures

Event Aggregated fuzzy numbers FPS FFR (dminus1) Failure probability (in 1 year)X1 (01288 02288 03288 04838) 02951 83969eminus 04 26402eminus 1X2 (01325 02325 03163 04713) 02909 80032eminus 04 25336eminus 1X3 (01000 02163 02700 03825) 02420 42986eminus 04 14518eminus 1X4 (00450 00900 01125 01800) 01082 22492eminus 05 81803eminus 3X5 (01363 02488 02775 04263) 02747 66022eminus 04 214155eminus 1X6 (01488 02488 03225 04713) 03004 89125eminus 04 27770eminus 1X7 (01163 02388 03125 04675) 02855 75157eminus 04 24002eminus 1X8 (01450 02538 02950 03100) 02463 45643eminus 04 15338eminus 1CE1 (01413 02413 03513 04838) 03058 94598eminus 04 29202eminus 1CE2 (01288 02513 03038 04713) 02916 80679eminus 04 25496eminus 1CE3 (01450 02450 03363 04713) 03010 89722eminus 04 27937eminus 1

08299

03155

01223 010800419

01301

00504 00445 00173

Occ

urre

nce p

roba

bilit

y (in

1 y

ear)

00

01

02

03

04

05

06

07

08

09

OE1 OE2 OE3 OE4 OE5 OE6 OE7 OE8LE

Figure 12 Occurrence probability of surface settlement and otheroutcome events

Table 15 Calculation of importance measure of influential factors

SymbolImportance measure

BM RAW FVX1 2311eminus 1 7352eminus 02 7352eminus 02X2 2279eminus 1 6958eminus 02 6958eminus 02X3 1990eminus 1 3481eminus 02 3481eminus 02X4 1716eminus 1 1691eminus 03 1691eminus 03X5 2165eminus 1 5587eminus 02 5587eminus 02X6 2356eminus 1 7884eminus 02 7884eminus 02X7 2239eminus 1 6476eminus 02 6476eminus 02X8 2010eminus 1 3715eminus 02 3715eminus 02X9 1370eminus 6 6306eminus 08 6306eminus 08X10 8300eminus 7 6291eminus 08 6291eminus 08X11 2040eminus 6 6293eminus 08 6293eminus 08X12 1030eminus 6 6280eminus 08 6280eminus 08X13 5300eminus 7 6303eminus 08 6303eminus 08

Table 16 Ranking results of the key events

Rank SymbolNormalization weighting (Rlowast) Total

weighting(Rlowast)

RlowastBM RlowastRAW RlowastFV

1 X6 13805 18942 18942 516892 X1 13541 17664 17664 488693 X2 13354 16717 16717 467884 X7 13120 15559 15559 442385 X5 12686 13423 13423 395326 X8 11778 8926 89255 296297 X3 11661 8363 8363 283878 X4 10055 0406 0406 108689 X11 00002 1512eminus 05 1512eminus 05 1498eminus 0410 X9 8028eminus 05 1515eminus 05 1515eminus 05 1106eminus 0411 X12 6035eminus 05 1509eminus 05 1509eminus 05 9053eminus 0512 X10 4863eminus 05 1511eminus 05 1511eminus 05 7886eminus 0513 X13 3106eminus 05 1514eminus 05 1514eminus 05 6134eminus 05Total 100 100 100 100

02822

01073

00416 0036700142

0044200172 00151 00059

Occ

urre

nce p

roba

bilit

y (in

1 y

ear)

000

005

010

015

020

025

030

OE1 OE2 OE3 OE4 OE5 OE6 OE7 OE8LE

Figure 13 Occurrence probability when safety is ensured at keynodes

Advances in Civil Engineering 17

hydrological conditions that may be encounteredDuring excavation the advanced geological pre-diction technologymay be employed to detect adversegeological and hydrological conditions ahead of theTBM in real time including confined water groundcavity and flow sand

(3) Node X6 (seal failure at shield tail) belongs tomultiple failures e quality of the tail brush needsto be enhanced and tail brush should promptly bereplaced when it is worn

By adopting corresponding safety measures in shieldtunnel excavation the occurrence probability of variousdegrees of surface collapse (OE3 OE4 OE6 OE7 and OE8)was significantly decreased (Figure 13) Finally the TBMssuccessfully passed through the left track of DCS on March3 2017 and the right track on June 11 2017 without anysurface collapse accident demonstrating the effectiveness ofour proposed hybrid method

5 Conclusions and Future Works

In this work we first defined the ldquonormal excavation phaserdquoof shield tunneling based on the fuzzy statistical test theoryData were extracted from the construction log of the XWS inthe Wuhan metro line 7 to determine the occurrenceprobability of facility fault and expert opinions were soli-cited to determine the occurrence probability of environ-mental failure operational error and multiple failuresProbabilistic safety assessment (PSA) of the normal shieldtunnel excavation system was then performed accordingly

We employed the bow-tie analysis to evaluate the oc-currence of excessive surface settlement during normaltunnel excavation e presence of emergency measurescould reduce the occurrence probability of surface collapsecaused by excessive surface settlement (OE3 OE4 OE6 OE7and OE8) but have limited effect on the prevention of ac-cidents of OE1 OE2 and OE5 It is essential to decrease theprobability of excessive surface settlement in order to pre-vent the resulting outcome events (OEs)

By mapping the bow-tie analysis to Bayesian networks(ie BT-BN analysis) we determined the key nodes thatcould cause excessive surface settlement (LE) e key nodesincluded the following X6 (seal failure at shield tail) X1(confined water) X2 (ground cavity or flow sand) X5 (ab-normal TBM shutdown) and X7 (excessive deviation fromthe axis) Effective safety measures at these nodes couldreduce the occurrence probability of excessive surface set-tlement (LE) by 66

To ensure safety careful geological exploration shouldbe carried out before the tunneling project During thetunneling safety management and supervision should bestrengthened at the construction site Advanced geo-logical prediction technology should be used to detectpoor geological and hydrological conditions ahead of theTBM in real time Advanced laser locator should be usedto monitor and alarm excessive axial deviation equality of the tail brush should be improved and tailbrush should be replaced timely when it becomes worn

e occurrence probability of excessive surface settlementwas decreased by adopting these safety measures and theoccurrence of the resulting surface collapse was sub-sequently decreased

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

e authors thank the workers foremen and safety co-ordinators of the main contractors for their participatione authors also wish to thank the engineers Yun Zhang andPeilun Tu for assistance in gathering field data

References

[1] T Zhao W Liu and Z Ye ldquoEffects of water inrush fromtunnel excavation face on the deformation and mechanicalperformance of shield tunnel segment jointsrdquo Advances inCivil Engineering vol 2017 Article ID 5913640 9 pages 2017

[2] W Liu T Zhao W Zhou and J Tang ldquoSafety risk factors ofmetro tunnel construction in China an integrated study withEFA and SEMrdquo Safety Science vol 105 pp 98ndash113 2018

[3] K Li ldquoHangzhou metro site collapse accidentrdquo 2008 httpnewssohucom20081115n260653551shtml

[4] S Liu ldquoConstruction of Nanchang metro line 2 constructionsection pavement collapsesrdquo 2017 httpnewssohucom20160514n449414512shtml

[5] R B Peck ldquoDeep excavations and tunneling in soft groundrdquo7th International Conference on Soil Mechanics and Foun-dation Engineering vol 7 no 3 pp 225ndash290 1969

[6] P B Attewell I W Farmer and N H Glossop ldquoGrounddeformation caused by tunnelling in a silty alluvial clayrdquoGround Engineering vol 11 no 8 pp 32ndash41 1978

[7] W J Rankin ldquoGround movements resulting from urbantunnelling predictions and effectsrdquo Geological Society Lon-don Engineering Geology Special Publications vol 5 no 1pp 79ndash92 1988

[8] P B Attewell and J P Woodman ldquoPredicting the dynamicsof ground settlement and its derivatives caused by tunnelingin soilrdquo Ground Engineering vol 15 no 8 pp 13ndash20 1982

[9] M P OrsquoReilly and B M New ldquoSettlement above tunnels inthe United Kingdommdashtheir magnitude and prediction intunnelling 82 proceedings of the 3rd international sympo-sium brighton 7ndash11 June 1982 P173ndash181 Publ LondonIMM 1982rdquo International Journal of Rock Mechanics ampMining Sciences amp Geomechanics Abstracts vol 20 no 1pp 1ndash18 1983

[10] R J Mair R N Taylor and A Bracegirdle ldquoSubsurfacesettlement profiles above tunnels in claysrdquo Geotechniquevol 45 no 2 pp 361-362 1995

[11] X L Yang and J MWang ldquoGroundmovement prediction fortunnels using simplified procedurerdquo Tunnelling and Un-derground Space Technology vol 26 no 3 pp 462ndash471 2011

18 Advances in Civil Engineering

e set of normal excavation speed in Zadehrsquos form wasordered as shown in equations (4) and (5) usv0 20ndash44mmmin was considered as the range of normalexcavation speed in the ensuing PSA analysis

1113957A(v) 05020

+05421

+05922

+06423

+06924

+07525

+08026

+08527

+09028

+09429

+09730

+09931

+132

+09933

+09734

+09435

+09036

+08537

+08038

+07539

+06940

+06441

+05942

+05443

+05044

(4)

supp 1113957A(v) 111386420 21 22 23 24 25 26 27 28 29 30 31 32

33 34 35 36 37 38 39 40 41 42 43 441113865

(5)

Table 5 Membership frequency of the ldquonormal excavation speedrdquo

No Group Count Frequency1 15ndash25 1 00012 25ndash35 2 00033 35ndash45 2 00034 45ndash55 2 00035 55ndash65 5 00076 65ndash75 6 00087 75ndash85 17 00248 85ndash95 21 00299 95ndash105 31 004310 105ndash115 34 004811 115ndash125 46 006412 125ndash135 60 008413 135ndash145 66 009214 145ndash155 100 01415 155ndash165 132 018516 165ndash175 168 023517 175ndash185 217 030318 185ndash195 240 033619 195ndash205 366 051220 205ndash215 396 055421 215ndash225 425 059422 225ndash235 470 065723 235ndash245 500 069924 245ndash255 535 074825 255ndash265 563 078726 265ndash275 588 082227 275ndash285 609 085228 285ndash295 619 086629 295ndash305 668 093430 305ndash315 686 095931 315ndash325 715 132 325ndash335 698 097633 335ndash345 685 095834 345ndash355 670 093735 355ndash365 643 089936 365ndash375 623 087137 375ndash385 586 08238 385ndash395 562 078639 395ndash405 536 07540 405ndash415 495 069241 415ndash425 456 063842 425ndash435 406 056843 435ndash445 358 050144 445ndash455 332 046445 455ndash465 290 040646 465ndash475 246 034447 475ndash485 201 028148 485ndash495 157 02249 495ndash505 136 01950 505ndash515 116 016251 515ndash525 101 014152 525ndash535 91 012753 535ndash545 88 012354 545ndash555 77 010855 555ndash565 69 009756 565ndash575 62 008757 575ndash585 56 007858 585ndash595 51 007159 595ndash605 45 006360 605ndash615 41 0057

Table 5 Continued

No Group Count Frequency61 615ndash625 38 005362 625ndash635 35 004963 635ndash645 32 004564 645ndash655 30 004265 665ndash675 28 003966 675ndash685 28 003967 685ndash695 25 003568 695ndash705 23 003269 705ndash715 23 003270 715ndash725 21 002971 725ndash735 20 002872 735ndash745 19 002773 745ndash755 19 002774 755ndash765 18 002575 765ndash775 18 002576 775ndash785 18 002577 785ndash795 18 002578 795ndash805 16 002279 805ndash815 16 002280 815ndash825 15 002181 825ndash835 15 002182 835ndash845 12 001783 845ndash855 11 001584 855ndash865 8 001185 865ndash875 7 00186 875ndash885 6 000887 885ndash895 5 000788 895ndash905 4 000689 905ndash915 4 000690 915ndash925 4 000691 925ndash935 4 000692 935ndash945 4 000693 945ndash955 3 000494 955ndash965 2 000395 965ndash975 2 0003

Advances in Civil Engineering 7

313 Fuzzy Statistical Tests of Excavation Parameterse excavation speed of the TBM reflects the influenceexerted by the excavation parameters (eg total thrust facepressure and cutter head torque) on the force and dis-placement of the surrounding soil erefore it is necessaryto determine the realistic and practical excavation param-eters based on the excavation speed

Formation reinforcement during TBM launching and TBMarrival can exert a strong influence on the shield tunnel ex-cavation and lead to highly discrete parameters erefore thedata from the TBM launching and TBM arrival stages werediscarded in studying the relationship between excavation speedand TBMparameters Figure 6 shows how the TBMparametersvaried with the excavation speed during the construction of the715 segments in the XWSe curves were fitted viaMATLABand the slope of the curves was highly indicative of the cor-relation between the TBMparameters and the excavation speed

In Figure 6(a) the total thrust (F) increased with risingexcavation speed is was because bentonite was used as alubricant and injected around the shield of the TBM duringexcavation to reduce friction When the amount of injectedbentonite was appropriate the friction coefficient betweenthe shield and the surrounding soil would decrease and theexcavation speed would then increase when the thrust (F)was higher In Figure 6(b) the excavation speed decreasedwhen the cutter head torque (MT) increased is wasbecause when the soil body of the tunneling face wasrelatively difficult to cut a larger torque of the cutter headwould be needed and the excavation speed would decreaseFigure 6(c) shows that during normal excavation thepressure of the tunneling face increased slightly with risingexcavation speed Besides Mair pointed out that duringsegment assembly the downtime of TBM would decreasethe soil and water pressure on the tunneling face whichcould reduce the control pressure of the tunneling face [33]e same pattern was observed in the current constructionlogs and the R2 value of the curve in Figure 6(c) was hencerelatively low Figure 6(d) shows that the grouting pressuredecreased slightly with rising excavation speed However

since the pressure of primary grouting was read off from thegrouting pressure pump the actual grouting pressureexerted on the surrounding soil was smaller and theprimary grouting pressure hence had limited impact onexcavation speed

(1) Determination of Standard TBM Parameters It wasdetermined from the fuzzy statistical tests above that thestandard excavation speed was 32mmmin e corre-sponding standard TBM parameters could be determinedaccordingly from the following equation

TBMPstandard value 1113936

Nn1TBMPnv

N v321113868111386811138681113868 (6)

where TBMP is the TBM parameter and v is the excavationspeed (mmmin)

(2) Determination of the Range of TBM Parameters It wasdetermined from the fuzzy statistical tests above that therange of excavation speed was 20ndash44mmmin e corre-sponding boundaries of TBM parameters could be de-termined from the extreme values in the monitoring records(Figure 6) via the following equation

TBMPupper limit max TBMPv 20levle4411138681113868111386811138681113966 1113967

TBMPlower limit min TBMPv 20levle4411138681113868111386811138681113966 1113967

(7)

(3) ldquoNormal Excavation Phaserdquo of TBM According to thefuzzy set theory the excavation speed in the ldquonormal ex-cavation phaserdquo fell within 20ndash44mmmin e TBM wasconsidered to be in the ldquonormal excavation phaserdquo whenthe excavation speed and the TBM parameters all fellwithin the prescribed ranges specified above and listedagain in Table 6 e standard values and ranges were usedfurther in the subsequent PSA analysis Table 6 shows thatamong the examined parameters the face pressure had adeviation interval of merely 196 and was controlled the

Advance speed v (mmmin)

Mem

bers

hip

Atilde (v

)

Cov

erag

e fre

quen

cy A

(v)

04

02

06

08

1

10090807060504030201000

04

02

06

08

1

0

Fuzzy statistical experiment methodCauchy distribution curve

Figure 5 e histogram of membership frequency and the membership function of TBM excavation speed

8 Advances in Civil Engineering

best whereas the cutter head torque had a deviation in-terval of 7401 and was controlled the worst

(4) Statistical Relationship between TBM Parameters andExcavation Speed e monitoring results in Figure 6

demonstrated that in the ldquonormal excavation phaserdquo ofthe XWS the total thrust and the face pressure were posi-tively correlated with the excavation speed In particular thetotal thrust had a stronger correlation to the excavationspeed than the face pressure In contrast the cutter head

2000400060008000

1000012000140001600018000

Tota

l thr

ust

F (k

N)

20 25 30 35 40 45 50 55 60 6515Advance speed v (mmmin)

(a)

0500

10001500200025003000350040004500

Cutte

r hea

d to

rque

MT

(kNlowast

m)

20 25 30 35 40 45 50 55 60 6515Advance speed v (mmmin)

(b)

0

50

100

150

200

250

Face

pre

ssur

eP N

(kPa

)

20 25 30 35 40 45 50 55 60 6515Advance speed v (mmmin)

(c)

Gro

utin

g pr

essu

reP G

(kPa

)

100150200250300350400450500550

20 25 30 35 40 45 50 55 60 6515Advance speed v (mmmin)

(d)

Figure 6 Variations in the TBM parameters at different excavation speeds (data from XW section) (a) total thrust versus excavationspeed (b) cutter head torque versus excavation speed (c) face pressure versus excavation speed (d) grouting pressure versus excavationspeed

Table 6 Standard values and ranges of excavation speed and TBMPs

Factors v (mmmin) F (kN) P N (kPa) M T (kNmiddotm) P G (kPa)Parameter range [20 44] [8300 13100] [117 143] [1294 2974] [197 302]Standard value 32 9700 1326 2270 302Deviation range () [minus375 375] [minus1443 3505] [minus1176 784] [minus430 3101] [minus3477 0]

Advances in Civil Engineering 9

torque and the primary grouting pressure were negativelycorrelated with the excavation speed

32 Bow-Tie-Bayesian Network Analysis e bow-tie anal-ysis combines FTand ETanalysese FTanalysis in bow-tiecalculates the occurrence probability of the loss event (LE) aswell as the top event (TE) e occurrence probability of theTE can also be obtained from the occurrence probability ofthe basic event (BE) e events could be evaluated by theirlogical relationship and their occurrence probability in theBN Mapping the bow-tie analysis to BN involves convertingboth FT and ET analyses Figure 7(a) provides a brief de-scription of calculation steps

ree importance measures described in the followingBorst and Schoonakker [30] were introduced in the newmethodology according to the Bayes theorem Figure 7(b)gives a brief description of their calculation In the proposedmethodology the critical nodes that could more easilytrigger accidents were obtained by calculating these im-portance measures

33 Confirming Failure Occurrence Probability e BT-BNanalysis requires knowing the occurrence probability of eachbasic event (BE) e basic events fall into four categoriesenvironmental failure operational error multiple failuresand facility failures e occurrence rate of facility failureswas obtained from the construction log of the XWS for thetunneling project that spanned 179 days (715 segments intotal) and was converted into occurrence probability via thefollowing equation

F 1minus eminusλt

(8)

where F denotes the occurrence probability of the failure andλ denotes the occurrence rate of the failure

e occurrence probability of environmental failureoperational error and multiple failures cannot be readilyderived from existing data and was thus estimated via expertopinione fuzzymethod combines the opinions of differentexperts in a weighted manner to calculate the fuzzy fault rate(FFR) from the triangular fuzzy numbers or trapezoidal fuzzynumbers proposed by the experts e occurrence probabilityof environmental failure operational error and multiplefailures was then determined from the FFR [34] e generalprocedure of the fuzzy method is as follows

(1) Determine the weight of the opinion of each expertbased on the age education background work ex-perience and position of the consulted expert (Ta-ble 7) e crude weight score of each expert iscalculated via the following equation

Sn Sna+ Snb

+ Snc+ Snd

(9)

where Sn represents the total weight score of theexpert e relative weight score of each expert iscalculated via the following equation

Wn Sn

1113936mn1Sn

(10)

where m represents the number of experts(2) e occurrence probability is divided into the

following categories nonoccurrence absolute lowvery low low fairly low medium fairly high highvery high absolute high or occurrence e rankvalue of the categories escalates from 0 for non-occurrence to 1 for the occurrence (Table 8) eoccurrence probability of the event is then evalu-ated based on the corresponding triangular numberor trapezoidal number given by the experts

(3) Aggregation of the fuzzy numbers When the fuzzynumbers are all triangular number or trapezoidalnumber the aggregated fuzzy numbers of an event iscalculated via equation (11) [35] e aggregatedfuzzy number considering the expert weight isshown in equation (12)

1113957Aaggregated 1113944m

n1Wn otimes 1113957An (11)

where 1113957Aaggregated represents the aggregated fuzzifiednumber given by expert m and Wn represents theweight of the expertrsquos opinion

1113957AW 1113874W1a11 + W2a21 W1a12 + W2a22 W1a12

+W2a23 W1a13 + W2a241113875

(12)

(4) After the aggregated fuzzy numbers are determinedthe centroid index method (equation (13)) is used tohandle the fuzzy numbers and obtain the fuzzyprobability score (FPS) [36]

X 1113938g(x)x dx

1113938g(x)dx (13)

where X is the defuzzified output g(x) is themembership function and x is the output variableAssume 1113957An (an1 an2 an3) a triangular number and1113957An (an1 an2 an3) a trapezoidal number e FPS iscalculated via equation (14) when a fuzzy number is atriangular number and via equation (15) when thefuzzy number is a trapezoidal number

FPS 13

an1 + an2 + an3( 1113857 (14)

FPS 13

an3 + an4( 11138572 minus an3an4 minus an1 + an2( 1113857

2+ an1an2

an3 + an4 minus an1 minus an2( 1113857

(15)

10 Advances in Civil Engineering

(5) Finally the FPS is converted to FFR via equation(16) [37] and the FFR is further converted tothe occurrence probability of environmentalfailure operational error and multiple failures(equation (8))

FFR

110k

FPSne 0

0 FPS 0

k 2301 times(1minus FPS)

FPS1113890 1113891

13

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(16)

4 Results

41 Analysis of Excessive Surface Settlement inNormal TunnelExcavation Figure 8 shows that the normal excavation

(1) If the logical relationship is AND between events the TE occurs when all events occur The probability of TE can be calculated from the following equation

(A)

(2) If the logical relationship is OR between events the TE occurs when any of the event occurs The probability of TE can be calculated from the following equation

(B)

(3) By definition in the FT analysis the probability of TE is the same as that of LE Similarly the probability of the initial event (IE) in the ET analysis is the same as that of LE The probability of OE in ET analysis can be calculated from the following equation

(C)

(4) The BN an inference method based on the Bayes theorem combines both graph theory and probability theory

(D)

FTE = i=1

nFBEi

FTE = 1 ndashi=1

n(1 ndash FBEi)

FOEn = FIE middot i=1

nP (Ei = 0) middot

j=1

nP (Ej = 1)

P(B | A) = P(A | B) middot P(B)

P(A)

(a)

(1) The Birnbaum measure (BM) whichdetermines the increment of the occurrenceprobability of TE when BE occurs is shownin the following equation

(E)

where P(TE | BE = 1) denotes the occurrence probability of TE when BE occurs and P(TE | BE = 0) denotes the occurrence probability of TE when BE does not occur

(2) Risk achievement worth (RAW) evaluatesthe impact of BE on TE when the probabilityof BE is considered The RAW is adjustedby the probability of TE and BE as shown inthe following equation

(F)

where P(BE) denotes the occurrence probability of BE and P(TE) denotes the occurrence probability of TE under all circumstances

(3) The FussellndashVesely (FV) importance which describes the contribution of BE to system fault is shown in the following equation

IBBE

M = P(TE | BE = 1) ndash P(TE | BE = 0)

IRB

AE

W = IBBE

M middot P(BE)P(TE)

(G)

P(TE) ndash P(TE | BE = 0)P(TE)

IFB

VE =

(b)

Figure 7 Bow-tie-Bayesian network analysis Calculation of (a) event probability and (b) importance measures

Table 7 Weight scores for experts

Factor Category Score

Age (a)

lt30 130ndash39 240ndash49 3ge50 4

Education (b)

High school 1College 2Bachelor 3Master 4PhD 5

Work experience (c)

lt5 years 15ndash10 years 211ndash20 years 321ndash30 years 4ge30 years 5

Position (d)

Worker 1Technician 2

Junior scholarengineer 3Senior scholarengineer 4

Table 8 Rank value of each category

Classified occurrence probability Rank valueNonoccurrence 0Absolute low 01Very low 02Low 03Fairly low 04Medium 05Fairly high 06High 07Very high 08Absolute high 09Occurrence 10

Advances in Civil Engineering 11

phase involves the environment TBM operation supervi-sion management and emergency handling Risk analysis ofthe ldquonormal excavation phaserdquo in soft soil engineering basedon the XWS allows the identification of potential risk factorsthat may trigger surface settlement and consequently lead toaccidents Eskesen et al have described three principles forrisk analysis as follows (1) eliminate risk factors that are easyto detect and can be controlled timely and effectively (2)eliminate risk factors with low occurrence probability andno catastrophic consequences and (3) combine risk factorswith similar loss consequences [38] Accordingly the riskfactors during shield tunneling were organized into three

basic categories improper control of excavation parameters(eg poor control of face pressure) catastrophic geology (egground cavity or flow sand) and unforeseeable factors (egsegment damage) Figure 9 shows the bow-tie model builtfrom the categorized factors for the risk of surface collapsecaused by excessive surface settlement during shield tun-neling OEs of various degrees were successfully predictedbased on the CEs (Figure 9) Many risk factors exist in anygiven surface collapse In this section based on the previouscalculation results in Section 31 we selected the manageableshield excavation parameters (shield total thrust groutingpressure cutter head torque soil pressure etc) in the ldquonormal

Synchronousgrouting

ExcavationSegment

installationAttitudecontrol Tail sealing

Excavationcycle

Quality controlacceptance

Dangeroussituation exists Yes

Prepareemergencymeasures

Emergencymeasures

Execution of emergencymeasures

Acceptance ofexcavationprocedures

Excavationacceptance

report

Monitoring measurements

Monitored dataof excavationenvironment

Formation geologyTBM parametersExcavation axis

Segment installationSynchronous grouting

TBM construction parameter

No

TBM parametersv (mmmm) F (kN) PN (kPa)

MT (kNmiddotm) PG (kNmiddotm)TBM attitude TBM position TBM fault information

Soil bodyparameters

Soil evolutionmodel

Confined waterObstacles

Ground cavity orquicksand

Metro tunnel excavation

Emergencyhandling

Supervision

TBMoperation

TBM

Environment

Management

Figure 8 System diagram of the ldquonormal excavation phaserdquo

12 Advances in Civil Engineering

excavation phaserdquo as the base events assigning their weightsaccording to Section 33 and then performed PSA analysis

As mentioned earlier the ldquonormal excavation phaserdquo isunder the influence of excavation parameters catastrophicgeology and unforeseeable factors Surface settlement canoccur once the condition deteriorates Here we set excessivesurface settlement as the TE in the FT analysis Meanwhilethe tunneling system has a built-in emergency managementsystem Upon excessive surface settlement the emergencymanagement system will start to shut down the TBM timelyHence in the ETanalysis the excessive surface settlement isset as the IE and TBM shutdown is set as the CE OEs ofvarious degrees are obtained based on the considered CEFinally the surface settlement is set as the LE to connect theFT and the ET and furnish the BTmodel (Figure 9 Table 9)Eight OEs of various degrees were predicted based on theCEs including surface collapse events OE3 OE4 OE6 OE7and OE8 (Figure 9 Table 10) e TBM shuts down if CE1occurs and continues to operate if otherwise

e BN-BT model for excessive surface settlement isconstructed by mapping the FT and ET analyses in the BT(Figure 9) model to BN (Figure 10) All the nodes of BN havepreviously been described in the BT except the node OEwhich is the consequence node OE is added to accommodatethe outcomes of BT By connecting the node of excessivesurface settlement to OE another state also called the safe

state is added to the state set It includes consequences OE1 toOE8 to account for the nonoccurrence of the top event iewhen excessive surface settlement controlled To show thedependence among the safety barriers and the top eventcausal arcs are also drawn between TBM shutdown andgrouting in the settlement area and bentonite injection to soilchamber and TBM shield It is worth noting that since variouscombinations of the failure and success of the sequentialsafety barriers result in different consequences in the BT allthe safety nodes of BN are connected to node OE

42 Determination of Event Occurrence Probability emaximum surface settlement that resulted from the aber-ration of the ith TBM parameter is denoted as δmaxi eprobability of safety accident becomes higher when δmaxiapproaches the permitted surface settlement δi Whenδmaxi δi the accident will occur as soon as the TBM pa-rameter gives rise to a surface settlement of δmaxi eprobability of equipment fault for the normal excavationsystem was calculated via equation (8) from the engineeringlog data of the XWS over 179 days of construction (715segments rings in total) e construction of all 715 rings fellwithin the ldquonormal excavation phaserdquo as was defined by thefuzzy statistical test (v 20ndash44mmmin) Table 11 lists thecalculation results

X3X2X1

OR

M1

X7X6X5X4

OR

M2

X10X9 X11 X13X12

M3

OR

Excessive surface

settlement

X8

Caus

esLE

CE1

CE2

CE3

Con

sequ

ence

sSt

op

TBM

Gro

utin

g in

settl

emen

tar

ea

Bent

onite

inje

ctio

n

OE 1

OE 2

OE 3

OE 4

OE 5

OE 6

OE 7

OE 8

Success Failure

AND

Figure 9 Diagram of bow-tie analysis for excessive surface settlement

Advances in Civil Engineering 13

To address the uncertainty regarding the events ofenvironmental failure operational error and multiplefailure six domain experts who participated in the con-struction of the Wuhan metro system including two seniorengineers one senior academic professor one technicalconsultant one junior engineer and one worker wereinvited to evaluate the occurrence probability of events thatcannot be readily derived from existing data (Table 12)eweights of their opinion were then calculated by usingequations (9) and (10) and the distribution of each opinionweight is shown in Figure 11

In addition Table 13 lists the expert opinions regardingthe events of environmental failure operational error andmultiple failures in the form of fuzzy numbers based onTable 8 e fuzzy numbers were aggregated via equations(12) and converted to FPS and FFR via equations (13)ndash(16)(Table 14) e occurrence probabilities were finally derivedfrom FFR (Table 14) Generally the expert knowledge isconsidered as a scarce resource which cannot provide

universal consultation or real-time guidance us there ismuch room to improve the data use efficiency

43 Update in Occurrence Probability of LE and OE eoccurrence probability of basic events is calculated as de-scribed in Section 42 including the occurrence probabilityof facility failure from the engineering log data of the XWS aswell as that of environmental failure operational error andmultiple failures derived from expert opinion e occur-rence probability of excessive surface settlement (LE) isdetermined via equations (A) and (B) by considering thelogical relationship between events in Figure 7 Finally theoccurrence probability of OEs including surface collapse canbe calculated via equation (C) in the figure by mapping theFT and ET analyses in the BTmodel to BN Figure 12 showsthe occurrence probabilities of the LE (ie excessive surfacesettlement) and that of the OEs

e above analysis shows that the occurrence probabilityof excessive surface settlement within one year is 08299(Figure 12) is occurrence probability of surface collapse(OE3 OE4 OE6 OE7 and OE8) may be decreased whenemergency measures are put in place including grouting insettlement area and bentonite injection to soil chamber andTBM shield However these measures cannot help to reduceminor accidents since the occurrence probability remains athigh levels for OE1 OE2 and OE5 Admittedly grouting andbentonite injection are necessary measures and they candecrease the effects of excessive surface settlement duringshield tunneling However the key point of avoiding outcomeevents including surface collapse to ensure project safety is toprevent the excessive surface settlement from occurring in thefirst place Hence we sought to determine the key nodesleading to excessive surface settlement via BT-BN analysis andpropose the corresponding preventive measures

Table 10 Analysis of event occurrence

Symbol EventOE1 Excessive surface settlement

OE2Grouted cutter head and shield excessive surface

settlement and minor property damageOE3 Minor surface collapse and property damage

OE4Moderate surface collapse major property damage

and minor casualtiesOE5 Excessive surface settlement

OE6Grouted cutter head and shield moderate surface

collapse and minor property damage

OE7Moderate surface collapse and major property

damage

OE8Severe surface collapse major property damage and

major casualties

Table 9 Details of bow-tie components in Figure 9

Event Symbol Logic link type Failure modelGround settlement Excessive surface settlement OR gate mdashCatastrophic geology M1 OR gate mdashUnforeseeable factors M2 OR gate mdashExcavation parameters M3 AND gate mdashConfined water X1 mdash Environmental failureGround cavity or flow sand X2 mdash Environmental failureObstacles X3 mdash Environmental failureSegment damage X4 mdash Operational errorAbnormal TBM shutdown X5 mdash Multiple failureSeal failure at shield tail X6 mdash Multiple failureExcessive deviation from axis X7 mdash Operational errorEquipment failure X8 mdash Multiple failureUntimely grouting X9 mdash Facility failureExcessive cutter head torque X10 mdash Facility failureImproper control of face pressure X11 mdash Facility failureExcessive thrust X12 mdash Facility failureImproper control of excavation speed X13 mdash Facility failureTBM shutdown CE1 mdash Multiple failureGrouting in settlement area CE2 mdash Multiple failureBentonite injection to soil chamber and TBM shield CE3 mdash Multiple failure

14 Advances in Civil Engineering

Table 11 Probability of equipment fault

Event Surface settlementδmaxi (mm)

Permitted surfacesettlement δi (mm)

Value of TBMparameter

Occurrence rate(dminus1)

Occurrence probability(in 1 year)

X9 89 15 302 kPa 10675eminus 04 382eminus 02X10 84 10 2974 kNmiddotM 17792eminus 04 629eminus 02X11 86 15 143 kPa 71167eminus 05 256eminus 02X12 98 15 13100 kN 14233eminus 04 506eminus 02X13 120 15 41mmmin 28467eminus 04 987eminus 02All data were obtained from the operation log of the XWS

Table 12 Characteristics of experts participated in the occurrence probability evaluation

Expert Age Education Service (years) Professional position1 56 High school 25 Worker2 35 Master 10 Technician3 41 Master 15 Junior engineer4 47 Bachelor 20 Senior engineer5 50 PhD 18 Senior academic6 59 PhD 30 Senior engineer

0125 0125

01625 01625

020225

AgeEducationService

Professional positionWeighting

2 3 4 5 61Expert

0

005

01

015

02

025

Wei

ghtin

g

0

1

2

3

4

5

6

Wei

ghtin

g sc

ore

Figure 11 Distribution of each expert opinion weight

X1 X2 X3

M1

X5 X6 X7 X8

M2

X9 X11

M3

Excessive surface

settlement

X10 X12 X13X4

CE1 CE2 CE3

OE

Caus

esLE

CEC

onse

quen

ces

Figure 10 Bow-tie chart of excessive surface settlement

Advances in Civil Engineering 15

44 Identify Key Nodes and Provide Safety Measures Inorder to find the key nodes leading to excessive surfacesettlement the importance measure of each event was cal-culated via equations (E)ndash(G) in Figure 7 as shown inTable 15 Assume the number of events as ldquonrdquo e nor-malized weight Rlowast could be calculated from the importancemeasure Ii via the following equation

Rlowast

Ii

1113936ni1Ii

times 100 (17)

After the normalized weight Rlowast is calculated for eachimportance measure the total weight Rlowast could be calculatedvia equation (18) e total weight Rlowast of events was finally

ranked in descending order to find the key nodes as shownin Table 16

Rlowast R

lowastBM + R

lowastRAW + R

lowastFV (18)

It can be seen that X6 (seal failure at shield tail) X1(confined water) X2 (ground cavity or flow sand) X5 (ab-normal TBM shutdown) and X7 (excessive deviation fromaxis) have far higher weight than other events and are thusthe key nodes to accidents related to excessive surface set-tlement Measures can be taken to particularly ensure safetyat these nodes e occurrence probability of excessivesurface settlement can be reduced by 66 when X6 X1 X2X5 and X7 are ensured safe (Figure 13)

Table 13 Expert opinion on environmental failure operational error and multiple failures

Event Fuzzy numbers proposed by each expert

X1

Expert 1 Expert 2 Expert 3(02 03 04 05) (01 02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 02 03 05)

X2

Expert 1 Expert 2 Expert 3(01 02 03 05) (02 03 04) (01 02 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (02 03 05) (01 02 03 05)

X3

Expert 1 Expert 2 Expert 3(01 02 04 05) (01 02 03 05) (01 03 04)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03) (01 02 03)

X4

Expert 1 Expert 2 Expert 3(02 03 04 05) (01 02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(02 03 04) (02 03 05) (01 02 03 05)

X5

Expert 1 Expert 2 Expert 3(01 03 04) (01 02 03 05) (02 03 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (02 03 05) (01 02 03)

X6

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 03 05) (02 03 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (02 03 05) (01 02 04 05)

X7

Expert 1 Expert 2 Expert 3(01 02 04 05) (01 02 03 05) (02 03 04)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 03 05)

X8

Expert 1 Expert 2 Expert 3(01 03 04 05) (01 02 03 04) (02 03 04)

Expert 4 Expert 5 Expert 6(02 03 04) (01 02 03 05) (01 02 03)

CE1

Expert 1 Expert 2 Expert 3(02 03 04 05) (02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 02 04 05)

CE2

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 05) (02 03 04 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (01 02 03 05) (01 03 05)

CE3

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 03 05) (03 04 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (01 02 04 05) (01 02 03 05)

16 Advances in Civil Engineering

In accordance with the predictive and diagnosticanalysis results using the established model some safetymeasures for key nodes are displayed in time to reduce theexcessive surface settlement risk during the tunnelexcavation

(1) e nodes X5 (abnormal TBM shutdown) and X7(excessive deviation from the axis) mostly involveoperational error Safety management and supervi-sion need to be strengthened at the construction siteto eliminate such errors and ensure that the TBM isoperated properly Besides an advanced real-time

laser locator may help to alarm in the case of largeaxial deviation

(2) e nodes X1 (confined water) and X2 (ground cavityor flow sand) belong to environmental failure Inorder to reduce the influence of environmental failurecareful geological exploration should be carried outbefore tunneling to identify the poor geological and

Table 14 Calculation of FPS FFR and the occurrence probability of environmental failure operational error and multiple failures

Event Aggregated fuzzy numbers FPS FFR (dminus1) Failure probability (in 1 year)X1 (01288 02288 03288 04838) 02951 83969eminus 04 26402eminus 1X2 (01325 02325 03163 04713) 02909 80032eminus 04 25336eminus 1X3 (01000 02163 02700 03825) 02420 42986eminus 04 14518eminus 1X4 (00450 00900 01125 01800) 01082 22492eminus 05 81803eminus 3X5 (01363 02488 02775 04263) 02747 66022eminus 04 214155eminus 1X6 (01488 02488 03225 04713) 03004 89125eminus 04 27770eminus 1X7 (01163 02388 03125 04675) 02855 75157eminus 04 24002eminus 1X8 (01450 02538 02950 03100) 02463 45643eminus 04 15338eminus 1CE1 (01413 02413 03513 04838) 03058 94598eminus 04 29202eminus 1CE2 (01288 02513 03038 04713) 02916 80679eminus 04 25496eminus 1CE3 (01450 02450 03363 04713) 03010 89722eminus 04 27937eminus 1

08299

03155

01223 010800419

01301

00504 00445 00173

Occ

urre

nce p

roba

bilit

y (in

1 y

ear)

00

01

02

03

04

05

06

07

08

09

OE1 OE2 OE3 OE4 OE5 OE6 OE7 OE8LE

Figure 12 Occurrence probability of surface settlement and otheroutcome events

Table 15 Calculation of importance measure of influential factors

SymbolImportance measure

BM RAW FVX1 2311eminus 1 7352eminus 02 7352eminus 02X2 2279eminus 1 6958eminus 02 6958eminus 02X3 1990eminus 1 3481eminus 02 3481eminus 02X4 1716eminus 1 1691eminus 03 1691eminus 03X5 2165eminus 1 5587eminus 02 5587eminus 02X6 2356eminus 1 7884eminus 02 7884eminus 02X7 2239eminus 1 6476eminus 02 6476eminus 02X8 2010eminus 1 3715eminus 02 3715eminus 02X9 1370eminus 6 6306eminus 08 6306eminus 08X10 8300eminus 7 6291eminus 08 6291eminus 08X11 2040eminus 6 6293eminus 08 6293eminus 08X12 1030eminus 6 6280eminus 08 6280eminus 08X13 5300eminus 7 6303eminus 08 6303eminus 08

Table 16 Ranking results of the key events

Rank SymbolNormalization weighting (Rlowast) Total

weighting(Rlowast)

RlowastBM RlowastRAW RlowastFV

1 X6 13805 18942 18942 516892 X1 13541 17664 17664 488693 X2 13354 16717 16717 467884 X7 13120 15559 15559 442385 X5 12686 13423 13423 395326 X8 11778 8926 89255 296297 X3 11661 8363 8363 283878 X4 10055 0406 0406 108689 X11 00002 1512eminus 05 1512eminus 05 1498eminus 0410 X9 8028eminus 05 1515eminus 05 1515eminus 05 1106eminus 0411 X12 6035eminus 05 1509eminus 05 1509eminus 05 9053eminus 0512 X10 4863eminus 05 1511eminus 05 1511eminus 05 7886eminus 0513 X13 3106eminus 05 1514eminus 05 1514eminus 05 6134eminus 05Total 100 100 100 100

02822

01073

00416 0036700142

0044200172 00151 00059

Occ

urre

nce p

roba

bilit

y (in

1 y

ear)

000

005

010

015

020

025

030

OE1 OE2 OE3 OE4 OE5 OE6 OE7 OE8LE

Figure 13 Occurrence probability when safety is ensured at keynodes

Advances in Civil Engineering 17

hydrological conditions that may be encounteredDuring excavation the advanced geological pre-diction technologymay be employed to detect adversegeological and hydrological conditions ahead of theTBM in real time including confined water groundcavity and flow sand

(3) Node X6 (seal failure at shield tail) belongs tomultiple failures e quality of the tail brush needsto be enhanced and tail brush should promptly bereplaced when it is worn

By adopting corresponding safety measures in shieldtunnel excavation the occurrence probability of variousdegrees of surface collapse (OE3 OE4 OE6 OE7 and OE8)was significantly decreased (Figure 13) Finally the TBMssuccessfully passed through the left track of DCS on March3 2017 and the right track on June 11 2017 without anysurface collapse accident demonstrating the effectiveness ofour proposed hybrid method

5 Conclusions and Future Works

In this work we first defined the ldquonormal excavation phaserdquoof shield tunneling based on the fuzzy statistical test theoryData were extracted from the construction log of the XWS inthe Wuhan metro line 7 to determine the occurrenceprobability of facility fault and expert opinions were soli-cited to determine the occurrence probability of environ-mental failure operational error and multiple failuresProbabilistic safety assessment (PSA) of the normal shieldtunnel excavation system was then performed accordingly

We employed the bow-tie analysis to evaluate the oc-currence of excessive surface settlement during normaltunnel excavation e presence of emergency measurescould reduce the occurrence probability of surface collapsecaused by excessive surface settlement (OE3 OE4 OE6 OE7and OE8) but have limited effect on the prevention of ac-cidents of OE1 OE2 and OE5 It is essential to decrease theprobability of excessive surface settlement in order to pre-vent the resulting outcome events (OEs)

By mapping the bow-tie analysis to Bayesian networks(ie BT-BN analysis) we determined the key nodes thatcould cause excessive surface settlement (LE) e key nodesincluded the following X6 (seal failure at shield tail) X1(confined water) X2 (ground cavity or flow sand) X5 (ab-normal TBM shutdown) and X7 (excessive deviation fromthe axis) Effective safety measures at these nodes couldreduce the occurrence probability of excessive surface set-tlement (LE) by 66

To ensure safety careful geological exploration shouldbe carried out before the tunneling project During thetunneling safety management and supervision should bestrengthened at the construction site Advanced geo-logical prediction technology should be used to detectpoor geological and hydrological conditions ahead of theTBM in real time Advanced laser locator should be usedto monitor and alarm excessive axial deviation equality of the tail brush should be improved and tailbrush should be replaced timely when it becomes worn

e occurrence probability of excessive surface settlementwas decreased by adopting these safety measures and theoccurrence of the resulting surface collapse was sub-sequently decreased

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

e authors thank the workers foremen and safety co-ordinators of the main contractors for their participatione authors also wish to thank the engineers Yun Zhang andPeilun Tu for assistance in gathering field data

References

[1] T Zhao W Liu and Z Ye ldquoEffects of water inrush fromtunnel excavation face on the deformation and mechanicalperformance of shield tunnel segment jointsrdquo Advances inCivil Engineering vol 2017 Article ID 5913640 9 pages 2017

[2] W Liu T Zhao W Zhou and J Tang ldquoSafety risk factors ofmetro tunnel construction in China an integrated study withEFA and SEMrdquo Safety Science vol 105 pp 98ndash113 2018

[3] K Li ldquoHangzhou metro site collapse accidentrdquo 2008 httpnewssohucom20081115n260653551shtml

[4] S Liu ldquoConstruction of Nanchang metro line 2 constructionsection pavement collapsesrdquo 2017 httpnewssohucom20160514n449414512shtml

[5] R B Peck ldquoDeep excavations and tunneling in soft groundrdquo7th International Conference on Soil Mechanics and Foun-dation Engineering vol 7 no 3 pp 225ndash290 1969

[6] P B Attewell I W Farmer and N H Glossop ldquoGrounddeformation caused by tunnelling in a silty alluvial clayrdquoGround Engineering vol 11 no 8 pp 32ndash41 1978

[7] W J Rankin ldquoGround movements resulting from urbantunnelling predictions and effectsrdquo Geological Society Lon-don Engineering Geology Special Publications vol 5 no 1pp 79ndash92 1988

[8] P B Attewell and J P Woodman ldquoPredicting the dynamicsof ground settlement and its derivatives caused by tunnelingin soilrdquo Ground Engineering vol 15 no 8 pp 13ndash20 1982

[9] M P OrsquoReilly and B M New ldquoSettlement above tunnels inthe United Kingdommdashtheir magnitude and prediction intunnelling 82 proceedings of the 3rd international sympo-sium brighton 7ndash11 June 1982 P173ndash181 Publ LondonIMM 1982rdquo International Journal of Rock Mechanics ampMining Sciences amp Geomechanics Abstracts vol 20 no 1pp 1ndash18 1983

[10] R J Mair R N Taylor and A Bracegirdle ldquoSubsurfacesettlement profiles above tunnels in claysrdquo Geotechniquevol 45 no 2 pp 361-362 1995

[11] X L Yang and J MWang ldquoGroundmovement prediction fortunnels using simplified procedurerdquo Tunnelling and Un-derground Space Technology vol 26 no 3 pp 462ndash471 2011

18 Advances in Civil Engineering

313 Fuzzy Statistical Tests of Excavation Parameterse excavation speed of the TBM reflects the influenceexerted by the excavation parameters (eg total thrust facepressure and cutter head torque) on the force and dis-placement of the surrounding soil erefore it is necessaryto determine the realistic and practical excavation param-eters based on the excavation speed

Formation reinforcement during TBM launching and TBMarrival can exert a strong influence on the shield tunnel ex-cavation and lead to highly discrete parameters erefore thedata from the TBM launching and TBM arrival stages werediscarded in studying the relationship between excavation speedand TBMparameters Figure 6 shows how the TBMparametersvaried with the excavation speed during the construction of the715 segments in the XWSe curves were fitted viaMATLABand the slope of the curves was highly indicative of the cor-relation between the TBMparameters and the excavation speed

In Figure 6(a) the total thrust (F) increased with risingexcavation speed is was because bentonite was used as alubricant and injected around the shield of the TBM duringexcavation to reduce friction When the amount of injectedbentonite was appropriate the friction coefficient betweenthe shield and the surrounding soil would decrease and theexcavation speed would then increase when the thrust (F)was higher In Figure 6(b) the excavation speed decreasedwhen the cutter head torque (MT) increased is wasbecause when the soil body of the tunneling face wasrelatively difficult to cut a larger torque of the cutter headwould be needed and the excavation speed would decreaseFigure 6(c) shows that during normal excavation thepressure of the tunneling face increased slightly with risingexcavation speed Besides Mair pointed out that duringsegment assembly the downtime of TBM would decreasethe soil and water pressure on the tunneling face whichcould reduce the control pressure of the tunneling face [33]e same pattern was observed in the current constructionlogs and the R2 value of the curve in Figure 6(c) was hencerelatively low Figure 6(d) shows that the grouting pressuredecreased slightly with rising excavation speed However

since the pressure of primary grouting was read off from thegrouting pressure pump the actual grouting pressureexerted on the surrounding soil was smaller and theprimary grouting pressure hence had limited impact onexcavation speed

(1) Determination of Standard TBM Parameters It wasdetermined from the fuzzy statistical tests above that thestandard excavation speed was 32mmmin e corre-sponding standard TBM parameters could be determinedaccordingly from the following equation

TBMPstandard value 1113936

Nn1TBMPnv

N v321113868111386811138681113868 (6)

where TBMP is the TBM parameter and v is the excavationspeed (mmmin)

(2) Determination of the Range of TBM Parameters It wasdetermined from the fuzzy statistical tests above that therange of excavation speed was 20ndash44mmmin e corre-sponding boundaries of TBM parameters could be de-termined from the extreme values in the monitoring records(Figure 6) via the following equation

TBMPupper limit max TBMPv 20levle4411138681113868111386811138681113966 1113967

TBMPlower limit min TBMPv 20levle4411138681113868111386811138681113966 1113967

(7)

(3) ldquoNormal Excavation Phaserdquo of TBM According to thefuzzy set theory the excavation speed in the ldquonormal ex-cavation phaserdquo fell within 20ndash44mmmin e TBM wasconsidered to be in the ldquonormal excavation phaserdquo whenthe excavation speed and the TBM parameters all fellwithin the prescribed ranges specified above and listedagain in Table 6 e standard values and ranges were usedfurther in the subsequent PSA analysis Table 6 shows thatamong the examined parameters the face pressure had adeviation interval of merely 196 and was controlled the

Advance speed v (mmmin)

Mem

bers

hip

Atilde (v

)

Cov

erag

e fre

quen

cy A

(v)

04

02

06

08

1

10090807060504030201000

04

02

06

08

1

0

Fuzzy statistical experiment methodCauchy distribution curve

Figure 5 e histogram of membership frequency and the membership function of TBM excavation speed

8 Advances in Civil Engineering

best whereas the cutter head torque had a deviation in-terval of 7401 and was controlled the worst

(4) Statistical Relationship between TBM Parameters andExcavation Speed e monitoring results in Figure 6

demonstrated that in the ldquonormal excavation phaserdquo ofthe XWS the total thrust and the face pressure were posi-tively correlated with the excavation speed In particular thetotal thrust had a stronger correlation to the excavationspeed than the face pressure In contrast the cutter head

2000400060008000

1000012000140001600018000

Tota

l thr

ust

F (k

N)

20 25 30 35 40 45 50 55 60 6515Advance speed v (mmmin)

(a)

0500

10001500200025003000350040004500

Cutte

r hea

d to

rque

MT

(kNlowast

m)

20 25 30 35 40 45 50 55 60 6515Advance speed v (mmmin)

(b)

0

50

100

150

200

250

Face

pre

ssur

eP N

(kPa

)

20 25 30 35 40 45 50 55 60 6515Advance speed v (mmmin)

(c)

Gro

utin

g pr

essu

reP G

(kPa

)

100150200250300350400450500550

20 25 30 35 40 45 50 55 60 6515Advance speed v (mmmin)

(d)

Figure 6 Variations in the TBM parameters at different excavation speeds (data from XW section) (a) total thrust versus excavationspeed (b) cutter head torque versus excavation speed (c) face pressure versus excavation speed (d) grouting pressure versus excavationspeed

Table 6 Standard values and ranges of excavation speed and TBMPs

Factors v (mmmin) F (kN) P N (kPa) M T (kNmiddotm) P G (kPa)Parameter range [20 44] [8300 13100] [117 143] [1294 2974] [197 302]Standard value 32 9700 1326 2270 302Deviation range () [minus375 375] [minus1443 3505] [minus1176 784] [minus430 3101] [minus3477 0]

Advances in Civil Engineering 9

torque and the primary grouting pressure were negativelycorrelated with the excavation speed

32 Bow-Tie-Bayesian Network Analysis e bow-tie anal-ysis combines FTand ETanalysese FTanalysis in bow-tiecalculates the occurrence probability of the loss event (LE) aswell as the top event (TE) e occurrence probability of theTE can also be obtained from the occurrence probability ofthe basic event (BE) e events could be evaluated by theirlogical relationship and their occurrence probability in theBN Mapping the bow-tie analysis to BN involves convertingboth FT and ET analyses Figure 7(a) provides a brief de-scription of calculation steps

ree importance measures described in the followingBorst and Schoonakker [30] were introduced in the newmethodology according to the Bayes theorem Figure 7(b)gives a brief description of their calculation In the proposedmethodology the critical nodes that could more easilytrigger accidents were obtained by calculating these im-portance measures

33 Confirming Failure Occurrence Probability e BT-BNanalysis requires knowing the occurrence probability of eachbasic event (BE) e basic events fall into four categoriesenvironmental failure operational error multiple failuresand facility failures e occurrence rate of facility failureswas obtained from the construction log of the XWS for thetunneling project that spanned 179 days (715 segments intotal) and was converted into occurrence probability via thefollowing equation

F 1minus eminusλt

(8)

where F denotes the occurrence probability of the failure andλ denotes the occurrence rate of the failure

e occurrence probability of environmental failureoperational error and multiple failures cannot be readilyderived from existing data and was thus estimated via expertopinione fuzzymethod combines the opinions of differentexperts in a weighted manner to calculate the fuzzy fault rate(FFR) from the triangular fuzzy numbers or trapezoidal fuzzynumbers proposed by the experts e occurrence probabilityof environmental failure operational error and multiplefailures was then determined from the FFR [34] e generalprocedure of the fuzzy method is as follows

(1) Determine the weight of the opinion of each expertbased on the age education background work ex-perience and position of the consulted expert (Ta-ble 7) e crude weight score of each expert iscalculated via the following equation

Sn Sna+ Snb

+ Snc+ Snd

(9)

where Sn represents the total weight score of theexpert e relative weight score of each expert iscalculated via the following equation

Wn Sn

1113936mn1Sn

(10)

where m represents the number of experts(2) e occurrence probability is divided into the

following categories nonoccurrence absolute lowvery low low fairly low medium fairly high highvery high absolute high or occurrence e rankvalue of the categories escalates from 0 for non-occurrence to 1 for the occurrence (Table 8) eoccurrence probability of the event is then evalu-ated based on the corresponding triangular numberor trapezoidal number given by the experts

(3) Aggregation of the fuzzy numbers When the fuzzynumbers are all triangular number or trapezoidalnumber the aggregated fuzzy numbers of an event iscalculated via equation (11) [35] e aggregatedfuzzy number considering the expert weight isshown in equation (12)

1113957Aaggregated 1113944m

n1Wn otimes 1113957An (11)

where 1113957Aaggregated represents the aggregated fuzzifiednumber given by expert m and Wn represents theweight of the expertrsquos opinion

1113957AW 1113874W1a11 + W2a21 W1a12 + W2a22 W1a12

+W2a23 W1a13 + W2a241113875

(12)

(4) After the aggregated fuzzy numbers are determinedthe centroid index method (equation (13)) is used tohandle the fuzzy numbers and obtain the fuzzyprobability score (FPS) [36]

X 1113938g(x)x dx

1113938g(x)dx (13)

where X is the defuzzified output g(x) is themembership function and x is the output variableAssume 1113957An (an1 an2 an3) a triangular number and1113957An (an1 an2 an3) a trapezoidal number e FPS iscalculated via equation (14) when a fuzzy number is atriangular number and via equation (15) when thefuzzy number is a trapezoidal number

FPS 13

an1 + an2 + an3( 1113857 (14)

FPS 13

an3 + an4( 11138572 minus an3an4 minus an1 + an2( 1113857

2+ an1an2

an3 + an4 minus an1 minus an2( 1113857

(15)

10 Advances in Civil Engineering

(5) Finally the FPS is converted to FFR via equation(16) [37] and the FFR is further converted tothe occurrence probability of environmentalfailure operational error and multiple failures(equation (8))

FFR

110k

FPSne 0

0 FPS 0

k 2301 times(1minus FPS)

FPS1113890 1113891

13

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(16)

4 Results

41 Analysis of Excessive Surface Settlement inNormal TunnelExcavation Figure 8 shows that the normal excavation

(1) If the logical relationship is AND between events the TE occurs when all events occur The probability of TE can be calculated from the following equation

(A)

(2) If the logical relationship is OR between events the TE occurs when any of the event occurs The probability of TE can be calculated from the following equation

(B)

(3) By definition in the FT analysis the probability of TE is the same as that of LE Similarly the probability of the initial event (IE) in the ET analysis is the same as that of LE The probability of OE in ET analysis can be calculated from the following equation

(C)

(4) The BN an inference method based on the Bayes theorem combines both graph theory and probability theory

(D)

FTE = i=1

nFBEi

FTE = 1 ndashi=1

n(1 ndash FBEi)

FOEn = FIE middot i=1

nP (Ei = 0) middot

j=1

nP (Ej = 1)

P(B | A) = P(A | B) middot P(B)

P(A)

(a)

(1) The Birnbaum measure (BM) whichdetermines the increment of the occurrenceprobability of TE when BE occurs is shownin the following equation

(E)

where P(TE | BE = 1) denotes the occurrence probability of TE when BE occurs and P(TE | BE = 0) denotes the occurrence probability of TE when BE does not occur

(2) Risk achievement worth (RAW) evaluatesthe impact of BE on TE when the probabilityof BE is considered The RAW is adjustedby the probability of TE and BE as shown inthe following equation

(F)

where P(BE) denotes the occurrence probability of BE and P(TE) denotes the occurrence probability of TE under all circumstances

(3) The FussellndashVesely (FV) importance which describes the contribution of BE to system fault is shown in the following equation

IBBE

M = P(TE | BE = 1) ndash P(TE | BE = 0)

IRB

AE

W = IBBE

M middot P(BE)P(TE)

(G)

P(TE) ndash P(TE | BE = 0)P(TE)

IFB

VE =

(b)

Figure 7 Bow-tie-Bayesian network analysis Calculation of (a) event probability and (b) importance measures

Table 7 Weight scores for experts

Factor Category Score

Age (a)

lt30 130ndash39 240ndash49 3ge50 4

Education (b)

High school 1College 2Bachelor 3Master 4PhD 5

Work experience (c)

lt5 years 15ndash10 years 211ndash20 years 321ndash30 years 4ge30 years 5

Position (d)

Worker 1Technician 2

Junior scholarengineer 3Senior scholarengineer 4

Table 8 Rank value of each category

Classified occurrence probability Rank valueNonoccurrence 0Absolute low 01Very low 02Low 03Fairly low 04Medium 05Fairly high 06High 07Very high 08Absolute high 09Occurrence 10

Advances in Civil Engineering 11

phase involves the environment TBM operation supervi-sion management and emergency handling Risk analysis ofthe ldquonormal excavation phaserdquo in soft soil engineering basedon the XWS allows the identification of potential risk factorsthat may trigger surface settlement and consequently lead toaccidents Eskesen et al have described three principles forrisk analysis as follows (1) eliminate risk factors that are easyto detect and can be controlled timely and effectively (2)eliminate risk factors with low occurrence probability andno catastrophic consequences and (3) combine risk factorswith similar loss consequences [38] Accordingly the riskfactors during shield tunneling were organized into three

basic categories improper control of excavation parameters(eg poor control of face pressure) catastrophic geology (egground cavity or flow sand) and unforeseeable factors (egsegment damage) Figure 9 shows the bow-tie model builtfrom the categorized factors for the risk of surface collapsecaused by excessive surface settlement during shield tun-neling OEs of various degrees were successfully predictedbased on the CEs (Figure 9) Many risk factors exist in anygiven surface collapse In this section based on the previouscalculation results in Section 31 we selected the manageableshield excavation parameters (shield total thrust groutingpressure cutter head torque soil pressure etc) in the ldquonormal

Synchronousgrouting

ExcavationSegment

installationAttitudecontrol Tail sealing

Excavationcycle

Quality controlacceptance

Dangeroussituation exists Yes

Prepareemergencymeasures

Emergencymeasures

Execution of emergencymeasures

Acceptance ofexcavationprocedures

Excavationacceptance

report

Monitoring measurements

Monitored dataof excavationenvironment

Formation geologyTBM parametersExcavation axis

Segment installationSynchronous grouting

TBM construction parameter

No

TBM parametersv (mmmm) F (kN) PN (kPa)

MT (kNmiddotm) PG (kNmiddotm)TBM attitude TBM position TBM fault information

Soil bodyparameters

Soil evolutionmodel

Confined waterObstacles

Ground cavity orquicksand

Metro tunnel excavation

Emergencyhandling

Supervision

TBMoperation

TBM

Environment

Management

Figure 8 System diagram of the ldquonormal excavation phaserdquo

12 Advances in Civil Engineering

excavation phaserdquo as the base events assigning their weightsaccording to Section 33 and then performed PSA analysis

As mentioned earlier the ldquonormal excavation phaserdquo isunder the influence of excavation parameters catastrophicgeology and unforeseeable factors Surface settlement canoccur once the condition deteriorates Here we set excessivesurface settlement as the TE in the FT analysis Meanwhilethe tunneling system has a built-in emergency managementsystem Upon excessive surface settlement the emergencymanagement system will start to shut down the TBM timelyHence in the ETanalysis the excessive surface settlement isset as the IE and TBM shutdown is set as the CE OEs ofvarious degrees are obtained based on the considered CEFinally the surface settlement is set as the LE to connect theFT and the ET and furnish the BTmodel (Figure 9 Table 9)Eight OEs of various degrees were predicted based on theCEs including surface collapse events OE3 OE4 OE6 OE7and OE8 (Figure 9 Table 10) e TBM shuts down if CE1occurs and continues to operate if otherwise

e BN-BT model for excessive surface settlement isconstructed by mapping the FT and ET analyses in the BT(Figure 9) model to BN (Figure 10) All the nodes of BN havepreviously been described in the BT except the node OEwhich is the consequence node OE is added to accommodatethe outcomes of BT By connecting the node of excessivesurface settlement to OE another state also called the safe

state is added to the state set It includes consequences OE1 toOE8 to account for the nonoccurrence of the top event iewhen excessive surface settlement controlled To show thedependence among the safety barriers and the top eventcausal arcs are also drawn between TBM shutdown andgrouting in the settlement area and bentonite injection to soilchamber and TBM shield It is worth noting that since variouscombinations of the failure and success of the sequentialsafety barriers result in different consequences in the BT allthe safety nodes of BN are connected to node OE

42 Determination of Event Occurrence Probability emaximum surface settlement that resulted from the aber-ration of the ith TBM parameter is denoted as δmaxi eprobability of safety accident becomes higher when δmaxiapproaches the permitted surface settlement δi Whenδmaxi δi the accident will occur as soon as the TBM pa-rameter gives rise to a surface settlement of δmaxi eprobability of equipment fault for the normal excavationsystem was calculated via equation (8) from the engineeringlog data of the XWS over 179 days of construction (715segments rings in total) e construction of all 715 rings fellwithin the ldquonormal excavation phaserdquo as was defined by thefuzzy statistical test (v 20ndash44mmmin) Table 11 lists thecalculation results

X3X2X1

OR

M1

X7X6X5X4

OR

M2

X10X9 X11 X13X12

M3

OR

Excessive surface

settlement

X8

Caus

esLE

CE1

CE2

CE3

Con

sequ

ence

sSt

op

TBM

Gro

utin

g in

settl

emen

tar

ea

Bent

onite

inje

ctio

n

OE 1

OE 2

OE 3

OE 4

OE 5

OE 6

OE 7

OE 8

Success Failure

AND

Figure 9 Diagram of bow-tie analysis for excessive surface settlement

Advances in Civil Engineering 13

To address the uncertainty regarding the events ofenvironmental failure operational error and multiplefailure six domain experts who participated in the con-struction of the Wuhan metro system including two seniorengineers one senior academic professor one technicalconsultant one junior engineer and one worker wereinvited to evaluate the occurrence probability of events thatcannot be readily derived from existing data (Table 12)eweights of their opinion were then calculated by usingequations (9) and (10) and the distribution of each opinionweight is shown in Figure 11

In addition Table 13 lists the expert opinions regardingthe events of environmental failure operational error andmultiple failures in the form of fuzzy numbers based onTable 8 e fuzzy numbers were aggregated via equations(12) and converted to FPS and FFR via equations (13)ndash(16)(Table 14) e occurrence probabilities were finally derivedfrom FFR (Table 14) Generally the expert knowledge isconsidered as a scarce resource which cannot provide

universal consultation or real-time guidance us there ismuch room to improve the data use efficiency

43 Update in Occurrence Probability of LE and OE eoccurrence probability of basic events is calculated as de-scribed in Section 42 including the occurrence probabilityof facility failure from the engineering log data of the XWS aswell as that of environmental failure operational error andmultiple failures derived from expert opinion e occur-rence probability of excessive surface settlement (LE) isdetermined via equations (A) and (B) by considering thelogical relationship between events in Figure 7 Finally theoccurrence probability of OEs including surface collapse canbe calculated via equation (C) in the figure by mapping theFT and ET analyses in the BTmodel to BN Figure 12 showsthe occurrence probabilities of the LE (ie excessive surfacesettlement) and that of the OEs

e above analysis shows that the occurrence probabilityof excessive surface settlement within one year is 08299(Figure 12) is occurrence probability of surface collapse(OE3 OE4 OE6 OE7 and OE8) may be decreased whenemergency measures are put in place including grouting insettlement area and bentonite injection to soil chamber andTBM shield However these measures cannot help to reduceminor accidents since the occurrence probability remains athigh levels for OE1 OE2 and OE5 Admittedly grouting andbentonite injection are necessary measures and they candecrease the effects of excessive surface settlement duringshield tunneling However the key point of avoiding outcomeevents including surface collapse to ensure project safety is toprevent the excessive surface settlement from occurring in thefirst place Hence we sought to determine the key nodesleading to excessive surface settlement via BT-BN analysis andpropose the corresponding preventive measures

Table 10 Analysis of event occurrence

Symbol EventOE1 Excessive surface settlement

OE2Grouted cutter head and shield excessive surface

settlement and minor property damageOE3 Minor surface collapse and property damage

OE4Moderate surface collapse major property damage

and minor casualtiesOE5 Excessive surface settlement

OE6Grouted cutter head and shield moderate surface

collapse and minor property damage

OE7Moderate surface collapse and major property

damage

OE8Severe surface collapse major property damage and

major casualties

Table 9 Details of bow-tie components in Figure 9

Event Symbol Logic link type Failure modelGround settlement Excessive surface settlement OR gate mdashCatastrophic geology M1 OR gate mdashUnforeseeable factors M2 OR gate mdashExcavation parameters M3 AND gate mdashConfined water X1 mdash Environmental failureGround cavity or flow sand X2 mdash Environmental failureObstacles X3 mdash Environmental failureSegment damage X4 mdash Operational errorAbnormal TBM shutdown X5 mdash Multiple failureSeal failure at shield tail X6 mdash Multiple failureExcessive deviation from axis X7 mdash Operational errorEquipment failure X8 mdash Multiple failureUntimely grouting X9 mdash Facility failureExcessive cutter head torque X10 mdash Facility failureImproper control of face pressure X11 mdash Facility failureExcessive thrust X12 mdash Facility failureImproper control of excavation speed X13 mdash Facility failureTBM shutdown CE1 mdash Multiple failureGrouting in settlement area CE2 mdash Multiple failureBentonite injection to soil chamber and TBM shield CE3 mdash Multiple failure

14 Advances in Civil Engineering

Table 11 Probability of equipment fault

Event Surface settlementδmaxi (mm)

Permitted surfacesettlement δi (mm)

Value of TBMparameter

Occurrence rate(dminus1)

Occurrence probability(in 1 year)

X9 89 15 302 kPa 10675eminus 04 382eminus 02X10 84 10 2974 kNmiddotM 17792eminus 04 629eminus 02X11 86 15 143 kPa 71167eminus 05 256eminus 02X12 98 15 13100 kN 14233eminus 04 506eminus 02X13 120 15 41mmmin 28467eminus 04 987eminus 02All data were obtained from the operation log of the XWS

Table 12 Characteristics of experts participated in the occurrence probability evaluation

Expert Age Education Service (years) Professional position1 56 High school 25 Worker2 35 Master 10 Technician3 41 Master 15 Junior engineer4 47 Bachelor 20 Senior engineer5 50 PhD 18 Senior academic6 59 PhD 30 Senior engineer

0125 0125

01625 01625

020225

AgeEducationService

Professional positionWeighting

2 3 4 5 61Expert

0

005

01

015

02

025

Wei

ghtin

g

0

1

2

3

4

5

6

Wei

ghtin

g sc

ore

Figure 11 Distribution of each expert opinion weight

X1 X2 X3

M1

X5 X6 X7 X8

M2

X9 X11

M3

Excessive surface

settlement

X10 X12 X13X4

CE1 CE2 CE3

OE

Caus

esLE

CEC

onse

quen

ces

Figure 10 Bow-tie chart of excessive surface settlement

Advances in Civil Engineering 15

44 Identify Key Nodes and Provide Safety Measures Inorder to find the key nodes leading to excessive surfacesettlement the importance measure of each event was cal-culated via equations (E)ndash(G) in Figure 7 as shown inTable 15 Assume the number of events as ldquonrdquo e nor-malized weight Rlowast could be calculated from the importancemeasure Ii via the following equation

Rlowast

Ii

1113936ni1Ii

times 100 (17)

After the normalized weight Rlowast is calculated for eachimportance measure the total weight Rlowast could be calculatedvia equation (18) e total weight Rlowast of events was finally

ranked in descending order to find the key nodes as shownin Table 16

Rlowast R

lowastBM + R

lowastRAW + R

lowastFV (18)

It can be seen that X6 (seal failure at shield tail) X1(confined water) X2 (ground cavity or flow sand) X5 (ab-normal TBM shutdown) and X7 (excessive deviation fromaxis) have far higher weight than other events and are thusthe key nodes to accidents related to excessive surface set-tlement Measures can be taken to particularly ensure safetyat these nodes e occurrence probability of excessivesurface settlement can be reduced by 66 when X6 X1 X2X5 and X7 are ensured safe (Figure 13)

Table 13 Expert opinion on environmental failure operational error and multiple failures

Event Fuzzy numbers proposed by each expert

X1

Expert 1 Expert 2 Expert 3(02 03 04 05) (01 02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 02 03 05)

X2

Expert 1 Expert 2 Expert 3(01 02 03 05) (02 03 04) (01 02 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (02 03 05) (01 02 03 05)

X3

Expert 1 Expert 2 Expert 3(01 02 04 05) (01 02 03 05) (01 03 04)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03) (01 02 03)

X4

Expert 1 Expert 2 Expert 3(02 03 04 05) (01 02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(02 03 04) (02 03 05) (01 02 03 05)

X5

Expert 1 Expert 2 Expert 3(01 03 04) (01 02 03 05) (02 03 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (02 03 05) (01 02 03)

X6

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 03 05) (02 03 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (02 03 05) (01 02 04 05)

X7

Expert 1 Expert 2 Expert 3(01 02 04 05) (01 02 03 05) (02 03 04)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 03 05)

X8

Expert 1 Expert 2 Expert 3(01 03 04 05) (01 02 03 04) (02 03 04)

Expert 4 Expert 5 Expert 6(02 03 04) (01 02 03 05) (01 02 03)

CE1

Expert 1 Expert 2 Expert 3(02 03 04 05) (02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 02 04 05)

CE2

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 05) (02 03 04 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (01 02 03 05) (01 03 05)

CE3

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 03 05) (03 04 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (01 02 04 05) (01 02 03 05)

16 Advances in Civil Engineering

In accordance with the predictive and diagnosticanalysis results using the established model some safetymeasures for key nodes are displayed in time to reduce theexcessive surface settlement risk during the tunnelexcavation

(1) e nodes X5 (abnormal TBM shutdown) and X7(excessive deviation from the axis) mostly involveoperational error Safety management and supervi-sion need to be strengthened at the construction siteto eliminate such errors and ensure that the TBM isoperated properly Besides an advanced real-time

laser locator may help to alarm in the case of largeaxial deviation

(2) e nodes X1 (confined water) and X2 (ground cavityor flow sand) belong to environmental failure Inorder to reduce the influence of environmental failurecareful geological exploration should be carried outbefore tunneling to identify the poor geological and

Table 14 Calculation of FPS FFR and the occurrence probability of environmental failure operational error and multiple failures

Event Aggregated fuzzy numbers FPS FFR (dminus1) Failure probability (in 1 year)X1 (01288 02288 03288 04838) 02951 83969eminus 04 26402eminus 1X2 (01325 02325 03163 04713) 02909 80032eminus 04 25336eminus 1X3 (01000 02163 02700 03825) 02420 42986eminus 04 14518eminus 1X4 (00450 00900 01125 01800) 01082 22492eminus 05 81803eminus 3X5 (01363 02488 02775 04263) 02747 66022eminus 04 214155eminus 1X6 (01488 02488 03225 04713) 03004 89125eminus 04 27770eminus 1X7 (01163 02388 03125 04675) 02855 75157eminus 04 24002eminus 1X8 (01450 02538 02950 03100) 02463 45643eminus 04 15338eminus 1CE1 (01413 02413 03513 04838) 03058 94598eminus 04 29202eminus 1CE2 (01288 02513 03038 04713) 02916 80679eminus 04 25496eminus 1CE3 (01450 02450 03363 04713) 03010 89722eminus 04 27937eminus 1

08299

03155

01223 010800419

01301

00504 00445 00173

Occ

urre

nce p

roba

bilit

y (in

1 y

ear)

00

01

02

03

04

05

06

07

08

09

OE1 OE2 OE3 OE4 OE5 OE6 OE7 OE8LE

Figure 12 Occurrence probability of surface settlement and otheroutcome events

Table 15 Calculation of importance measure of influential factors

SymbolImportance measure

BM RAW FVX1 2311eminus 1 7352eminus 02 7352eminus 02X2 2279eminus 1 6958eminus 02 6958eminus 02X3 1990eminus 1 3481eminus 02 3481eminus 02X4 1716eminus 1 1691eminus 03 1691eminus 03X5 2165eminus 1 5587eminus 02 5587eminus 02X6 2356eminus 1 7884eminus 02 7884eminus 02X7 2239eminus 1 6476eminus 02 6476eminus 02X8 2010eminus 1 3715eminus 02 3715eminus 02X9 1370eminus 6 6306eminus 08 6306eminus 08X10 8300eminus 7 6291eminus 08 6291eminus 08X11 2040eminus 6 6293eminus 08 6293eminus 08X12 1030eminus 6 6280eminus 08 6280eminus 08X13 5300eminus 7 6303eminus 08 6303eminus 08

Table 16 Ranking results of the key events

Rank SymbolNormalization weighting (Rlowast) Total

weighting(Rlowast)

RlowastBM RlowastRAW RlowastFV

1 X6 13805 18942 18942 516892 X1 13541 17664 17664 488693 X2 13354 16717 16717 467884 X7 13120 15559 15559 442385 X5 12686 13423 13423 395326 X8 11778 8926 89255 296297 X3 11661 8363 8363 283878 X4 10055 0406 0406 108689 X11 00002 1512eminus 05 1512eminus 05 1498eminus 0410 X9 8028eminus 05 1515eminus 05 1515eminus 05 1106eminus 0411 X12 6035eminus 05 1509eminus 05 1509eminus 05 9053eminus 0512 X10 4863eminus 05 1511eminus 05 1511eminus 05 7886eminus 0513 X13 3106eminus 05 1514eminus 05 1514eminus 05 6134eminus 05Total 100 100 100 100

02822

01073

00416 0036700142

0044200172 00151 00059

Occ

urre

nce p

roba

bilit

y (in

1 y

ear)

000

005

010

015

020

025

030

OE1 OE2 OE3 OE4 OE5 OE6 OE7 OE8LE

Figure 13 Occurrence probability when safety is ensured at keynodes

Advances in Civil Engineering 17

hydrological conditions that may be encounteredDuring excavation the advanced geological pre-diction technologymay be employed to detect adversegeological and hydrological conditions ahead of theTBM in real time including confined water groundcavity and flow sand

(3) Node X6 (seal failure at shield tail) belongs tomultiple failures e quality of the tail brush needsto be enhanced and tail brush should promptly bereplaced when it is worn

By adopting corresponding safety measures in shieldtunnel excavation the occurrence probability of variousdegrees of surface collapse (OE3 OE4 OE6 OE7 and OE8)was significantly decreased (Figure 13) Finally the TBMssuccessfully passed through the left track of DCS on March3 2017 and the right track on June 11 2017 without anysurface collapse accident demonstrating the effectiveness ofour proposed hybrid method

5 Conclusions and Future Works

In this work we first defined the ldquonormal excavation phaserdquoof shield tunneling based on the fuzzy statistical test theoryData were extracted from the construction log of the XWS inthe Wuhan metro line 7 to determine the occurrenceprobability of facility fault and expert opinions were soli-cited to determine the occurrence probability of environ-mental failure operational error and multiple failuresProbabilistic safety assessment (PSA) of the normal shieldtunnel excavation system was then performed accordingly

We employed the bow-tie analysis to evaluate the oc-currence of excessive surface settlement during normaltunnel excavation e presence of emergency measurescould reduce the occurrence probability of surface collapsecaused by excessive surface settlement (OE3 OE4 OE6 OE7and OE8) but have limited effect on the prevention of ac-cidents of OE1 OE2 and OE5 It is essential to decrease theprobability of excessive surface settlement in order to pre-vent the resulting outcome events (OEs)

By mapping the bow-tie analysis to Bayesian networks(ie BT-BN analysis) we determined the key nodes thatcould cause excessive surface settlement (LE) e key nodesincluded the following X6 (seal failure at shield tail) X1(confined water) X2 (ground cavity or flow sand) X5 (ab-normal TBM shutdown) and X7 (excessive deviation fromthe axis) Effective safety measures at these nodes couldreduce the occurrence probability of excessive surface set-tlement (LE) by 66

To ensure safety careful geological exploration shouldbe carried out before the tunneling project During thetunneling safety management and supervision should bestrengthened at the construction site Advanced geo-logical prediction technology should be used to detectpoor geological and hydrological conditions ahead of theTBM in real time Advanced laser locator should be usedto monitor and alarm excessive axial deviation equality of the tail brush should be improved and tailbrush should be replaced timely when it becomes worn

e occurrence probability of excessive surface settlementwas decreased by adopting these safety measures and theoccurrence of the resulting surface collapse was sub-sequently decreased

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

e authors thank the workers foremen and safety co-ordinators of the main contractors for their participatione authors also wish to thank the engineers Yun Zhang andPeilun Tu for assistance in gathering field data

References

[1] T Zhao W Liu and Z Ye ldquoEffects of water inrush fromtunnel excavation face on the deformation and mechanicalperformance of shield tunnel segment jointsrdquo Advances inCivil Engineering vol 2017 Article ID 5913640 9 pages 2017

[2] W Liu T Zhao W Zhou and J Tang ldquoSafety risk factors ofmetro tunnel construction in China an integrated study withEFA and SEMrdquo Safety Science vol 105 pp 98ndash113 2018

[3] K Li ldquoHangzhou metro site collapse accidentrdquo 2008 httpnewssohucom20081115n260653551shtml

[4] S Liu ldquoConstruction of Nanchang metro line 2 constructionsection pavement collapsesrdquo 2017 httpnewssohucom20160514n449414512shtml

[5] R B Peck ldquoDeep excavations and tunneling in soft groundrdquo7th International Conference on Soil Mechanics and Foun-dation Engineering vol 7 no 3 pp 225ndash290 1969

[6] P B Attewell I W Farmer and N H Glossop ldquoGrounddeformation caused by tunnelling in a silty alluvial clayrdquoGround Engineering vol 11 no 8 pp 32ndash41 1978

[7] W J Rankin ldquoGround movements resulting from urbantunnelling predictions and effectsrdquo Geological Society Lon-don Engineering Geology Special Publications vol 5 no 1pp 79ndash92 1988

[8] P B Attewell and J P Woodman ldquoPredicting the dynamicsof ground settlement and its derivatives caused by tunnelingin soilrdquo Ground Engineering vol 15 no 8 pp 13ndash20 1982

[9] M P OrsquoReilly and B M New ldquoSettlement above tunnels inthe United Kingdommdashtheir magnitude and prediction intunnelling 82 proceedings of the 3rd international sympo-sium brighton 7ndash11 June 1982 P173ndash181 Publ LondonIMM 1982rdquo International Journal of Rock Mechanics ampMining Sciences amp Geomechanics Abstracts vol 20 no 1pp 1ndash18 1983

[10] R J Mair R N Taylor and A Bracegirdle ldquoSubsurfacesettlement profiles above tunnels in claysrdquo Geotechniquevol 45 no 2 pp 361-362 1995

[11] X L Yang and J MWang ldquoGroundmovement prediction fortunnels using simplified procedurerdquo Tunnelling and Un-derground Space Technology vol 26 no 3 pp 462ndash471 2011

18 Advances in Civil Engineering

best whereas the cutter head torque had a deviation in-terval of 7401 and was controlled the worst

(4) Statistical Relationship between TBM Parameters andExcavation Speed e monitoring results in Figure 6

demonstrated that in the ldquonormal excavation phaserdquo ofthe XWS the total thrust and the face pressure were posi-tively correlated with the excavation speed In particular thetotal thrust had a stronger correlation to the excavationspeed than the face pressure In contrast the cutter head

2000400060008000

1000012000140001600018000

Tota

l thr

ust

F (k

N)

20 25 30 35 40 45 50 55 60 6515Advance speed v (mmmin)

(a)

0500

10001500200025003000350040004500

Cutte

r hea

d to

rque

MT

(kNlowast

m)

20 25 30 35 40 45 50 55 60 6515Advance speed v (mmmin)

(b)

0

50

100

150

200

250

Face

pre

ssur

eP N

(kPa

)

20 25 30 35 40 45 50 55 60 6515Advance speed v (mmmin)

(c)

Gro

utin

g pr

essu

reP G

(kPa

)

100150200250300350400450500550

20 25 30 35 40 45 50 55 60 6515Advance speed v (mmmin)

(d)

Figure 6 Variations in the TBM parameters at different excavation speeds (data from XW section) (a) total thrust versus excavationspeed (b) cutter head torque versus excavation speed (c) face pressure versus excavation speed (d) grouting pressure versus excavationspeed

Table 6 Standard values and ranges of excavation speed and TBMPs

Factors v (mmmin) F (kN) P N (kPa) M T (kNmiddotm) P G (kPa)Parameter range [20 44] [8300 13100] [117 143] [1294 2974] [197 302]Standard value 32 9700 1326 2270 302Deviation range () [minus375 375] [minus1443 3505] [minus1176 784] [minus430 3101] [minus3477 0]

Advances in Civil Engineering 9

torque and the primary grouting pressure were negativelycorrelated with the excavation speed

32 Bow-Tie-Bayesian Network Analysis e bow-tie anal-ysis combines FTand ETanalysese FTanalysis in bow-tiecalculates the occurrence probability of the loss event (LE) aswell as the top event (TE) e occurrence probability of theTE can also be obtained from the occurrence probability ofthe basic event (BE) e events could be evaluated by theirlogical relationship and their occurrence probability in theBN Mapping the bow-tie analysis to BN involves convertingboth FT and ET analyses Figure 7(a) provides a brief de-scription of calculation steps

ree importance measures described in the followingBorst and Schoonakker [30] were introduced in the newmethodology according to the Bayes theorem Figure 7(b)gives a brief description of their calculation In the proposedmethodology the critical nodes that could more easilytrigger accidents were obtained by calculating these im-portance measures

33 Confirming Failure Occurrence Probability e BT-BNanalysis requires knowing the occurrence probability of eachbasic event (BE) e basic events fall into four categoriesenvironmental failure operational error multiple failuresand facility failures e occurrence rate of facility failureswas obtained from the construction log of the XWS for thetunneling project that spanned 179 days (715 segments intotal) and was converted into occurrence probability via thefollowing equation

F 1minus eminusλt

(8)

where F denotes the occurrence probability of the failure andλ denotes the occurrence rate of the failure

e occurrence probability of environmental failureoperational error and multiple failures cannot be readilyderived from existing data and was thus estimated via expertopinione fuzzymethod combines the opinions of differentexperts in a weighted manner to calculate the fuzzy fault rate(FFR) from the triangular fuzzy numbers or trapezoidal fuzzynumbers proposed by the experts e occurrence probabilityof environmental failure operational error and multiplefailures was then determined from the FFR [34] e generalprocedure of the fuzzy method is as follows

(1) Determine the weight of the opinion of each expertbased on the age education background work ex-perience and position of the consulted expert (Ta-ble 7) e crude weight score of each expert iscalculated via the following equation

Sn Sna+ Snb

+ Snc+ Snd

(9)

where Sn represents the total weight score of theexpert e relative weight score of each expert iscalculated via the following equation

Wn Sn

1113936mn1Sn

(10)

where m represents the number of experts(2) e occurrence probability is divided into the

following categories nonoccurrence absolute lowvery low low fairly low medium fairly high highvery high absolute high or occurrence e rankvalue of the categories escalates from 0 for non-occurrence to 1 for the occurrence (Table 8) eoccurrence probability of the event is then evalu-ated based on the corresponding triangular numberor trapezoidal number given by the experts

(3) Aggregation of the fuzzy numbers When the fuzzynumbers are all triangular number or trapezoidalnumber the aggregated fuzzy numbers of an event iscalculated via equation (11) [35] e aggregatedfuzzy number considering the expert weight isshown in equation (12)

1113957Aaggregated 1113944m

n1Wn otimes 1113957An (11)

where 1113957Aaggregated represents the aggregated fuzzifiednumber given by expert m and Wn represents theweight of the expertrsquos opinion

1113957AW 1113874W1a11 + W2a21 W1a12 + W2a22 W1a12

+W2a23 W1a13 + W2a241113875

(12)

(4) After the aggregated fuzzy numbers are determinedthe centroid index method (equation (13)) is used tohandle the fuzzy numbers and obtain the fuzzyprobability score (FPS) [36]

X 1113938g(x)x dx

1113938g(x)dx (13)

where X is the defuzzified output g(x) is themembership function and x is the output variableAssume 1113957An (an1 an2 an3) a triangular number and1113957An (an1 an2 an3) a trapezoidal number e FPS iscalculated via equation (14) when a fuzzy number is atriangular number and via equation (15) when thefuzzy number is a trapezoidal number

FPS 13

an1 + an2 + an3( 1113857 (14)

FPS 13

an3 + an4( 11138572 minus an3an4 minus an1 + an2( 1113857

2+ an1an2

an3 + an4 minus an1 minus an2( 1113857

(15)

10 Advances in Civil Engineering

(5) Finally the FPS is converted to FFR via equation(16) [37] and the FFR is further converted tothe occurrence probability of environmentalfailure operational error and multiple failures(equation (8))

FFR

110k

FPSne 0

0 FPS 0

k 2301 times(1minus FPS)

FPS1113890 1113891

13

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(16)

4 Results

41 Analysis of Excessive Surface Settlement inNormal TunnelExcavation Figure 8 shows that the normal excavation

(1) If the logical relationship is AND between events the TE occurs when all events occur The probability of TE can be calculated from the following equation

(A)

(2) If the logical relationship is OR between events the TE occurs when any of the event occurs The probability of TE can be calculated from the following equation

(B)

(3) By definition in the FT analysis the probability of TE is the same as that of LE Similarly the probability of the initial event (IE) in the ET analysis is the same as that of LE The probability of OE in ET analysis can be calculated from the following equation

(C)

(4) The BN an inference method based on the Bayes theorem combines both graph theory and probability theory

(D)

FTE = i=1

nFBEi

FTE = 1 ndashi=1

n(1 ndash FBEi)

FOEn = FIE middot i=1

nP (Ei = 0) middot

j=1

nP (Ej = 1)

P(B | A) = P(A | B) middot P(B)

P(A)

(a)

(1) The Birnbaum measure (BM) whichdetermines the increment of the occurrenceprobability of TE when BE occurs is shownin the following equation

(E)

where P(TE | BE = 1) denotes the occurrence probability of TE when BE occurs and P(TE | BE = 0) denotes the occurrence probability of TE when BE does not occur

(2) Risk achievement worth (RAW) evaluatesthe impact of BE on TE when the probabilityof BE is considered The RAW is adjustedby the probability of TE and BE as shown inthe following equation

(F)

where P(BE) denotes the occurrence probability of BE and P(TE) denotes the occurrence probability of TE under all circumstances

(3) The FussellndashVesely (FV) importance which describes the contribution of BE to system fault is shown in the following equation

IBBE

M = P(TE | BE = 1) ndash P(TE | BE = 0)

IRB

AE

W = IBBE

M middot P(BE)P(TE)

(G)

P(TE) ndash P(TE | BE = 0)P(TE)

IFB

VE =

(b)

Figure 7 Bow-tie-Bayesian network analysis Calculation of (a) event probability and (b) importance measures

Table 7 Weight scores for experts

Factor Category Score

Age (a)

lt30 130ndash39 240ndash49 3ge50 4

Education (b)

High school 1College 2Bachelor 3Master 4PhD 5

Work experience (c)

lt5 years 15ndash10 years 211ndash20 years 321ndash30 years 4ge30 years 5

Position (d)

Worker 1Technician 2

Junior scholarengineer 3Senior scholarengineer 4

Table 8 Rank value of each category

Classified occurrence probability Rank valueNonoccurrence 0Absolute low 01Very low 02Low 03Fairly low 04Medium 05Fairly high 06High 07Very high 08Absolute high 09Occurrence 10

Advances in Civil Engineering 11

phase involves the environment TBM operation supervi-sion management and emergency handling Risk analysis ofthe ldquonormal excavation phaserdquo in soft soil engineering basedon the XWS allows the identification of potential risk factorsthat may trigger surface settlement and consequently lead toaccidents Eskesen et al have described three principles forrisk analysis as follows (1) eliminate risk factors that are easyto detect and can be controlled timely and effectively (2)eliminate risk factors with low occurrence probability andno catastrophic consequences and (3) combine risk factorswith similar loss consequences [38] Accordingly the riskfactors during shield tunneling were organized into three

basic categories improper control of excavation parameters(eg poor control of face pressure) catastrophic geology (egground cavity or flow sand) and unforeseeable factors (egsegment damage) Figure 9 shows the bow-tie model builtfrom the categorized factors for the risk of surface collapsecaused by excessive surface settlement during shield tun-neling OEs of various degrees were successfully predictedbased on the CEs (Figure 9) Many risk factors exist in anygiven surface collapse In this section based on the previouscalculation results in Section 31 we selected the manageableshield excavation parameters (shield total thrust groutingpressure cutter head torque soil pressure etc) in the ldquonormal

Synchronousgrouting

ExcavationSegment

installationAttitudecontrol Tail sealing

Excavationcycle

Quality controlacceptance

Dangeroussituation exists Yes

Prepareemergencymeasures

Emergencymeasures

Execution of emergencymeasures

Acceptance ofexcavationprocedures

Excavationacceptance

report

Monitoring measurements

Monitored dataof excavationenvironment

Formation geologyTBM parametersExcavation axis

Segment installationSynchronous grouting

TBM construction parameter

No

TBM parametersv (mmmm) F (kN) PN (kPa)

MT (kNmiddotm) PG (kNmiddotm)TBM attitude TBM position TBM fault information

Soil bodyparameters

Soil evolutionmodel

Confined waterObstacles

Ground cavity orquicksand

Metro tunnel excavation

Emergencyhandling

Supervision

TBMoperation

TBM

Environment

Management

Figure 8 System diagram of the ldquonormal excavation phaserdquo

12 Advances in Civil Engineering

excavation phaserdquo as the base events assigning their weightsaccording to Section 33 and then performed PSA analysis

As mentioned earlier the ldquonormal excavation phaserdquo isunder the influence of excavation parameters catastrophicgeology and unforeseeable factors Surface settlement canoccur once the condition deteriorates Here we set excessivesurface settlement as the TE in the FT analysis Meanwhilethe tunneling system has a built-in emergency managementsystem Upon excessive surface settlement the emergencymanagement system will start to shut down the TBM timelyHence in the ETanalysis the excessive surface settlement isset as the IE and TBM shutdown is set as the CE OEs ofvarious degrees are obtained based on the considered CEFinally the surface settlement is set as the LE to connect theFT and the ET and furnish the BTmodel (Figure 9 Table 9)Eight OEs of various degrees were predicted based on theCEs including surface collapse events OE3 OE4 OE6 OE7and OE8 (Figure 9 Table 10) e TBM shuts down if CE1occurs and continues to operate if otherwise

e BN-BT model for excessive surface settlement isconstructed by mapping the FT and ET analyses in the BT(Figure 9) model to BN (Figure 10) All the nodes of BN havepreviously been described in the BT except the node OEwhich is the consequence node OE is added to accommodatethe outcomes of BT By connecting the node of excessivesurface settlement to OE another state also called the safe

state is added to the state set It includes consequences OE1 toOE8 to account for the nonoccurrence of the top event iewhen excessive surface settlement controlled To show thedependence among the safety barriers and the top eventcausal arcs are also drawn between TBM shutdown andgrouting in the settlement area and bentonite injection to soilchamber and TBM shield It is worth noting that since variouscombinations of the failure and success of the sequentialsafety barriers result in different consequences in the BT allthe safety nodes of BN are connected to node OE

42 Determination of Event Occurrence Probability emaximum surface settlement that resulted from the aber-ration of the ith TBM parameter is denoted as δmaxi eprobability of safety accident becomes higher when δmaxiapproaches the permitted surface settlement δi Whenδmaxi δi the accident will occur as soon as the TBM pa-rameter gives rise to a surface settlement of δmaxi eprobability of equipment fault for the normal excavationsystem was calculated via equation (8) from the engineeringlog data of the XWS over 179 days of construction (715segments rings in total) e construction of all 715 rings fellwithin the ldquonormal excavation phaserdquo as was defined by thefuzzy statistical test (v 20ndash44mmmin) Table 11 lists thecalculation results

X3X2X1

OR

M1

X7X6X5X4

OR

M2

X10X9 X11 X13X12

M3

OR

Excessive surface

settlement

X8

Caus

esLE

CE1

CE2

CE3

Con

sequ

ence

sSt

op

TBM

Gro

utin

g in

settl

emen

tar

ea

Bent

onite

inje

ctio

n

OE 1

OE 2

OE 3

OE 4

OE 5

OE 6

OE 7

OE 8

Success Failure

AND

Figure 9 Diagram of bow-tie analysis for excessive surface settlement

Advances in Civil Engineering 13

To address the uncertainty regarding the events ofenvironmental failure operational error and multiplefailure six domain experts who participated in the con-struction of the Wuhan metro system including two seniorengineers one senior academic professor one technicalconsultant one junior engineer and one worker wereinvited to evaluate the occurrence probability of events thatcannot be readily derived from existing data (Table 12)eweights of their opinion were then calculated by usingequations (9) and (10) and the distribution of each opinionweight is shown in Figure 11

In addition Table 13 lists the expert opinions regardingthe events of environmental failure operational error andmultiple failures in the form of fuzzy numbers based onTable 8 e fuzzy numbers were aggregated via equations(12) and converted to FPS and FFR via equations (13)ndash(16)(Table 14) e occurrence probabilities were finally derivedfrom FFR (Table 14) Generally the expert knowledge isconsidered as a scarce resource which cannot provide

universal consultation or real-time guidance us there ismuch room to improve the data use efficiency

43 Update in Occurrence Probability of LE and OE eoccurrence probability of basic events is calculated as de-scribed in Section 42 including the occurrence probabilityof facility failure from the engineering log data of the XWS aswell as that of environmental failure operational error andmultiple failures derived from expert opinion e occur-rence probability of excessive surface settlement (LE) isdetermined via equations (A) and (B) by considering thelogical relationship between events in Figure 7 Finally theoccurrence probability of OEs including surface collapse canbe calculated via equation (C) in the figure by mapping theFT and ET analyses in the BTmodel to BN Figure 12 showsthe occurrence probabilities of the LE (ie excessive surfacesettlement) and that of the OEs

e above analysis shows that the occurrence probabilityof excessive surface settlement within one year is 08299(Figure 12) is occurrence probability of surface collapse(OE3 OE4 OE6 OE7 and OE8) may be decreased whenemergency measures are put in place including grouting insettlement area and bentonite injection to soil chamber andTBM shield However these measures cannot help to reduceminor accidents since the occurrence probability remains athigh levels for OE1 OE2 and OE5 Admittedly grouting andbentonite injection are necessary measures and they candecrease the effects of excessive surface settlement duringshield tunneling However the key point of avoiding outcomeevents including surface collapse to ensure project safety is toprevent the excessive surface settlement from occurring in thefirst place Hence we sought to determine the key nodesleading to excessive surface settlement via BT-BN analysis andpropose the corresponding preventive measures

Table 10 Analysis of event occurrence

Symbol EventOE1 Excessive surface settlement

OE2Grouted cutter head and shield excessive surface

settlement and minor property damageOE3 Minor surface collapse and property damage

OE4Moderate surface collapse major property damage

and minor casualtiesOE5 Excessive surface settlement

OE6Grouted cutter head and shield moderate surface

collapse and minor property damage

OE7Moderate surface collapse and major property

damage

OE8Severe surface collapse major property damage and

major casualties

Table 9 Details of bow-tie components in Figure 9

Event Symbol Logic link type Failure modelGround settlement Excessive surface settlement OR gate mdashCatastrophic geology M1 OR gate mdashUnforeseeable factors M2 OR gate mdashExcavation parameters M3 AND gate mdashConfined water X1 mdash Environmental failureGround cavity or flow sand X2 mdash Environmental failureObstacles X3 mdash Environmental failureSegment damage X4 mdash Operational errorAbnormal TBM shutdown X5 mdash Multiple failureSeal failure at shield tail X6 mdash Multiple failureExcessive deviation from axis X7 mdash Operational errorEquipment failure X8 mdash Multiple failureUntimely grouting X9 mdash Facility failureExcessive cutter head torque X10 mdash Facility failureImproper control of face pressure X11 mdash Facility failureExcessive thrust X12 mdash Facility failureImproper control of excavation speed X13 mdash Facility failureTBM shutdown CE1 mdash Multiple failureGrouting in settlement area CE2 mdash Multiple failureBentonite injection to soil chamber and TBM shield CE3 mdash Multiple failure

14 Advances in Civil Engineering

Table 11 Probability of equipment fault

Event Surface settlementδmaxi (mm)

Permitted surfacesettlement δi (mm)

Value of TBMparameter

Occurrence rate(dminus1)

Occurrence probability(in 1 year)

X9 89 15 302 kPa 10675eminus 04 382eminus 02X10 84 10 2974 kNmiddotM 17792eminus 04 629eminus 02X11 86 15 143 kPa 71167eminus 05 256eminus 02X12 98 15 13100 kN 14233eminus 04 506eminus 02X13 120 15 41mmmin 28467eminus 04 987eminus 02All data were obtained from the operation log of the XWS

Table 12 Characteristics of experts participated in the occurrence probability evaluation

Expert Age Education Service (years) Professional position1 56 High school 25 Worker2 35 Master 10 Technician3 41 Master 15 Junior engineer4 47 Bachelor 20 Senior engineer5 50 PhD 18 Senior academic6 59 PhD 30 Senior engineer

0125 0125

01625 01625

020225

AgeEducationService

Professional positionWeighting

2 3 4 5 61Expert

0

005

01

015

02

025

Wei

ghtin

g

0

1

2

3

4

5

6

Wei

ghtin

g sc

ore

Figure 11 Distribution of each expert opinion weight

X1 X2 X3

M1

X5 X6 X7 X8

M2

X9 X11

M3

Excessive surface

settlement

X10 X12 X13X4

CE1 CE2 CE3

OE

Caus

esLE

CEC

onse

quen

ces

Figure 10 Bow-tie chart of excessive surface settlement

Advances in Civil Engineering 15

44 Identify Key Nodes and Provide Safety Measures Inorder to find the key nodes leading to excessive surfacesettlement the importance measure of each event was cal-culated via equations (E)ndash(G) in Figure 7 as shown inTable 15 Assume the number of events as ldquonrdquo e nor-malized weight Rlowast could be calculated from the importancemeasure Ii via the following equation

Rlowast

Ii

1113936ni1Ii

times 100 (17)

After the normalized weight Rlowast is calculated for eachimportance measure the total weight Rlowast could be calculatedvia equation (18) e total weight Rlowast of events was finally

ranked in descending order to find the key nodes as shownin Table 16

Rlowast R

lowastBM + R

lowastRAW + R

lowastFV (18)

It can be seen that X6 (seal failure at shield tail) X1(confined water) X2 (ground cavity or flow sand) X5 (ab-normal TBM shutdown) and X7 (excessive deviation fromaxis) have far higher weight than other events and are thusthe key nodes to accidents related to excessive surface set-tlement Measures can be taken to particularly ensure safetyat these nodes e occurrence probability of excessivesurface settlement can be reduced by 66 when X6 X1 X2X5 and X7 are ensured safe (Figure 13)

Table 13 Expert opinion on environmental failure operational error and multiple failures

Event Fuzzy numbers proposed by each expert

X1

Expert 1 Expert 2 Expert 3(02 03 04 05) (01 02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 02 03 05)

X2

Expert 1 Expert 2 Expert 3(01 02 03 05) (02 03 04) (01 02 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (02 03 05) (01 02 03 05)

X3

Expert 1 Expert 2 Expert 3(01 02 04 05) (01 02 03 05) (01 03 04)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03) (01 02 03)

X4

Expert 1 Expert 2 Expert 3(02 03 04 05) (01 02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(02 03 04) (02 03 05) (01 02 03 05)

X5

Expert 1 Expert 2 Expert 3(01 03 04) (01 02 03 05) (02 03 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (02 03 05) (01 02 03)

X6

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 03 05) (02 03 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (02 03 05) (01 02 04 05)

X7

Expert 1 Expert 2 Expert 3(01 02 04 05) (01 02 03 05) (02 03 04)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 03 05)

X8

Expert 1 Expert 2 Expert 3(01 03 04 05) (01 02 03 04) (02 03 04)

Expert 4 Expert 5 Expert 6(02 03 04) (01 02 03 05) (01 02 03)

CE1

Expert 1 Expert 2 Expert 3(02 03 04 05) (02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 02 04 05)

CE2

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 05) (02 03 04 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (01 02 03 05) (01 03 05)

CE3

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 03 05) (03 04 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (01 02 04 05) (01 02 03 05)

16 Advances in Civil Engineering

In accordance with the predictive and diagnosticanalysis results using the established model some safetymeasures for key nodes are displayed in time to reduce theexcessive surface settlement risk during the tunnelexcavation

(1) e nodes X5 (abnormal TBM shutdown) and X7(excessive deviation from the axis) mostly involveoperational error Safety management and supervi-sion need to be strengthened at the construction siteto eliminate such errors and ensure that the TBM isoperated properly Besides an advanced real-time

laser locator may help to alarm in the case of largeaxial deviation

(2) e nodes X1 (confined water) and X2 (ground cavityor flow sand) belong to environmental failure Inorder to reduce the influence of environmental failurecareful geological exploration should be carried outbefore tunneling to identify the poor geological and

Table 14 Calculation of FPS FFR and the occurrence probability of environmental failure operational error and multiple failures

Event Aggregated fuzzy numbers FPS FFR (dminus1) Failure probability (in 1 year)X1 (01288 02288 03288 04838) 02951 83969eminus 04 26402eminus 1X2 (01325 02325 03163 04713) 02909 80032eminus 04 25336eminus 1X3 (01000 02163 02700 03825) 02420 42986eminus 04 14518eminus 1X4 (00450 00900 01125 01800) 01082 22492eminus 05 81803eminus 3X5 (01363 02488 02775 04263) 02747 66022eminus 04 214155eminus 1X6 (01488 02488 03225 04713) 03004 89125eminus 04 27770eminus 1X7 (01163 02388 03125 04675) 02855 75157eminus 04 24002eminus 1X8 (01450 02538 02950 03100) 02463 45643eminus 04 15338eminus 1CE1 (01413 02413 03513 04838) 03058 94598eminus 04 29202eminus 1CE2 (01288 02513 03038 04713) 02916 80679eminus 04 25496eminus 1CE3 (01450 02450 03363 04713) 03010 89722eminus 04 27937eminus 1

08299

03155

01223 010800419

01301

00504 00445 00173

Occ

urre

nce p

roba

bilit

y (in

1 y

ear)

00

01

02

03

04

05

06

07

08

09

OE1 OE2 OE3 OE4 OE5 OE6 OE7 OE8LE

Figure 12 Occurrence probability of surface settlement and otheroutcome events

Table 15 Calculation of importance measure of influential factors

SymbolImportance measure

BM RAW FVX1 2311eminus 1 7352eminus 02 7352eminus 02X2 2279eminus 1 6958eminus 02 6958eminus 02X3 1990eminus 1 3481eminus 02 3481eminus 02X4 1716eminus 1 1691eminus 03 1691eminus 03X5 2165eminus 1 5587eminus 02 5587eminus 02X6 2356eminus 1 7884eminus 02 7884eminus 02X7 2239eminus 1 6476eminus 02 6476eminus 02X8 2010eminus 1 3715eminus 02 3715eminus 02X9 1370eminus 6 6306eminus 08 6306eminus 08X10 8300eminus 7 6291eminus 08 6291eminus 08X11 2040eminus 6 6293eminus 08 6293eminus 08X12 1030eminus 6 6280eminus 08 6280eminus 08X13 5300eminus 7 6303eminus 08 6303eminus 08

Table 16 Ranking results of the key events

Rank SymbolNormalization weighting (Rlowast) Total

weighting(Rlowast)

RlowastBM RlowastRAW RlowastFV

1 X6 13805 18942 18942 516892 X1 13541 17664 17664 488693 X2 13354 16717 16717 467884 X7 13120 15559 15559 442385 X5 12686 13423 13423 395326 X8 11778 8926 89255 296297 X3 11661 8363 8363 283878 X4 10055 0406 0406 108689 X11 00002 1512eminus 05 1512eminus 05 1498eminus 0410 X9 8028eminus 05 1515eminus 05 1515eminus 05 1106eminus 0411 X12 6035eminus 05 1509eminus 05 1509eminus 05 9053eminus 0512 X10 4863eminus 05 1511eminus 05 1511eminus 05 7886eminus 0513 X13 3106eminus 05 1514eminus 05 1514eminus 05 6134eminus 05Total 100 100 100 100

02822

01073

00416 0036700142

0044200172 00151 00059

Occ

urre

nce p

roba

bilit

y (in

1 y

ear)

000

005

010

015

020

025

030

OE1 OE2 OE3 OE4 OE5 OE6 OE7 OE8LE

Figure 13 Occurrence probability when safety is ensured at keynodes

Advances in Civil Engineering 17

hydrological conditions that may be encounteredDuring excavation the advanced geological pre-diction technologymay be employed to detect adversegeological and hydrological conditions ahead of theTBM in real time including confined water groundcavity and flow sand

(3) Node X6 (seal failure at shield tail) belongs tomultiple failures e quality of the tail brush needsto be enhanced and tail brush should promptly bereplaced when it is worn

By adopting corresponding safety measures in shieldtunnel excavation the occurrence probability of variousdegrees of surface collapse (OE3 OE4 OE6 OE7 and OE8)was significantly decreased (Figure 13) Finally the TBMssuccessfully passed through the left track of DCS on March3 2017 and the right track on June 11 2017 without anysurface collapse accident demonstrating the effectiveness ofour proposed hybrid method

5 Conclusions and Future Works

In this work we first defined the ldquonormal excavation phaserdquoof shield tunneling based on the fuzzy statistical test theoryData were extracted from the construction log of the XWS inthe Wuhan metro line 7 to determine the occurrenceprobability of facility fault and expert opinions were soli-cited to determine the occurrence probability of environ-mental failure operational error and multiple failuresProbabilistic safety assessment (PSA) of the normal shieldtunnel excavation system was then performed accordingly

We employed the bow-tie analysis to evaluate the oc-currence of excessive surface settlement during normaltunnel excavation e presence of emergency measurescould reduce the occurrence probability of surface collapsecaused by excessive surface settlement (OE3 OE4 OE6 OE7and OE8) but have limited effect on the prevention of ac-cidents of OE1 OE2 and OE5 It is essential to decrease theprobability of excessive surface settlement in order to pre-vent the resulting outcome events (OEs)

By mapping the bow-tie analysis to Bayesian networks(ie BT-BN analysis) we determined the key nodes thatcould cause excessive surface settlement (LE) e key nodesincluded the following X6 (seal failure at shield tail) X1(confined water) X2 (ground cavity or flow sand) X5 (ab-normal TBM shutdown) and X7 (excessive deviation fromthe axis) Effective safety measures at these nodes couldreduce the occurrence probability of excessive surface set-tlement (LE) by 66

To ensure safety careful geological exploration shouldbe carried out before the tunneling project During thetunneling safety management and supervision should bestrengthened at the construction site Advanced geo-logical prediction technology should be used to detectpoor geological and hydrological conditions ahead of theTBM in real time Advanced laser locator should be usedto monitor and alarm excessive axial deviation equality of the tail brush should be improved and tailbrush should be replaced timely when it becomes worn

e occurrence probability of excessive surface settlementwas decreased by adopting these safety measures and theoccurrence of the resulting surface collapse was sub-sequently decreased

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

e authors thank the workers foremen and safety co-ordinators of the main contractors for their participatione authors also wish to thank the engineers Yun Zhang andPeilun Tu for assistance in gathering field data

References

[1] T Zhao W Liu and Z Ye ldquoEffects of water inrush fromtunnel excavation face on the deformation and mechanicalperformance of shield tunnel segment jointsrdquo Advances inCivil Engineering vol 2017 Article ID 5913640 9 pages 2017

[2] W Liu T Zhao W Zhou and J Tang ldquoSafety risk factors ofmetro tunnel construction in China an integrated study withEFA and SEMrdquo Safety Science vol 105 pp 98ndash113 2018

[3] K Li ldquoHangzhou metro site collapse accidentrdquo 2008 httpnewssohucom20081115n260653551shtml

[4] S Liu ldquoConstruction of Nanchang metro line 2 constructionsection pavement collapsesrdquo 2017 httpnewssohucom20160514n449414512shtml

[5] R B Peck ldquoDeep excavations and tunneling in soft groundrdquo7th International Conference on Soil Mechanics and Foun-dation Engineering vol 7 no 3 pp 225ndash290 1969

[6] P B Attewell I W Farmer and N H Glossop ldquoGrounddeformation caused by tunnelling in a silty alluvial clayrdquoGround Engineering vol 11 no 8 pp 32ndash41 1978

[7] W J Rankin ldquoGround movements resulting from urbantunnelling predictions and effectsrdquo Geological Society Lon-don Engineering Geology Special Publications vol 5 no 1pp 79ndash92 1988

[8] P B Attewell and J P Woodman ldquoPredicting the dynamicsof ground settlement and its derivatives caused by tunnelingin soilrdquo Ground Engineering vol 15 no 8 pp 13ndash20 1982

[9] M P OrsquoReilly and B M New ldquoSettlement above tunnels inthe United Kingdommdashtheir magnitude and prediction intunnelling 82 proceedings of the 3rd international sympo-sium brighton 7ndash11 June 1982 P173ndash181 Publ LondonIMM 1982rdquo International Journal of Rock Mechanics ampMining Sciences amp Geomechanics Abstracts vol 20 no 1pp 1ndash18 1983

[10] R J Mair R N Taylor and A Bracegirdle ldquoSubsurfacesettlement profiles above tunnels in claysrdquo Geotechniquevol 45 no 2 pp 361-362 1995

[11] X L Yang and J MWang ldquoGroundmovement prediction fortunnels using simplified procedurerdquo Tunnelling and Un-derground Space Technology vol 26 no 3 pp 462ndash471 2011

18 Advances in Civil Engineering

torque and the primary grouting pressure were negativelycorrelated with the excavation speed

32 Bow-Tie-Bayesian Network Analysis e bow-tie anal-ysis combines FTand ETanalysese FTanalysis in bow-tiecalculates the occurrence probability of the loss event (LE) aswell as the top event (TE) e occurrence probability of theTE can also be obtained from the occurrence probability ofthe basic event (BE) e events could be evaluated by theirlogical relationship and their occurrence probability in theBN Mapping the bow-tie analysis to BN involves convertingboth FT and ET analyses Figure 7(a) provides a brief de-scription of calculation steps

ree importance measures described in the followingBorst and Schoonakker [30] were introduced in the newmethodology according to the Bayes theorem Figure 7(b)gives a brief description of their calculation In the proposedmethodology the critical nodes that could more easilytrigger accidents were obtained by calculating these im-portance measures

33 Confirming Failure Occurrence Probability e BT-BNanalysis requires knowing the occurrence probability of eachbasic event (BE) e basic events fall into four categoriesenvironmental failure operational error multiple failuresand facility failures e occurrence rate of facility failureswas obtained from the construction log of the XWS for thetunneling project that spanned 179 days (715 segments intotal) and was converted into occurrence probability via thefollowing equation

F 1minus eminusλt

(8)

where F denotes the occurrence probability of the failure andλ denotes the occurrence rate of the failure

e occurrence probability of environmental failureoperational error and multiple failures cannot be readilyderived from existing data and was thus estimated via expertopinione fuzzymethod combines the opinions of differentexperts in a weighted manner to calculate the fuzzy fault rate(FFR) from the triangular fuzzy numbers or trapezoidal fuzzynumbers proposed by the experts e occurrence probabilityof environmental failure operational error and multiplefailures was then determined from the FFR [34] e generalprocedure of the fuzzy method is as follows

(1) Determine the weight of the opinion of each expertbased on the age education background work ex-perience and position of the consulted expert (Ta-ble 7) e crude weight score of each expert iscalculated via the following equation

Sn Sna+ Snb

+ Snc+ Snd

(9)

where Sn represents the total weight score of theexpert e relative weight score of each expert iscalculated via the following equation

Wn Sn

1113936mn1Sn

(10)

where m represents the number of experts(2) e occurrence probability is divided into the

following categories nonoccurrence absolute lowvery low low fairly low medium fairly high highvery high absolute high or occurrence e rankvalue of the categories escalates from 0 for non-occurrence to 1 for the occurrence (Table 8) eoccurrence probability of the event is then evalu-ated based on the corresponding triangular numberor trapezoidal number given by the experts

(3) Aggregation of the fuzzy numbers When the fuzzynumbers are all triangular number or trapezoidalnumber the aggregated fuzzy numbers of an event iscalculated via equation (11) [35] e aggregatedfuzzy number considering the expert weight isshown in equation (12)

1113957Aaggregated 1113944m

n1Wn otimes 1113957An (11)

where 1113957Aaggregated represents the aggregated fuzzifiednumber given by expert m and Wn represents theweight of the expertrsquos opinion

1113957AW 1113874W1a11 + W2a21 W1a12 + W2a22 W1a12

+W2a23 W1a13 + W2a241113875

(12)

(4) After the aggregated fuzzy numbers are determinedthe centroid index method (equation (13)) is used tohandle the fuzzy numbers and obtain the fuzzyprobability score (FPS) [36]

X 1113938g(x)x dx

1113938g(x)dx (13)

where X is the defuzzified output g(x) is themembership function and x is the output variableAssume 1113957An (an1 an2 an3) a triangular number and1113957An (an1 an2 an3) a trapezoidal number e FPS iscalculated via equation (14) when a fuzzy number is atriangular number and via equation (15) when thefuzzy number is a trapezoidal number

FPS 13

an1 + an2 + an3( 1113857 (14)

FPS 13

an3 + an4( 11138572 minus an3an4 minus an1 + an2( 1113857

2+ an1an2

an3 + an4 minus an1 minus an2( 1113857

(15)

10 Advances in Civil Engineering

(5) Finally the FPS is converted to FFR via equation(16) [37] and the FFR is further converted tothe occurrence probability of environmentalfailure operational error and multiple failures(equation (8))

FFR

110k

FPSne 0

0 FPS 0

k 2301 times(1minus FPS)

FPS1113890 1113891

13

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(16)

4 Results

41 Analysis of Excessive Surface Settlement inNormal TunnelExcavation Figure 8 shows that the normal excavation

(1) If the logical relationship is AND between events the TE occurs when all events occur The probability of TE can be calculated from the following equation

(A)

(2) If the logical relationship is OR between events the TE occurs when any of the event occurs The probability of TE can be calculated from the following equation

(B)

(3) By definition in the FT analysis the probability of TE is the same as that of LE Similarly the probability of the initial event (IE) in the ET analysis is the same as that of LE The probability of OE in ET analysis can be calculated from the following equation

(C)

(4) The BN an inference method based on the Bayes theorem combines both graph theory and probability theory

(D)

FTE = i=1

nFBEi

FTE = 1 ndashi=1

n(1 ndash FBEi)

FOEn = FIE middot i=1

nP (Ei = 0) middot

j=1

nP (Ej = 1)

P(B | A) = P(A | B) middot P(B)

P(A)

(a)

(1) The Birnbaum measure (BM) whichdetermines the increment of the occurrenceprobability of TE when BE occurs is shownin the following equation

(E)

where P(TE | BE = 1) denotes the occurrence probability of TE when BE occurs and P(TE | BE = 0) denotes the occurrence probability of TE when BE does not occur

(2) Risk achievement worth (RAW) evaluatesthe impact of BE on TE when the probabilityof BE is considered The RAW is adjustedby the probability of TE and BE as shown inthe following equation

(F)

where P(BE) denotes the occurrence probability of BE and P(TE) denotes the occurrence probability of TE under all circumstances

(3) The FussellndashVesely (FV) importance which describes the contribution of BE to system fault is shown in the following equation

IBBE

M = P(TE | BE = 1) ndash P(TE | BE = 0)

IRB

AE

W = IBBE

M middot P(BE)P(TE)

(G)

P(TE) ndash P(TE | BE = 0)P(TE)

IFB

VE =

(b)

Figure 7 Bow-tie-Bayesian network analysis Calculation of (a) event probability and (b) importance measures

Table 7 Weight scores for experts

Factor Category Score

Age (a)

lt30 130ndash39 240ndash49 3ge50 4

Education (b)

High school 1College 2Bachelor 3Master 4PhD 5

Work experience (c)

lt5 years 15ndash10 years 211ndash20 years 321ndash30 years 4ge30 years 5

Position (d)

Worker 1Technician 2

Junior scholarengineer 3Senior scholarengineer 4

Table 8 Rank value of each category

Classified occurrence probability Rank valueNonoccurrence 0Absolute low 01Very low 02Low 03Fairly low 04Medium 05Fairly high 06High 07Very high 08Absolute high 09Occurrence 10

Advances in Civil Engineering 11

phase involves the environment TBM operation supervi-sion management and emergency handling Risk analysis ofthe ldquonormal excavation phaserdquo in soft soil engineering basedon the XWS allows the identification of potential risk factorsthat may trigger surface settlement and consequently lead toaccidents Eskesen et al have described three principles forrisk analysis as follows (1) eliminate risk factors that are easyto detect and can be controlled timely and effectively (2)eliminate risk factors with low occurrence probability andno catastrophic consequences and (3) combine risk factorswith similar loss consequences [38] Accordingly the riskfactors during shield tunneling were organized into three

basic categories improper control of excavation parameters(eg poor control of face pressure) catastrophic geology (egground cavity or flow sand) and unforeseeable factors (egsegment damage) Figure 9 shows the bow-tie model builtfrom the categorized factors for the risk of surface collapsecaused by excessive surface settlement during shield tun-neling OEs of various degrees were successfully predictedbased on the CEs (Figure 9) Many risk factors exist in anygiven surface collapse In this section based on the previouscalculation results in Section 31 we selected the manageableshield excavation parameters (shield total thrust groutingpressure cutter head torque soil pressure etc) in the ldquonormal

Synchronousgrouting

ExcavationSegment

installationAttitudecontrol Tail sealing

Excavationcycle

Quality controlacceptance

Dangeroussituation exists Yes

Prepareemergencymeasures

Emergencymeasures

Execution of emergencymeasures

Acceptance ofexcavationprocedures

Excavationacceptance

report

Monitoring measurements

Monitored dataof excavationenvironment

Formation geologyTBM parametersExcavation axis

Segment installationSynchronous grouting

TBM construction parameter

No

TBM parametersv (mmmm) F (kN) PN (kPa)

MT (kNmiddotm) PG (kNmiddotm)TBM attitude TBM position TBM fault information

Soil bodyparameters

Soil evolutionmodel

Confined waterObstacles

Ground cavity orquicksand

Metro tunnel excavation

Emergencyhandling

Supervision

TBMoperation

TBM

Environment

Management

Figure 8 System diagram of the ldquonormal excavation phaserdquo

12 Advances in Civil Engineering

excavation phaserdquo as the base events assigning their weightsaccording to Section 33 and then performed PSA analysis

As mentioned earlier the ldquonormal excavation phaserdquo isunder the influence of excavation parameters catastrophicgeology and unforeseeable factors Surface settlement canoccur once the condition deteriorates Here we set excessivesurface settlement as the TE in the FT analysis Meanwhilethe tunneling system has a built-in emergency managementsystem Upon excessive surface settlement the emergencymanagement system will start to shut down the TBM timelyHence in the ETanalysis the excessive surface settlement isset as the IE and TBM shutdown is set as the CE OEs ofvarious degrees are obtained based on the considered CEFinally the surface settlement is set as the LE to connect theFT and the ET and furnish the BTmodel (Figure 9 Table 9)Eight OEs of various degrees were predicted based on theCEs including surface collapse events OE3 OE4 OE6 OE7and OE8 (Figure 9 Table 10) e TBM shuts down if CE1occurs and continues to operate if otherwise

e BN-BT model for excessive surface settlement isconstructed by mapping the FT and ET analyses in the BT(Figure 9) model to BN (Figure 10) All the nodes of BN havepreviously been described in the BT except the node OEwhich is the consequence node OE is added to accommodatethe outcomes of BT By connecting the node of excessivesurface settlement to OE another state also called the safe

state is added to the state set It includes consequences OE1 toOE8 to account for the nonoccurrence of the top event iewhen excessive surface settlement controlled To show thedependence among the safety barriers and the top eventcausal arcs are also drawn between TBM shutdown andgrouting in the settlement area and bentonite injection to soilchamber and TBM shield It is worth noting that since variouscombinations of the failure and success of the sequentialsafety barriers result in different consequences in the BT allthe safety nodes of BN are connected to node OE

42 Determination of Event Occurrence Probability emaximum surface settlement that resulted from the aber-ration of the ith TBM parameter is denoted as δmaxi eprobability of safety accident becomes higher when δmaxiapproaches the permitted surface settlement δi Whenδmaxi δi the accident will occur as soon as the TBM pa-rameter gives rise to a surface settlement of δmaxi eprobability of equipment fault for the normal excavationsystem was calculated via equation (8) from the engineeringlog data of the XWS over 179 days of construction (715segments rings in total) e construction of all 715 rings fellwithin the ldquonormal excavation phaserdquo as was defined by thefuzzy statistical test (v 20ndash44mmmin) Table 11 lists thecalculation results

X3X2X1

OR

M1

X7X6X5X4

OR

M2

X10X9 X11 X13X12

M3

OR

Excessive surface

settlement

X8

Caus

esLE

CE1

CE2

CE3

Con

sequ

ence

sSt

op

TBM

Gro

utin

g in

settl

emen

tar

ea

Bent

onite

inje

ctio

n

OE 1

OE 2

OE 3

OE 4

OE 5

OE 6

OE 7

OE 8

Success Failure

AND

Figure 9 Diagram of bow-tie analysis for excessive surface settlement

Advances in Civil Engineering 13

To address the uncertainty regarding the events ofenvironmental failure operational error and multiplefailure six domain experts who participated in the con-struction of the Wuhan metro system including two seniorengineers one senior academic professor one technicalconsultant one junior engineer and one worker wereinvited to evaluate the occurrence probability of events thatcannot be readily derived from existing data (Table 12)eweights of their opinion were then calculated by usingequations (9) and (10) and the distribution of each opinionweight is shown in Figure 11

In addition Table 13 lists the expert opinions regardingthe events of environmental failure operational error andmultiple failures in the form of fuzzy numbers based onTable 8 e fuzzy numbers were aggregated via equations(12) and converted to FPS and FFR via equations (13)ndash(16)(Table 14) e occurrence probabilities were finally derivedfrom FFR (Table 14) Generally the expert knowledge isconsidered as a scarce resource which cannot provide

universal consultation or real-time guidance us there ismuch room to improve the data use efficiency

43 Update in Occurrence Probability of LE and OE eoccurrence probability of basic events is calculated as de-scribed in Section 42 including the occurrence probabilityof facility failure from the engineering log data of the XWS aswell as that of environmental failure operational error andmultiple failures derived from expert opinion e occur-rence probability of excessive surface settlement (LE) isdetermined via equations (A) and (B) by considering thelogical relationship between events in Figure 7 Finally theoccurrence probability of OEs including surface collapse canbe calculated via equation (C) in the figure by mapping theFT and ET analyses in the BTmodel to BN Figure 12 showsthe occurrence probabilities of the LE (ie excessive surfacesettlement) and that of the OEs

e above analysis shows that the occurrence probabilityof excessive surface settlement within one year is 08299(Figure 12) is occurrence probability of surface collapse(OE3 OE4 OE6 OE7 and OE8) may be decreased whenemergency measures are put in place including grouting insettlement area and bentonite injection to soil chamber andTBM shield However these measures cannot help to reduceminor accidents since the occurrence probability remains athigh levels for OE1 OE2 and OE5 Admittedly grouting andbentonite injection are necessary measures and they candecrease the effects of excessive surface settlement duringshield tunneling However the key point of avoiding outcomeevents including surface collapse to ensure project safety is toprevent the excessive surface settlement from occurring in thefirst place Hence we sought to determine the key nodesleading to excessive surface settlement via BT-BN analysis andpropose the corresponding preventive measures

Table 10 Analysis of event occurrence

Symbol EventOE1 Excessive surface settlement

OE2Grouted cutter head and shield excessive surface

settlement and minor property damageOE3 Minor surface collapse and property damage

OE4Moderate surface collapse major property damage

and minor casualtiesOE5 Excessive surface settlement

OE6Grouted cutter head and shield moderate surface

collapse and minor property damage

OE7Moderate surface collapse and major property

damage

OE8Severe surface collapse major property damage and

major casualties

Table 9 Details of bow-tie components in Figure 9

Event Symbol Logic link type Failure modelGround settlement Excessive surface settlement OR gate mdashCatastrophic geology M1 OR gate mdashUnforeseeable factors M2 OR gate mdashExcavation parameters M3 AND gate mdashConfined water X1 mdash Environmental failureGround cavity or flow sand X2 mdash Environmental failureObstacles X3 mdash Environmental failureSegment damage X4 mdash Operational errorAbnormal TBM shutdown X5 mdash Multiple failureSeal failure at shield tail X6 mdash Multiple failureExcessive deviation from axis X7 mdash Operational errorEquipment failure X8 mdash Multiple failureUntimely grouting X9 mdash Facility failureExcessive cutter head torque X10 mdash Facility failureImproper control of face pressure X11 mdash Facility failureExcessive thrust X12 mdash Facility failureImproper control of excavation speed X13 mdash Facility failureTBM shutdown CE1 mdash Multiple failureGrouting in settlement area CE2 mdash Multiple failureBentonite injection to soil chamber and TBM shield CE3 mdash Multiple failure

14 Advances in Civil Engineering

Table 11 Probability of equipment fault

Event Surface settlementδmaxi (mm)

Permitted surfacesettlement δi (mm)

Value of TBMparameter

Occurrence rate(dminus1)

Occurrence probability(in 1 year)

X9 89 15 302 kPa 10675eminus 04 382eminus 02X10 84 10 2974 kNmiddotM 17792eminus 04 629eminus 02X11 86 15 143 kPa 71167eminus 05 256eminus 02X12 98 15 13100 kN 14233eminus 04 506eminus 02X13 120 15 41mmmin 28467eminus 04 987eminus 02All data were obtained from the operation log of the XWS

Table 12 Characteristics of experts participated in the occurrence probability evaluation

Expert Age Education Service (years) Professional position1 56 High school 25 Worker2 35 Master 10 Technician3 41 Master 15 Junior engineer4 47 Bachelor 20 Senior engineer5 50 PhD 18 Senior academic6 59 PhD 30 Senior engineer

0125 0125

01625 01625

020225

AgeEducationService

Professional positionWeighting

2 3 4 5 61Expert

0

005

01

015

02

025

Wei

ghtin

g

0

1

2

3

4

5

6

Wei

ghtin

g sc

ore

Figure 11 Distribution of each expert opinion weight

X1 X2 X3

M1

X5 X6 X7 X8

M2

X9 X11

M3

Excessive surface

settlement

X10 X12 X13X4

CE1 CE2 CE3

OE

Caus

esLE

CEC

onse

quen

ces

Figure 10 Bow-tie chart of excessive surface settlement

Advances in Civil Engineering 15

44 Identify Key Nodes and Provide Safety Measures Inorder to find the key nodes leading to excessive surfacesettlement the importance measure of each event was cal-culated via equations (E)ndash(G) in Figure 7 as shown inTable 15 Assume the number of events as ldquonrdquo e nor-malized weight Rlowast could be calculated from the importancemeasure Ii via the following equation

Rlowast

Ii

1113936ni1Ii

times 100 (17)

After the normalized weight Rlowast is calculated for eachimportance measure the total weight Rlowast could be calculatedvia equation (18) e total weight Rlowast of events was finally

ranked in descending order to find the key nodes as shownin Table 16

Rlowast R

lowastBM + R

lowastRAW + R

lowastFV (18)

It can be seen that X6 (seal failure at shield tail) X1(confined water) X2 (ground cavity or flow sand) X5 (ab-normal TBM shutdown) and X7 (excessive deviation fromaxis) have far higher weight than other events and are thusthe key nodes to accidents related to excessive surface set-tlement Measures can be taken to particularly ensure safetyat these nodes e occurrence probability of excessivesurface settlement can be reduced by 66 when X6 X1 X2X5 and X7 are ensured safe (Figure 13)

Table 13 Expert opinion on environmental failure operational error and multiple failures

Event Fuzzy numbers proposed by each expert

X1

Expert 1 Expert 2 Expert 3(02 03 04 05) (01 02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 02 03 05)

X2

Expert 1 Expert 2 Expert 3(01 02 03 05) (02 03 04) (01 02 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (02 03 05) (01 02 03 05)

X3

Expert 1 Expert 2 Expert 3(01 02 04 05) (01 02 03 05) (01 03 04)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03) (01 02 03)

X4

Expert 1 Expert 2 Expert 3(02 03 04 05) (01 02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(02 03 04) (02 03 05) (01 02 03 05)

X5

Expert 1 Expert 2 Expert 3(01 03 04) (01 02 03 05) (02 03 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (02 03 05) (01 02 03)

X6

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 03 05) (02 03 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (02 03 05) (01 02 04 05)

X7

Expert 1 Expert 2 Expert 3(01 02 04 05) (01 02 03 05) (02 03 04)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 03 05)

X8

Expert 1 Expert 2 Expert 3(01 03 04 05) (01 02 03 04) (02 03 04)

Expert 4 Expert 5 Expert 6(02 03 04) (01 02 03 05) (01 02 03)

CE1

Expert 1 Expert 2 Expert 3(02 03 04 05) (02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 02 04 05)

CE2

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 05) (02 03 04 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (01 02 03 05) (01 03 05)

CE3

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 03 05) (03 04 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (01 02 04 05) (01 02 03 05)

16 Advances in Civil Engineering

In accordance with the predictive and diagnosticanalysis results using the established model some safetymeasures for key nodes are displayed in time to reduce theexcessive surface settlement risk during the tunnelexcavation

(1) e nodes X5 (abnormal TBM shutdown) and X7(excessive deviation from the axis) mostly involveoperational error Safety management and supervi-sion need to be strengthened at the construction siteto eliminate such errors and ensure that the TBM isoperated properly Besides an advanced real-time

laser locator may help to alarm in the case of largeaxial deviation

(2) e nodes X1 (confined water) and X2 (ground cavityor flow sand) belong to environmental failure Inorder to reduce the influence of environmental failurecareful geological exploration should be carried outbefore tunneling to identify the poor geological and

Table 14 Calculation of FPS FFR and the occurrence probability of environmental failure operational error and multiple failures

Event Aggregated fuzzy numbers FPS FFR (dminus1) Failure probability (in 1 year)X1 (01288 02288 03288 04838) 02951 83969eminus 04 26402eminus 1X2 (01325 02325 03163 04713) 02909 80032eminus 04 25336eminus 1X3 (01000 02163 02700 03825) 02420 42986eminus 04 14518eminus 1X4 (00450 00900 01125 01800) 01082 22492eminus 05 81803eminus 3X5 (01363 02488 02775 04263) 02747 66022eminus 04 214155eminus 1X6 (01488 02488 03225 04713) 03004 89125eminus 04 27770eminus 1X7 (01163 02388 03125 04675) 02855 75157eminus 04 24002eminus 1X8 (01450 02538 02950 03100) 02463 45643eminus 04 15338eminus 1CE1 (01413 02413 03513 04838) 03058 94598eminus 04 29202eminus 1CE2 (01288 02513 03038 04713) 02916 80679eminus 04 25496eminus 1CE3 (01450 02450 03363 04713) 03010 89722eminus 04 27937eminus 1

08299

03155

01223 010800419

01301

00504 00445 00173

Occ

urre

nce p

roba

bilit

y (in

1 y

ear)

00

01

02

03

04

05

06

07

08

09

OE1 OE2 OE3 OE4 OE5 OE6 OE7 OE8LE

Figure 12 Occurrence probability of surface settlement and otheroutcome events

Table 15 Calculation of importance measure of influential factors

SymbolImportance measure

BM RAW FVX1 2311eminus 1 7352eminus 02 7352eminus 02X2 2279eminus 1 6958eminus 02 6958eminus 02X3 1990eminus 1 3481eminus 02 3481eminus 02X4 1716eminus 1 1691eminus 03 1691eminus 03X5 2165eminus 1 5587eminus 02 5587eminus 02X6 2356eminus 1 7884eminus 02 7884eminus 02X7 2239eminus 1 6476eminus 02 6476eminus 02X8 2010eminus 1 3715eminus 02 3715eminus 02X9 1370eminus 6 6306eminus 08 6306eminus 08X10 8300eminus 7 6291eminus 08 6291eminus 08X11 2040eminus 6 6293eminus 08 6293eminus 08X12 1030eminus 6 6280eminus 08 6280eminus 08X13 5300eminus 7 6303eminus 08 6303eminus 08

Table 16 Ranking results of the key events

Rank SymbolNormalization weighting (Rlowast) Total

weighting(Rlowast)

RlowastBM RlowastRAW RlowastFV

1 X6 13805 18942 18942 516892 X1 13541 17664 17664 488693 X2 13354 16717 16717 467884 X7 13120 15559 15559 442385 X5 12686 13423 13423 395326 X8 11778 8926 89255 296297 X3 11661 8363 8363 283878 X4 10055 0406 0406 108689 X11 00002 1512eminus 05 1512eminus 05 1498eminus 0410 X9 8028eminus 05 1515eminus 05 1515eminus 05 1106eminus 0411 X12 6035eminus 05 1509eminus 05 1509eminus 05 9053eminus 0512 X10 4863eminus 05 1511eminus 05 1511eminus 05 7886eminus 0513 X13 3106eminus 05 1514eminus 05 1514eminus 05 6134eminus 05Total 100 100 100 100

02822

01073

00416 0036700142

0044200172 00151 00059

Occ

urre

nce p

roba

bilit

y (in

1 y

ear)

000

005

010

015

020

025

030

OE1 OE2 OE3 OE4 OE5 OE6 OE7 OE8LE

Figure 13 Occurrence probability when safety is ensured at keynodes

Advances in Civil Engineering 17

hydrological conditions that may be encounteredDuring excavation the advanced geological pre-diction technologymay be employed to detect adversegeological and hydrological conditions ahead of theTBM in real time including confined water groundcavity and flow sand

(3) Node X6 (seal failure at shield tail) belongs tomultiple failures e quality of the tail brush needsto be enhanced and tail brush should promptly bereplaced when it is worn

By adopting corresponding safety measures in shieldtunnel excavation the occurrence probability of variousdegrees of surface collapse (OE3 OE4 OE6 OE7 and OE8)was significantly decreased (Figure 13) Finally the TBMssuccessfully passed through the left track of DCS on March3 2017 and the right track on June 11 2017 without anysurface collapse accident demonstrating the effectiveness ofour proposed hybrid method

5 Conclusions and Future Works

In this work we first defined the ldquonormal excavation phaserdquoof shield tunneling based on the fuzzy statistical test theoryData were extracted from the construction log of the XWS inthe Wuhan metro line 7 to determine the occurrenceprobability of facility fault and expert opinions were soli-cited to determine the occurrence probability of environ-mental failure operational error and multiple failuresProbabilistic safety assessment (PSA) of the normal shieldtunnel excavation system was then performed accordingly

We employed the bow-tie analysis to evaluate the oc-currence of excessive surface settlement during normaltunnel excavation e presence of emergency measurescould reduce the occurrence probability of surface collapsecaused by excessive surface settlement (OE3 OE4 OE6 OE7and OE8) but have limited effect on the prevention of ac-cidents of OE1 OE2 and OE5 It is essential to decrease theprobability of excessive surface settlement in order to pre-vent the resulting outcome events (OEs)

By mapping the bow-tie analysis to Bayesian networks(ie BT-BN analysis) we determined the key nodes thatcould cause excessive surface settlement (LE) e key nodesincluded the following X6 (seal failure at shield tail) X1(confined water) X2 (ground cavity or flow sand) X5 (ab-normal TBM shutdown) and X7 (excessive deviation fromthe axis) Effective safety measures at these nodes couldreduce the occurrence probability of excessive surface set-tlement (LE) by 66

To ensure safety careful geological exploration shouldbe carried out before the tunneling project During thetunneling safety management and supervision should bestrengthened at the construction site Advanced geo-logical prediction technology should be used to detectpoor geological and hydrological conditions ahead of theTBM in real time Advanced laser locator should be usedto monitor and alarm excessive axial deviation equality of the tail brush should be improved and tailbrush should be replaced timely when it becomes worn

e occurrence probability of excessive surface settlementwas decreased by adopting these safety measures and theoccurrence of the resulting surface collapse was sub-sequently decreased

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

e authors thank the workers foremen and safety co-ordinators of the main contractors for their participatione authors also wish to thank the engineers Yun Zhang andPeilun Tu for assistance in gathering field data

References

[1] T Zhao W Liu and Z Ye ldquoEffects of water inrush fromtunnel excavation face on the deformation and mechanicalperformance of shield tunnel segment jointsrdquo Advances inCivil Engineering vol 2017 Article ID 5913640 9 pages 2017

[2] W Liu T Zhao W Zhou and J Tang ldquoSafety risk factors ofmetro tunnel construction in China an integrated study withEFA and SEMrdquo Safety Science vol 105 pp 98ndash113 2018

[3] K Li ldquoHangzhou metro site collapse accidentrdquo 2008 httpnewssohucom20081115n260653551shtml

[4] S Liu ldquoConstruction of Nanchang metro line 2 constructionsection pavement collapsesrdquo 2017 httpnewssohucom20160514n449414512shtml

[5] R B Peck ldquoDeep excavations and tunneling in soft groundrdquo7th International Conference on Soil Mechanics and Foun-dation Engineering vol 7 no 3 pp 225ndash290 1969

[6] P B Attewell I W Farmer and N H Glossop ldquoGrounddeformation caused by tunnelling in a silty alluvial clayrdquoGround Engineering vol 11 no 8 pp 32ndash41 1978

[7] W J Rankin ldquoGround movements resulting from urbantunnelling predictions and effectsrdquo Geological Society Lon-don Engineering Geology Special Publications vol 5 no 1pp 79ndash92 1988

[8] P B Attewell and J P Woodman ldquoPredicting the dynamicsof ground settlement and its derivatives caused by tunnelingin soilrdquo Ground Engineering vol 15 no 8 pp 13ndash20 1982

[9] M P OrsquoReilly and B M New ldquoSettlement above tunnels inthe United Kingdommdashtheir magnitude and prediction intunnelling 82 proceedings of the 3rd international sympo-sium brighton 7ndash11 June 1982 P173ndash181 Publ LondonIMM 1982rdquo International Journal of Rock Mechanics ampMining Sciences amp Geomechanics Abstracts vol 20 no 1pp 1ndash18 1983

[10] R J Mair R N Taylor and A Bracegirdle ldquoSubsurfacesettlement profiles above tunnels in claysrdquo Geotechniquevol 45 no 2 pp 361-362 1995

[11] X L Yang and J MWang ldquoGroundmovement prediction fortunnels using simplified procedurerdquo Tunnelling and Un-derground Space Technology vol 26 no 3 pp 462ndash471 2011

18 Advances in Civil Engineering

(5) Finally the FPS is converted to FFR via equation(16) [37] and the FFR is further converted tothe occurrence probability of environmentalfailure operational error and multiple failures(equation (8))

FFR

110k

FPSne 0

0 FPS 0

k 2301 times(1minus FPS)

FPS1113890 1113891

13

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(16)

4 Results

41 Analysis of Excessive Surface Settlement inNormal TunnelExcavation Figure 8 shows that the normal excavation

(1) If the logical relationship is AND between events the TE occurs when all events occur The probability of TE can be calculated from the following equation

(A)

(2) If the logical relationship is OR between events the TE occurs when any of the event occurs The probability of TE can be calculated from the following equation

(B)

(3) By definition in the FT analysis the probability of TE is the same as that of LE Similarly the probability of the initial event (IE) in the ET analysis is the same as that of LE The probability of OE in ET analysis can be calculated from the following equation

(C)

(4) The BN an inference method based on the Bayes theorem combines both graph theory and probability theory

(D)

FTE = i=1

nFBEi

FTE = 1 ndashi=1

n(1 ndash FBEi)

FOEn = FIE middot i=1

nP (Ei = 0) middot

j=1

nP (Ej = 1)

P(B | A) = P(A | B) middot P(B)

P(A)

(a)

(1) The Birnbaum measure (BM) whichdetermines the increment of the occurrenceprobability of TE when BE occurs is shownin the following equation

(E)

where P(TE | BE = 1) denotes the occurrence probability of TE when BE occurs and P(TE | BE = 0) denotes the occurrence probability of TE when BE does not occur

(2) Risk achievement worth (RAW) evaluatesthe impact of BE on TE when the probabilityof BE is considered The RAW is adjustedby the probability of TE and BE as shown inthe following equation

(F)

where P(BE) denotes the occurrence probability of BE and P(TE) denotes the occurrence probability of TE under all circumstances

(3) The FussellndashVesely (FV) importance which describes the contribution of BE to system fault is shown in the following equation

IBBE

M = P(TE | BE = 1) ndash P(TE | BE = 0)

IRB

AE

W = IBBE

M middot P(BE)P(TE)

(G)

P(TE) ndash P(TE | BE = 0)P(TE)

IFB

VE =

(b)

Figure 7 Bow-tie-Bayesian network analysis Calculation of (a) event probability and (b) importance measures

Table 7 Weight scores for experts

Factor Category Score

Age (a)

lt30 130ndash39 240ndash49 3ge50 4

Education (b)

High school 1College 2Bachelor 3Master 4PhD 5

Work experience (c)

lt5 years 15ndash10 years 211ndash20 years 321ndash30 years 4ge30 years 5

Position (d)

Worker 1Technician 2

Junior scholarengineer 3Senior scholarengineer 4

Table 8 Rank value of each category

Classified occurrence probability Rank valueNonoccurrence 0Absolute low 01Very low 02Low 03Fairly low 04Medium 05Fairly high 06High 07Very high 08Absolute high 09Occurrence 10

Advances in Civil Engineering 11

phase involves the environment TBM operation supervi-sion management and emergency handling Risk analysis ofthe ldquonormal excavation phaserdquo in soft soil engineering basedon the XWS allows the identification of potential risk factorsthat may trigger surface settlement and consequently lead toaccidents Eskesen et al have described three principles forrisk analysis as follows (1) eliminate risk factors that are easyto detect and can be controlled timely and effectively (2)eliminate risk factors with low occurrence probability andno catastrophic consequences and (3) combine risk factorswith similar loss consequences [38] Accordingly the riskfactors during shield tunneling were organized into three

basic categories improper control of excavation parameters(eg poor control of face pressure) catastrophic geology (egground cavity or flow sand) and unforeseeable factors (egsegment damage) Figure 9 shows the bow-tie model builtfrom the categorized factors for the risk of surface collapsecaused by excessive surface settlement during shield tun-neling OEs of various degrees were successfully predictedbased on the CEs (Figure 9) Many risk factors exist in anygiven surface collapse In this section based on the previouscalculation results in Section 31 we selected the manageableshield excavation parameters (shield total thrust groutingpressure cutter head torque soil pressure etc) in the ldquonormal

Synchronousgrouting

ExcavationSegment

installationAttitudecontrol Tail sealing

Excavationcycle

Quality controlacceptance

Dangeroussituation exists Yes

Prepareemergencymeasures

Emergencymeasures

Execution of emergencymeasures

Acceptance ofexcavationprocedures

Excavationacceptance

report

Monitoring measurements

Monitored dataof excavationenvironment

Formation geologyTBM parametersExcavation axis

Segment installationSynchronous grouting

TBM construction parameter

No

TBM parametersv (mmmm) F (kN) PN (kPa)

MT (kNmiddotm) PG (kNmiddotm)TBM attitude TBM position TBM fault information

Soil bodyparameters

Soil evolutionmodel

Confined waterObstacles

Ground cavity orquicksand

Metro tunnel excavation

Emergencyhandling

Supervision

TBMoperation

TBM

Environment

Management

Figure 8 System diagram of the ldquonormal excavation phaserdquo

12 Advances in Civil Engineering

excavation phaserdquo as the base events assigning their weightsaccording to Section 33 and then performed PSA analysis

As mentioned earlier the ldquonormal excavation phaserdquo isunder the influence of excavation parameters catastrophicgeology and unforeseeable factors Surface settlement canoccur once the condition deteriorates Here we set excessivesurface settlement as the TE in the FT analysis Meanwhilethe tunneling system has a built-in emergency managementsystem Upon excessive surface settlement the emergencymanagement system will start to shut down the TBM timelyHence in the ETanalysis the excessive surface settlement isset as the IE and TBM shutdown is set as the CE OEs ofvarious degrees are obtained based on the considered CEFinally the surface settlement is set as the LE to connect theFT and the ET and furnish the BTmodel (Figure 9 Table 9)Eight OEs of various degrees were predicted based on theCEs including surface collapse events OE3 OE4 OE6 OE7and OE8 (Figure 9 Table 10) e TBM shuts down if CE1occurs and continues to operate if otherwise

e BN-BT model for excessive surface settlement isconstructed by mapping the FT and ET analyses in the BT(Figure 9) model to BN (Figure 10) All the nodes of BN havepreviously been described in the BT except the node OEwhich is the consequence node OE is added to accommodatethe outcomes of BT By connecting the node of excessivesurface settlement to OE another state also called the safe

state is added to the state set It includes consequences OE1 toOE8 to account for the nonoccurrence of the top event iewhen excessive surface settlement controlled To show thedependence among the safety barriers and the top eventcausal arcs are also drawn between TBM shutdown andgrouting in the settlement area and bentonite injection to soilchamber and TBM shield It is worth noting that since variouscombinations of the failure and success of the sequentialsafety barriers result in different consequences in the BT allthe safety nodes of BN are connected to node OE

42 Determination of Event Occurrence Probability emaximum surface settlement that resulted from the aber-ration of the ith TBM parameter is denoted as δmaxi eprobability of safety accident becomes higher when δmaxiapproaches the permitted surface settlement δi Whenδmaxi δi the accident will occur as soon as the TBM pa-rameter gives rise to a surface settlement of δmaxi eprobability of equipment fault for the normal excavationsystem was calculated via equation (8) from the engineeringlog data of the XWS over 179 days of construction (715segments rings in total) e construction of all 715 rings fellwithin the ldquonormal excavation phaserdquo as was defined by thefuzzy statistical test (v 20ndash44mmmin) Table 11 lists thecalculation results

X3X2X1

OR

M1

X7X6X5X4

OR

M2

X10X9 X11 X13X12

M3

OR

Excessive surface

settlement

X8

Caus

esLE

CE1

CE2

CE3

Con

sequ

ence

sSt

op

TBM

Gro

utin

g in

settl

emen

tar

ea

Bent

onite

inje

ctio

n

OE 1

OE 2

OE 3

OE 4

OE 5

OE 6

OE 7

OE 8

Success Failure

AND

Figure 9 Diagram of bow-tie analysis for excessive surface settlement

Advances in Civil Engineering 13

To address the uncertainty regarding the events ofenvironmental failure operational error and multiplefailure six domain experts who participated in the con-struction of the Wuhan metro system including two seniorengineers one senior academic professor one technicalconsultant one junior engineer and one worker wereinvited to evaluate the occurrence probability of events thatcannot be readily derived from existing data (Table 12)eweights of their opinion were then calculated by usingequations (9) and (10) and the distribution of each opinionweight is shown in Figure 11

In addition Table 13 lists the expert opinions regardingthe events of environmental failure operational error andmultiple failures in the form of fuzzy numbers based onTable 8 e fuzzy numbers were aggregated via equations(12) and converted to FPS and FFR via equations (13)ndash(16)(Table 14) e occurrence probabilities were finally derivedfrom FFR (Table 14) Generally the expert knowledge isconsidered as a scarce resource which cannot provide

universal consultation or real-time guidance us there ismuch room to improve the data use efficiency

43 Update in Occurrence Probability of LE and OE eoccurrence probability of basic events is calculated as de-scribed in Section 42 including the occurrence probabilityof facility failure from the engineering log data of the XWS aswell as that of environmental failure operational error andmultiple failures derived from expert opinion e occur-rence probability of excessive surface settlement (LE) isdetermined via equations (A) and (B) by considering thelogical relationship between events in Figure 7 Finally theoccurrence probability of OEs including surface collapse canbe calculated via equation (C) in the figure by mapping theFT and ET analyses in the BTmodel to BN Figure 12 showsthe occurrence probabilities of the LE (ie excessive surfacesettlement) and that of the OEs

e above analysis shows that the occurrence probabilityof excessive surface settlement within one year is 08299(Figure 12) is occurrence probability of surface collapse(OE3 OE4 OE6 OE7 and OE8) may be decreased whenemergency measures are put in place including grouting insettlement area and bentonite injection to soil chamber andTBM shield However these measures cannot help to reduceminor accidents since the occurrence probability remains athigh levels for OE1 OE2 and OE5 Admittedly grouting andbentonite injection are necessary measures and they candecrease the effects of excessive surface settlement duringshield tunneling However the key point of avoiding outcomeevents including surface collapse to ensure project safety is toprevent the excessive surface settlement from occurring in thefirst place Hence we sought to determine the key nodesleading to excessive surface settlement via BT-BN analysis andpropose the corresponding preventive measures

Table 10 Analysis of event occurrence

Symbol EventOE1 Excessive surface settlement

OE2Grouted cutter head and shield excessive surface

settlement and minor property damageOE3 Minor surface collapse and property damage

OE4Moderate surface collapse major property damage

and minor casualtiesOE5 Excessive surface settlement

OE6Grouted cutter head and shield moderate surface

collapse and minor property damage

OE7Moderate surface collapse and major property

damage

OE8Severe surface collapse major property damage and

major casualties

Table 9 Details of bow-tie components in Figure 9

Event Symbol Logic link type Failure modelGround settlement Excessive surface settlement OR gate mdashCatastrophic geology M1 OR gate mdashUnforeseeable factors M2 OR gate mdashExcavation parameters M3 AND gate mdashConfined water X1 mdash Environmental failureGround cavity or flow sand X2 mdash Environmental failureObstacles X3 mdash Environmental failureSegment damage X4 mdash Operational errorAbnormal TBM shutdown X5 mdash Multiple failureSeal failure at shield tail X6 mdash Multiple failureExcessive deviation from axis X7 mdash Operational errorEquipment failure X8 mdash Multiple failureUntimely grouting X9 mdash Facility failureExcessive cutter head torque X10 mdash Facility failureImproper control of face pressure X11 mdash Facility failureExcessive thrust X12 mdash Facility failureImproper control of excavation speed X13 mdash Facility failureTBM shutdown CE1 mdash Multiple failureGrouting in settlement area CE2 mdash Multiple failureBentonite injection to soil chamber and TBM shield CE3 mdash Multiple failure

14 Advances in Civil Engineering

Table 11 Probability of equipment fault

Event Surface settlementδmaxi (mm)

Permitted surfacesettlement δi (mm)

Value of TBMparameter

Occurrence rate(dminus1)

Occurrence probability(in 1 year)

X9 89 15 302 kPa 10675eminus 04 382eminus 02X10 84 10 2974 kNmiddotM 17792eminus 04 629eminus 02X11 86 15 143 kPa 71167eminus 05 256eminus 02X12 98 15 13100 kN 14233eminus 04 506eminus 02X13 120 15 41mmmin 28467eminus 04 987eminus 02All data were obtained from the operation log of the XWS

Table 12 Characteristics of experts participated in the occurrence probability evaluation

Expert Age Education Service (years) Professional position1 56 High school 25 Worker2 35 Master 10 Technician3 41 Master 15 Junior engineer4 47 Bachelor 20 Senior engineer5 50 PhD 18 Senior academic6 59 PhD 30 Senior engineer

0125 0125

01625 01625

020225

AgeEducationService

Professional positionWeighting

2 3 4 5 61Expert

0

005

01

015

02

025

Wei

ghtin

g

0

1

2

3

4

5

6

Wei

ghtin

g sc

ore

Figure 11 Distribution of each expert opinion weight

X1 X2 X3

M1

X5 X6 X7 X8

M2

X9 X11

M3

Excessive surface

settlement

X10 X12 X13X4

CE1 CE2 CE3

OE

Caus

esLE

CEC

onse

quen

ces

Figure 10 Bow-tie chart of excessive surface settlement

Advances in Civil Engineering 15

44 Identify Key Nodes and Provide Safety Measures Inorder to find the key nodes leading to excessive surfacesettlement the importance measure of each event was cal-culated via equations (E)ndash(G) in Figure 7 as shown inTable 15 Assume the number of events as ldquonrdquo e nor-malized weight Rlowast could be calculated from the importancemeasure Ii via the following equation

Rlowast

Ii

1113936ni1Ii

times 100 (17)

After the normalized weight Rlowast is calculated for eachimportance measure the total weight Rlowast could be calculatedvia equation (18) e total weight Rlowast of events was finally

ranked in descending order to find the key nodes as shownin Table 16

Rlowast R

lowastBM + R

lowastRAW + R

lowastFV (18)

It can be seen that X6 (seal failure at shield tail) X1(confined water) X2 (ground cavity or flow sand) X5 (ab-normal TBM shutdown) and X7 (excessive deviation fromaxis) have far higher weight than other events and are thusthe key nodes to accidents related to excessive surface set-tlement Measures can be taken to particularly ensure safetyat these nodes e occurrence probability of excessivesurface settlement can be reduced by 66 when X6 X1 X2X5 and X7 are ensured safe (Figure 13)

Table 13 Expert opinion on environmental failure operational error and multiple failures

Event Fuzzy numbers proposed by each expert

X1

Expert 1 Expert 2 Expert 3(02 03 04 05) (01 02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 02 03 05)

X2

Expert 1 Expert 2 Expert 3(01 02 03 05) (02 03 04) (01 02 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (02 03 05) (01 02 03 05)

X3

Expert 1 Expert 2 Expert 3(01 02 04 05) (01 02 03 05) (01 03 04)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03) (01 02 03)

X4

Expert 1 Expert 2 Expert 3(02 03 04 05) (01 02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(02 03 04) (02 03 05) (01 02 03 05)

X5

Expert 1 Expert 2 Expert 3(01 03 04) (01 02 03 05) (02 03 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (02 03 05) (01 02 03)

X6

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 03 05) (02 03 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (02 03 05) (01 02 04 05)

X7

Expert 1 Expert 2 Expert 3(01 02 04 05) (01 02 03 05) (02 03 04)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 03 05)

X8

Expert 1 Expert 2 Expert 3(01 03 04 05) (01 02 03 04) (02 03 04)

Expert 4 Expert 5 Expert 6(02 03 04) (01 02 03 05) (01 02 03)

CE1

Expert 1 Expert 2 Expert 3(02 03 04 05) (02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 02 04 05)

CE2

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 05) (02 03 04 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (01 02 03 05) (01 03 05)

CE3

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 03 05) (03 04 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (01 02 04 05) (01 02 03 05)

16 Advances in Civil Engineering

In accordance with the predictive and diagnosticanalysis results using the established model some safetymeasures for key nodes are displayed in time to reduce theexcessive surface settlement risk during the tunnelexcavation

(1) e nodes X5 (abnormal TBM shutdown) and X7(excessive deviation from the axis) mostly involveoperational error Safety management and supervi-sion need to be strengthened at the construction siteto eliminate such errors and ensure that the TBM isoperated properly Besides an advanced real-time

laser locator may help to alarm in the case of largeaxial deviation

(2) e nodes X1 (confined water) and X2 (ground cavityor flow sand) belong to environmental failure Inorder to reduce the influence of environmental failurecareful geological exploration should be carried outbefore tunneling to identify the poor geological and

Table 14 Calculation of FPS FFR and the occurrence probability of environmental failure operational error and multiple failures

Event Aggregated fuzzy numbers FPS FFR (dminus1) Failure probability (in 1 year)X1 (01288 02288 03288 04838) 02951 83969eminus 04 26402eminus 1X2 (01325 02325 03163 04713) 02909 80032eminus 04 25336eminus 1X3 (01000 02163 02700 03825) 02420 42986eminus 04 14518eminus 1X4 (00450 00900 01125 01800) 01082 22492eminus 05 81803eminus 3X5 (01363 02488 02775 04263) 02747 66022eminus 04 214155eminus 1X6 (01488 02488 03225 04713) 03004 89125eminus 04 27770eminus 1X7 (01163 02388 03125 04675) 02855 75157eminus 04 24002eminus 1X8 (01450 02538 02950 03100) 02463 45643eminus 04 15338eminus 1CE1 (01413 02413 03513 04838) 03058 94598eminus 04 29202eminus 1CE2 (01288 02513 03038 04713) 02916 80679eminus 04 25496eminus 1CE3 (01450 02450 03363 04713) 03010 89722eminus 04 27937eminus 1

08299

03155

01223 010800419

01301

00504 00445 00173

Occ

urre

nce p

roba

bilit

y (in

1 y

ear)

00

01

02

03

04

05

06

07

08

09

OE1 OE2 OE3 OE4 OE5 OE6 OE7 OE8LE

Figure 12 Occurrence probability of surface settlement and otheroutcome events

Table 15 Calculation of importance measure of influential factors

SymbolImportance measure

BM RAW FVX1 2311eminus 1 7352eminus 02 7352eminus 02X2 2279eminus 1 6958eminus 02 6958eminus 02X3 1990eminus 1 3481eminus 02 3481eminus 02X4 1716eminus 1 1691eminus 03 1691eminus 03X5 2165eminus 1 5587eminus 02 5587eminus 02X6 2356eminus 1 7884eminus 02 7884eminus 02X7 2239eminus 1 6476eminus 02 6476eminus 02X8 2010eminus 1 3715eminus 02 3715eminus 02X9 1370eminus 6 6306eminus 08 6306eminus 08X10 8300eminus 7 6291eminus 08 6291eminus 08X11 2040eminus 6 6293eminus 08 6293eminus 08X12 1030eminus 6 6280eminus 08 6280eminus 08X13 5300eminus 7 6303eminus 08 6303eminus 08

Table 16 Ranking results of the key events

Rank SymbolNormalization weighting (Rlowast) Total

weighting(Rlowast)

RlowastBM RlowastRAW RlowastFV

1 X6 13805 18942 18942 516892 X1 13541 17664 17664 488693 X2 13354 16717 16717 467884 X7 13120 15559 15559 442385 X5 12686 13423 13423 395326 X8 11778 8926 89255 296297 X3 11661 8363 8363 283878 X4 10055 0406 0406 108689 X11 00002 1512eminus 05 1512eminus 05 1498eminus 0410 X9 8028eminus 05 1515eminus 05 1515eminus 05 1106eminus 0411 X12 6035eminus 05 1509eminus 05 1509eminus 05 9053eminus 0512 X10 4863eminus 05 1511eminus 05 1511eminus 05 7886eminus 0513 X13 3106eminus 05 1514eminus 05 1514eminus 05 6134eminus 05Total 100 100 100 100

02822

01073

00416 0036700142

0044200172 00151 00059

Occ

urre

nce p

roba

bilit

y (in

1 y

ear)

000

005

010

015

020

025

030

OE1 OE2 OE3 OE4 OE5 OE6 OE7 OE8LE

Figure 13 Occurrence probability when safety is ensured at keynodes

Advances in Civil Engineering 17

hydrological conditions that may be encounteredDuring excavation the advanced geological pre-diction technologymay be employed to detect adversegeological and hydrological conditions ahead of theTBM in real time including confined water groundcavity and flow sand

(3) Node X6 (seal failure at shield tail) belongs tomultiple failures e quality of the tail brush needsto be enhanced and tail brush should promptly bereplaced when it is worn

By adopting corresponding safety measures in shieldtunnel excavation the occurrence probability of variousdegrees of surface collapse (OE3 OE4 OE6 OE7 and OE8)was significantly decreased (Figure 13) Finally the TBMssuccessfully passed through the left track of DCS on March3 2017 and the right track on June 11 2017 without anysurface collapse accident demonstrating the effectiveness ofour proposed hybrid method

5 Conclusions and Future Works

In this work we first defined the ldquonormal excavation phaserdquoof shield tunneling based on the fuzzy statistical test theoryData were extracted from the construction log of the XWS inthe Wuhan metro line 7 to determine the occurrenceprobability of facility fault and expert opinions were soli-cited to determine the occurrence probability of environ-mental failure operational error and multiple failuresProbabilistic safety assessment (PSA) of the normal shieldtunnel excavation system was then performed accordingly

We employed the bow-tie analysis to evaluate the oc-currence of excessive surface settlement during normaltunnel excavation e presence of emergency measurescould reduce the occurrence probability of surface collapsecaused by excessive surface settlement (OE3 OE4 OE6 OE7and OE8) but have limited effect on the prevention of ac-cidents of OE1 OE2 and OE5 It is essential to decrease theprobability of excessive surface settlement in order to pre-vent the resulting outcome events (OEs)

By mapping the bow-tie analysis to Bayesian networks(ie BT-BN analysis) we determined the key nodes thatcould cause excessive surface settlement (LE) e key nodesincluded the following X6 (seal failure at shield tail) X1(confined water) X2 (ground cavity or flow sand) X5 (ab-normal TBM shutdown) and X7 (excessive deviation fromthe axis) Effective safety measures at these nodes couldreduce the occurrence probability of excessive surface set-tlement (LE) by 66

To ensure safety careful geological exploration shouldbe carried out before the tunneling project During thetunneling safety management and supervision should bestrengthened at the construction site Advanced geo-logical prediction technology should be used to detectpoor geological and hydrological conditions ahead of theTBM in real time Advanced laser locator should be usedto monitor and alarm excessive axial deviation equality of the tail brush should be improved and tailbrush should be replaced timely when it becomes worn

e occurrence probability of excessive surface settlementwas decreased by adopting these safety measures and theoccurrence of the resulting surface collapse was sub-sequently decreased

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

e authors thank the workers foremen and safety co-ordinators of the main contractors for their participatione authors also wish to thank the engineers Yun Zhang andPeilun Tu for assistance in gathering field data

References

[1] T Zhao W Liu and Z Ye ldquoEffects of water inrush fromtunnel excavation face on the deformation and mechanicalperformance of shield tunnel segment jointsrdquo Advances inCivil Engineering vol 2017 Article ID 5913640 9 pages 2017

[2] W Liu T Zhao W Zhou and J Tang ldquoSafety risk factors ofmetro tunnel construction in China an integrated study withEFA and SEMrdquo Safety Science vol 105 pp 98ndash113 2018

[3] K Li ldquoHangzhou metro site collapse accidentrdquo 2008 httpnewssohucom20081115n260653551shtml

[4] S Liu ldquoConstruction of Nanchang metro line 2 constructionsection pavement collapsesrdquo 2017 httpnewssohucom20160514n449414512shtml

[5] R B Peck ldquoDeep excavations and tunneling in soft groundrdquo7th International Conference on Soil Mechanics and Foun-dation Engineering vol 7 no 3 pp 225ndash290 1969

[6] P B Attewell I W Farmer and N H Glossop ldquoGrounddeformation caused by tunnelling in a silty alluvial clayrdquoGround Engineering vol 11 no 8 pp 32ndash41 1978

[7] W J Rankin ldquoGround movements resulting from urbantunnelling predictions and effectsrdquo Geological Society Lon-don Engineering Geology Special Publications vol 5 no 1pp 79ndash92 1988

[8] P B Attewell and J P Woodman ldquoPredicting the dynamicsof ground settlement and its derivatives caused by tunnelingin soilrdquo Ground Engineering vol 15 no 8 pp 13ndash20 1982

[9] M P OrsquoReilly and B M New ldquoSettlement above tunnels inthe United Kingdommdashtheir magnitude and prediction intunnelling 82 proceedings of the 3rd international sympo-sium brighton 7ndash11 June 1982 P173ndash181 Publ LondonIMM 1982rdquo International Journal of Rock Mechanics ampMining Sciences amp Geomechanics Abstracts vol 20 no 1pp 1ndash18 1983

[10] R J Mair R N Taylor and A Bracegirdle ldquoSubsurfacesettlement profiles above tunnels in claysrdquo Geotechniquevol 45 no 2 pp 361-362 1995

[11] X L Yang and J MWang ldquoGroundmovement prediction fortunnels using simplified procedurerdquo Tunnelling and Un-derground Space Technology vol 26 no 3 pp 462ndash471 2011

18 Advances in Civil Engineering

phase involves the environment TBM operation supervi-sion management and emergency handling Risk analysis ofthe ldquonormal excavation phaserdquo in soft soil engineering basedon the XWS allows the identification of potential risk factorsthat may trigger surface settlement and consequently lead toaccidents Eskesen et al have described three principles forrisk analysis as follows (1) eliminate risk factors that are easyto detect and can be controlled timely and effectively (2)eliminate risk factors with low occurrence probability andno catastrophic consequences and (3) combine risk factorswith similar loss consequences [38] Accordingly the riskfactors during shield tunneling were organized into three

basic categories improper control of excavation parameters(eg poor control of face pressure) catastrophic geology (egground cavity or flow sand) and unforeseeable factors (egsegment damage) Figure 9 shows the bow-tie model builtfrom the categorized factors for the risk of surface collapsecaused by excessive surface settlement during shield tun-neling OEs of various degrees were successfully predictedbased on the CEs (Figure 9) Many risk factors exist in anygiven surface collapse In this section based on the previouscalculation results in Section 31 we selected the manageableshield excavation parameters (shield total thrust groutingpressure cutter head torque soil pressure etc) in the ldquonormal

Synchronousgrouting

ExcavationSegment

installationAttitudecontrol Tail sealing

Excavationcycle

Quality controlacceptance

Dangeroussituation exists Yes

Prepareemergencymeasures

Emergencymeasures

Execution of emergencymeasures

Acceptance ofexcavationprocedures

Excavationacceptance

report

Monitoring measurements

Monitored dataof excavationenvironment

Formation geologyTBM parametersExcavation axis

Segment installationSynchronous grouting

TBM construction parameter

No

TBM parametersv (mmmm) F (kN) PN (kPa)

MT (kNmiddotm) PG (kNmiddotm)TBM attitude TBM position TBM fault information

Soil bodyparameters

Soil evolutionmodel

Confined waterObstacles

Ground cavity orquicksand

Metro tunnel excavation

Emergencyhandling

Supervision

TBMoperation

TBM

Environment

Management

Figure 8 System diagram of the ldquonormal excavation phaserdquo

12 Advances in Civil Engineering

excavation phaserdquo as the base events assigning their weightsaccording to Section 33 and then performed PSA analysis

As mentioned earlier the ldquonormal excavation phaserdquo isunder the influence of excavation parameters catastrophicgeology and unforeseeable factors Surface settlement canoccur once the condition deteriorates Here we set excessivesurface settlement as the TE in the FT analysis Meanwhilethe tunneling system has a built-in emergency managementsystem Upon excessive surface settlement the emergencymanagement system will start to shut down the TBM timelyHence in the ETanalysis the excessive surface settlement isset as the IE and TBM shutdown is set as the CE OEs ofvarious degrees are obtained based on the considered CEFinally the surface settlement is set as the LE to connect theFT and the ET and furnish the BTmodel (Figure 9 Table 9)Eight OEs of various degrees were predicted based on theCEs including surface collapse events OE3 OE4 OE6 OE7and OE8 (Figure 9 Table 10) e TBM shuts down if CE1occurs and continues to operate if otherwise

e BN-BT model for excessive surface settlement isconstructed by mapping the FT and ET analyses in the BT(Figure 9) model to BN (Figure 10) All the nodes of BN havepreviously been described in the BT except the node OEwhich is the consequence node OE is added to accommodatethe outcomes of BT By connecting the node of excessivesurface settlement to OE another state also called the safe

state is added to the state set It includes consequences OE1 toOE8 to account for the nonoccurrence of the top event iewhen excessive surface settlement controlled To show thedependence among the safety barriers and the top eventcausal arcs are also drawn between TBM shutdown andgrouting in the settlement area and bentonite injection to soilchamber and TBM shield It is worth noting that since variouscombinations of the failure and success of the sequentialsafety barriers result in different consequences in the BT allthe safety nodes of BN are connected to node OE

42 Determination of Event Occurrence Probability emaximum surface settlement that resulted from the aber-ration of the ith TBM parameter is denoted as δmaxi eprobability of safety accident becomes higher when δmaxiapproaches the permitted surface settlement δi Whenδmaxi δi the accident will occur as soon as the TBM pa-rameter gives rise to a surface settlement of δmaxi eprobability of equipment fault for the normal excavationsystem was calculated via equation (8) from the engineeringlog data of the XWS over 179 days of construction (715segments rings in total) e construction of all 715 rings fellwithin the ldquonormal excavation phaserdquo as was defined by thefuzzy statistical test (v 20ndash44mmmin) Table 11 lists thecalculation results

X3X2X1

OR

M1

X7X6X5X4

OR

M2

X10X9 X11 X13X12

M3

OR

Excessive surface

settlement

X8

Caus

esLE

CE1

CE2

CE3

Con

sequ

ence

sSt

op

TBM

Gro

utin

g in

settl

emen

tar

ea

Bent

onite

inje

ctio

n

OE 1

OE 2

OE 3

OE 4

OE 5

OE 6

OE 7

OE 8

Success Failure

AND

Figure 9 Diagram of bow-tie analysis for excessive surface settlement

Advances in Civil Engineering 13

To address the uncertainty regarding the events ofenvironmental failure operational error and multiplefailure six domain experts who participated in the con-struction of the Wuhan metro system including two seniorengineers one senior academic professor one technicalconsultant one junior engineer and one worker wereinvited to evaluate the occurrence probability of events thatcannot be readily derived from existing data (Table 12)eweights of their opinion were then calculated by usingequations (9) and (10) and the distribution of each opinionweight is shown in Figure 11

In addition Table 13 lists the expert opinions regardingthe events of environmental failure operational error andmultiple failures in the form of fuzzy numbers based onTable 8 e fuzzy numbers were aggregated via equations(12) and converted to FPS and FFR via equations (13)ndash(16)(Table 14) e occurrence probabilities were finally derivedfrom FFR (Table 14) Generally the expert knowledge isconsidered as a scarce resource which cannot provide

universal consultation or real-time guidance us there ismuch room to improve the data use efficiency

43 Update in Occurrence Probability of LE and OE eoccurrence probability of basic events is calculated as de-scribed in Section 42 including the occurrence probabilityof facility failure from the engineering log data of the XWS aswell as that of environmental failure operational error andmultiple failures derived from expert opinion e occur-rence probability of excessive surface settlement (LE) isdetermined via equations (A) and (B) by considering thelogical relationship between events in Figure 7 Finally theoccurrence probability of OEs including surface collapse canbe calculated via equation (C) in the figure by mapping theFT and ET analyses in the BTmodel to BN Figure 12 showsthe occurrence probabilities of the LE (ie excessive surfacesettlement) and that of the OEs

e above analysis shows that the occurrence probabilityof excessive surface settlement within one year is 08299(Figure 12) is occurrence probability of surface collapse(OE3 OE4 OE6 OE7 and OE8) may be decreased whenemergency measures are put in place including grouting insettlement area and bentonite injection to soil chamber andTBM shield However these measures cannot help to reduceminor accidents since the occurrence probability remains athigh levels for OE1 OE2 and OE5 Admittedly grouting andbentonite injection are necessary measures and they candecrease the effects of excessive surface settlement duringshield tunneling However the key point of avoiding outcomeevents including surface collapse to ensure project safety is toprevent the excessive surface settlement from occurring in thefirst place Hence we sought to determine the key nodesleading to excessive surface settlement via BT-BN analysis andpropose the corresponding preventive measures

Table 10 Analysis of event occurrence

Symbol EventOE1 Excessive surface settlement

OE2Grouted cutter head and shield excessive surface

settlement and minor property damageOE3 Minor surface collapse and property damage

OE4Moderate surface collapse major property damage

and minor casualtiesOE5 Excessive surface settlement

OE6Grouted cutter head and shield moderate surface

collapse and minor property damage

OE7Moderate surface collapse and major property

damage

OE8Severe surface collapse major property damage and

major casualties

Table 9 Details of bow-tie components in Figure 9

Event Symbol Logic link type Failure modelGround settlement Excessive surface settlement OR gate mdashCatastrophic geology M1 OR gate mdashUnforeseeable factors M2 OR gate mdashExcavation parameters M3 AND gate mdashConfined water X1 mdash Environmental failureGround cavity or flow sand X2 mdash Environmental failureObstacles X3 mdash Environmental failureSegment damage X4 mdash Operational errorAbnormal TBM shutdown X5 mdash Multiple failureSeal failure at shield tail X6 mdash Multiple failureExcessive deviation from axis X7 mdash Operational errorEquipment failure X8 mdash Multiple failureUntimely grouting X9 mdash Facility failureExcessive cutter head torque X10 mdash Facility failureImproper control of face pressure X11 mdash Facility failureExcessive thrust X12 mdash Facility failureImproper control of excavation speed X13 mdash Facility failureTBM shutdown CE1 mdash Multiple failureGrouting in settlement area CE2 mdash Multiple failureBentonite injection to soil chamber and TBM shield CE3 mdash Multiple failure

14 Advances in Civil Engineering

Table 11 Probability of equipment fault

Event Surface settlementδmaxi (mm)

Permitted surfacesettlement δi (mm)

Value of TBMparameter

Occurrence rate(dminus1)

Occurrence probability(in 1 year)

X9 89 15 302 kPa 10675eminus 04 382eminus 02X10 84 10 2974 kNmiddotM 17792eminus 04 629eminus 02X11 86 15 143 kPa 71167eminus 05 256eminus 02X12 98 15 13100 kN 14233eminus 04 506eminus 02X13 120 15 41mmmin 28467eminus 04 987eminus 02All data were obtained from the operation log of the XWS

Table 12 Characteristics of experts participated in the occurrence probability evaluation

Expert Age Education Service (years) Professional position1 56 High school 25 Worker2 35 Master 10 Technician3 41 Master 15 Junior engineer4 47 Bachelor 20 Senior engineer5 50 PhD 18 Senior academic6 59 PhD 30 Senior engineer

0125 0125

01625 01625

020225

AgeEducationService

Professional positionWeighting

2 3 4 5 61Expert

0

005

01

015

02

025

Wei

ghtin

g

0

1

2

3

4

5

6

Wei

ghtin

g sc

ore

Figure 11 Distribution of each expert opinion weight

X1 X2 X3

M1

X5 X6 X7 X8

M2

X9 X11

M3

Excessive surface

settlement

X10 X12 X13X4

CE1 CE2 CE3

OE

Caus

esLE

CEC

onse

quen

ces

Figure 10 Bow-tie chart of excessive surface settlement

Advances in Civil Engineering 15

44 Identify Key Nodes and Provide Safety Measures Inorder to find the key nodes leading to excessive surfacesettlement the importance measure of each event was cal-culated via equations (E)ndash(G) in Figure 7 as shown inTable 15 Assume the number of events as ldquonrdquo e nor-malized weight Rlowast could be calculated from the importancemeasure Ii via the following equation

Rlowast

Ii

1113936ni1Ii

times 100 (17)

After the normalized weight Rlowast is calculated for eachimportance measure the total weight Rlowast could be calculatedvia equation (18) e total weight Rlowast of events was finally

ranked in descending order to find the key nodes as shownin Table 16

Rlowast R

lowastBM + R

lowastRAW + R

lowastFV (18)

It can be seen that X6 (seal failure at shield tail) X1(confined water) X2 (ground cavity or flow sand) X5 (ab-normal TBM shutdown) and X7 (excessive deviation fromaxis) have far higher weight than other events and are thusthe key nodes to accidents related to excessive surface set-tlement Measures can be taken to particularly ensure safetyat these nodes e occurrence probability of excessivesurface settlement can be reduced by 66 when X6 X1 X2X5 and X7 are ensured safe (Figure 13)

Table 13 Expert opinion on environmental failure operational error and multiple failures

Event Fuzzy numbers proposed by each expert

X1

Expert 1 Expert 2 Expert 3(02 03 04 05) (01 02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 02 03 05)

X2

Expert 1 Expert 2 Expert 3(01 02 03 05) (02 03 04) (01 02 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (02 03 05) (01 02 03 05)

X3

Expert 1 Expert 2 Expert 3(01 02 04 05) (01 02 03 05) (01 03 04)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03) (01 02 03)

X4

Expert 1 Expert 2 Expert 3(02 03 04 05) (01 02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(02 03 04) (02 03 05) (01 02 03 05)

X5

Expert 1 Expert 2 Expert 3(01 03 04) (01 02 03 05) (02 03 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (02 03 05) (01 02 03)

X6

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 03 05) (02 03 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (02 03 05) (01 02 04 05)

X7

Expert 1 Expert 2 Expert 3(01 02 04 05) (01 02 03 05) (02 03 04)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 03 05)

X8

Expert 1 Expert 2 Expert 3(01 03 04 05) (01 02 03 04) (02 03 04)

Expert 4 Expert 5 Expert 6(02 03 04) (01 02 03 05) (01 02 03)

CE1

Expert 1 Expert 2 Expert 3(02 03 04 05) (02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 02 04 05)

CE2

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 05) (02 03 04 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (01 02 03 05) (01 03 05)

CE3

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 03 05) (03 04 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (01 02 04 05) (01 02 03 05)

16 Advances in Civil Engineering

In accordance with the predictive and diagnosticanalysis results using the established model some safetymeasures for key nodes are displayed in time to reduce theexcessive surface settlement risk during the tunnelexcavation

(1) e nodes X5 (abnormal TBM shutdown) and X7(excessive deviation from the axis) mostly involveoperational error Safety management and supervi-sion need to be strengthened at the construction siteto eliminate such errors and ensure that the TBM isoperated properly Besides an advanced real-time

laser locator may help to alarm in the case of largeaxial deviation

(2) e nodes X1 (confined water) and X2 (ground cavityor flow sand) belong to environmental failure Inorder to reduce the influence of environmental failurecareful geological exploration should be carried outbefore tunneling to identify the poor geological and

Table 14 Calculation of FPS FFR and the occurrence probability of environmental failure operational error and multiple failures

Event Aggregated fuzzy numbers FPS FFR (dminus1) Failure probability (in 1 year)X1 (01288 02288 03288 04838) 02951 83969eminus 04 26402eminus 1X2 (01325 02325 03163 04713) 02909 80032eminus 04 25336eminus 1X3 (01000 02163 02700 03825) 02420 42986eminus 04 14518eminus 1X4 (00450 00900 01125 01800) 01082 22492eminus 05 81803eminus 3X5 (01363 02488 02775 04263) 02747 66022eminus 04 214155eminus 1X6 (01488 02488 03225 04713) 03004 89125eminus 04 27770eminus 1X7 (01163 02388 03125 04675) 02855 75157eminus 04 24002eminus 1X8 (01450 02538 02950 03100) 02463 45643eminus 04 15338eminus 1CE1 (01413 02413 03513 04838) 03058 94598eminus 04 29202eminus 1CE2 (01288 02513 03038 04713) 02916 80679eminus 04 25496eminus 1CE3 (01450 02450 03363 04713) 03010 89722eminus 04 27937eminus 1

08299

03155

01223 010800419

01301

00504 00445 00173

Occ

urre

nce p

roba

bilit

y (in

1 y

ear)

00

01

02

03

04

05

06

07

08

09

OE1 OE2 OE3 OE4 OE5 OE6 OE7 OE8LE

Figure 12 Occurrence probability of surface settlement and otheroutcome events

Table 15 Calculation of importance measure of influential factors

SymbolImportance measure

BM RAW FVX1 2311eminus 1 7352eminus 02 7352eminus 02X2 2279eminus 1 6958eminus 02 6958eminus 02X3 1990eminus 1 3481eminus 02 3481eminus 02X4 1716eminus 1 1691eminus 03 1691eminus 03X5 2165eminus 1 5587eminus 02 5587eminus 02X6 2356eminus 1 7884eminus 02 7884eminus 02X7 2239eminus 1 6476eminus 02 6476eminus 02X8 2010eminus 1 3715eminus 02 3715eminus 02X9 1370eminus 6 6306eminus 08 6306eminus 08X10 8300eminus 7 6291eminus 08 6291eminus 08X11 2040eminus 6 6293eminus 08 6293eminus 08X12 1030eminus 6 6280eminus 08 6280eminus 08X13 5300eminus 7 6303eminus 08 6303eminus 08

Table 16 Ranking results of the key events

Rank SymbolNormalization weighting (Rlowast) Total

weighting(Rlowast)

RlowastBM RlowastRAW RlowastFV

1 X6 13805 18942 18942 516892 X1 13541 17664 17664 488693 X2 13354 16717 16717 467884 X7 13120 15559 15559 442385 X5 12686 13423 13423 395326 X8 11778 8926 89255 296297 X3 11661 8363 8363 283878 X4 10055 0406 0406 108689 X11 00002 1512eminus 05 1512eminus 05 1498eminus 0410 X9 8028eminus 05 1515eminus 05 1515eminus 05 1106eminus 0411 X12 6035eminus 05 1509eminus 05 1509eminus 05 9053eminus 0512 X10 4863eminus 05 1511eminus 05 1511eminus 05 7886eminus 0513 X13 3106eminus 05 1514eminus 05 1514eminus 05 6134eminus 05Total 100 100 100 100

02822

01073

00416 0036700142

0044200172 00151 00059

Occ

urre

nce p

roba

bilit

y (in

1 y

ear)

000

005

010

015

020

025

030

OE1 OE2 OE3 OE4 OE5 OE6 OE7 OE8LE

Figure 13 Occurrence probability when safety is ensured at keynodes

Advances in Civil Engineering 17

hydrological conditions that may be encounteredDuring excavation the advanced geological pre-diction technologymay be employed to detect adversegeological and hydrological conditions ahead of theTBM in real time including confined water groundcavity and flow sand

(3) Node X6 (seal failure at shield tail) belongs tomultiple failures e quality of the tail brush needsto be enhanced and tail brush should promptly bereplaced when it is worn

By adopting corresponding safety measures in shieldtunnel excavation the occurrence probability of variousdegrees of surface collapse (OE3 OE4 OE6 OE7 and OE8)was significantly decreased (Figure 13) Finally the TBMssuccessfully passed through the left track of DCS on March3 2017 and the right track on June 11 2017 without anysurface collapse accident demonstrating the effectiveness ofour proposed hybrid method

5 Conclusions and Future Works

In this work we first defined the ldquonormal excavation phaserdquoof shield tunneling based on the fuzzy statistical test theoryData were extracted from the construction log of the XWS inthe Wuhan metro line 7 to determine the occurrenceprobability of facility fault and expert opinions were soli-cited to determine the occurrence probability of environ-mental failure operational error and multiple failuresProbabilistic safety assessment (PSA) of the normal shieldtunnel excavation system was then performed accordingly

We employed the bow-tie analysis to evaluate the oc-currence of excessive surface settlement during normaltunnel excavation e presence of emergency measurescould reduce the occurrence probability of surface collapsecaused by excessive surface settlement (OE3 OE4 OE6 OE7and OE8) but have limited effect on the prevention of ac-cidents of OE1 OE2 and OE5 It is essential to decrease theprobability of excessive surface settlement in order to pre-vent the resulting outcome events (OEs)

By mapping the bow-tie analysis to Bayesian networks(ie BT-BN analysis) we determined the key nodes thatcould cause excessive surface settlement (LE) e key nodesincluded the following X6 (seal failure at shield tail) X1(confined water) X2 (ground cavity or flow sand) X5 (ab-normal TBM shutdown) and X7 (excessive deviation fromthe axis) Effective safety measures at these nodes couldreduce the occurrence probability of excessive surface set-tlement (LE) by 66

To ensure safety careful geological exploration shouldbe carried out before the tunneling project During thetunneling safety management and supervision should bestrengthened at the construction site Advanced geo-logical prediction technology should be used to detectpoor geological and hydrological conditions ahead of theTBM in real time Advanced laser locator should be usedto monitor and alarm excessive axial deviation equality of the tail brush should be improved and tailbrush should be replaced timely when it becomes worn

e occurrence probability of excessive surface settlementwas decreased by adopting these safety measures and theoccurrence of the resulting surface collapse was sub-sequently decreased

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

e authors thank the workers foremen and safety co-ordinators of the main contractors for their participatione authors also wish to thank the engineers Yun Zhang andPeilun Tu for assistance in gathering field data

References

[1] T Zhao W Liu and Z Ye ldquoEffects of water inrush fromtunnel excavation face on the deformation and mechanicalperformance of shield tunnel segment jointsrdquo Advances inCivil Engineering vol 2017 Article ID 5913640 9 pages 2017

[2] W Liu T Zhao W Zhou and J Tang ldquoSafety risk factors ofmetro tunnel construction in China an integrated study withEFA and SEMrdquo Safety Science vol 105 pp 98ndash113 2018

[3] K Li ldquoHangzhou metro site collapse accidentrdquo 2008 httpnewssohucom20081115n260653551shtml

[4] S Liu ldquoConstruction of Nanchang metro line 2 constructionsection pavement collapsesrdquo 2017 httpnewssohucom20160514n449414512shtml

[5] R B Peck ldquoDeep excavations and tunneling in soft groundrdquo7th International Conference on Soil Mechanics and Foun-dation Engineering vol 7 no 3 pp 225ndash290 1969

[6] P B Attewell I W Farmer and N H Glossop ldquoGrounddeformation caused by tunnelling in a silty alluvial clayrdquoGround Engineering vol 11 no 8 pp 32ndash41 1978

[7] W J Rankin ldquoGround movements resulting from urbantunnelling predictions and effectsrdquo Geological Society Lon-don Engineering Geology Special Publications vol 5 no 1pp 79ndash92 1988

[8] P B Attewell and J P Woodman ldquoPredicting the dynamicsof ground settlement and its derivatives caused by tunnelingin soilrdquo Ground Engineering vol 15 no 8 pp 13ndash20 1982

[9] M P OrsquoReilly and B M New ldquoSettlement above tunnels inthe United Kingdommdashtheir magnitude and prediction intunnelling 82 proceedings of the 3rd international sympo-sium brighton 7ndash11 June 1982 P173ndash181 Publ LondonIMM 1982rdquo International Journal of Rock Mechanics ampMining Sciences amp Geomechanics Abstracts vol 20 no 1pp 1ndash18 1983

[10] R J Mair R N Taylor and A Bracegirdle ldquoSubsurfacesettlement profiles above tunnels in claysrdquo Geotechniquevol 45 no 2 pp 361-362 1995

[11] X L Yang and J MWang ldquoGroundmovement prediction fortunnels using simplified procedurerdquo Tunnelling and Un-derground Space Technology vol 26 no 3 pp 462ndash471 2011

18 Advances in Civil Engineering

excavation phaserdquo as the base events assigning their weightsaccording to Section 33 and then performed PSA analysis

As mentioned earlier the ldquonormal excavation phaserdquo isunder the influence of excavation parameters catastrophicgeology and unforeseeable factors Surface settlement canoccur once the condition deteriorates Here we set excessivesurface settlement as the TE in the FT analysis Meanwhilethe tunneling system has a built-in emergency managementsystem Upon excessive surface settlement the emergencymanagement system will start to shut down the TBM timelyHence in the ETanalysis the excessive surface settlement isset as the IE and TBM shutdown is set as the CE OEs ofvarious degrees are obtained based on the considered CEFinally the surface settlement is set as the LE to connect theFT and the ET and furnish the BTmodel (Figure 9 Table 9)Eight OEs of various degrees were predicted based on theCEs including surface collapse events OE3 OE4 OE6 OE7and OE8 (Figure 9 Table 10) e TBM shuts down if CE1occurs and continues to operate if otherwise

e BN-BT model for excessive surface settlement isconstructed by mapping the FT and ET analyses in the BT(Figure 9) model to BN (Figure 10) All the nodes of BN havepreviously been described in the BT except the node OEwhich is the consequence node OE is added to accommodatethe outcomes of BT By connecting the node of excessivesurface settlement to OE another state also called the safe

state is added to the state set It includes consequences OE1 toOE8 to account for the nonoccurrence of the top event iewhen excessive surface settlement controlled To show thedependence among the safety barriers and the top eventcausal arcs are also drawn between TBM shutdown andgrouting in the settlement area and bentonite injection to soilchamber and TBM shield It is worth noting that since variouscombinations of the failure and success of the sequentialsafety barriers result in different consequences in the BT allthe safety nodes of BN are connected to node OE

42 Determination of Event Occurrence Probability emaximum surface settlement that resulted from the aber-ration of the ith TBM parameter is denoted as δmaxi eprobability of safety accident becomes higher when δmaxiapproaches the permitted surface settlement δi Whenδmaxi δi the accident will occur as soon as the TBM pa-rameter gives rise to a surface settlement of δmaxi eprobability of equipment fault for the normal excavationsystem was calculated via equation (8) from the engineeringlog data of the XWS over 179 days of construction (715segments rings in total) e construction of all 715 rings fellwithin the ldquonormal excavation phaserdquo as was defined by thefuzzy statistical test (v 20ndash44mmmin) Table 11 lists thecalculation results

X3X2X1

OR

M1

X7X6X5X4

OR

M2

X10X9 X11 X13X12

M3

OR

Excessive surface

settlement

X8

Caus

esLE

CE1

CE2

CE3

Con

sequ

ence

sSt

op

TBM

Gro

utin

g in

settl

emen

tar

ea

Bent

onite

inje

ctio

n

OE 1

OE 2

OE 3

OE 4

OE 5

OE 6

OE 7

OE 8

Success Failure

AND

Figure 9 Diagram of bow-tie analysis for excessive surface settlement

Advances in Civil Engineering 13

To address the uncertainty regarding the events ofenvironmental failure operational error and multiplefailure six domain experts who participated in the con-struction of the Wuhan metro system including two seniorengineers one senior academic professor one technicalconsultant one junior engineer and one worker wereinvited to evaluate the occurrence probability of events thatcannot be readily derived from existing data (Table 12)eweights of their opinion were then calculated by usingequations (9) and (10) and the distribution of each opinionweight is shown in Figure 11

In addition Table 13 lists the expert opinions regardingthe events of environmental failure operational error andmultiple failures in the form of fuzzy numbers based onTable 8 e fuzzy numbers were aggregated via equations(12) and converted to FPS and FFR via equations (13)ndash(16)(Table 14) e occurrence probabilities were finally derivedfrom FFR (Table 14) Generally the expert knowledge isconsidered as a scarce resource which cannot provide

universal consultation or real-time guidance us there ismuch room to improve the data use efficiency

43 Update in Occurrence Probability of LE and OE eoccurrence probability of basic events is calculated as de-scribed in Section 42 including the occurrence probabilityof facility failure from the engineering log data of the XWS aswell as that of environmental failure operational error andmultiple failures derived from expert opinion e occur-rence probability of excessive surface settlement (LE) isdetermined via equations (A) and (B) by considering thelogical relationship between events in Figure 7 Finally theoccurrence probability of OEs including surface collapse canbe calculated via equation (C) in the figure by mapping theFT and ET analyses in the BTmodel to BN Figure 12 showsthe occurrence probabilities of the LE (ie excessive surfacesettlement) and that of the OEs

e above analysis shows that the occurrence probabilityof excessive surface settlement within one year is 08299(Figure 12) is occurrence probability of surface collapse(OE3 OE4 OE6 OE7 and OE8) may be decreased whenemergency measures are put in place including grouting insettlement area and bentonite injection to soil chamber andTBM shield However these measures cannot help to reduceminor accidents since the occurrence probability remains athigh levels for OE1 OE2 and OE5 Admittedly grouting andbentonite injection are necessary measures and they candecrease the effects of excessive surface settlement duringshield tunneling However the key point of avoiding outcomeevents including surface collapse to ensure project safety is toprevent the excessive surface settlement from occurring in thefirst place Hence we sought to determine the key nodesleading to excessive surface settlement via BT-BN analysis andpropose the corresponding preventive measures

Table 10 Analysis of event occurrence

Symbol EventOE1 Excessive surface settlement

OE2Grouted cutter head and shield excessive surface

settlement and minor property damageOE3 Minor surface collapse and property damage

OE4Moderate surface collapse major property damage

and minor casualtiesOE5 Excessive surface settlement

OE6Grouted cutter head and shield moderate surface

collapse and minor property damage

OE7Moderate surface collapse and major property

damage

OE8Severe surface collapse major property damage and

major casualties

Table 9 Details of bow-tie components in Figure 9

Event Symbol Logic link type Failure modelGround settlement Excessive surface settlement OR gate mdashCatastrophic geology M1 OR gate mdashUnforeseeable factors M2 OR gate mdashExcavation parameters M3 AND gate mdashConfined water X1 mdash Environmental failureGround cavity or flow sand X2 mdash Environmental failureObstacles X3 mdash Environmental failureSegment damage X4 mdash Operational errorAbnormal TBM shutdown X5 mdash Multiple failureSeal failure at shield tail X6 mdash Multiple failureExcessive deviation from axis X7 mdash Operational errorEquipment failure X8 mdash Multiple failureUntimely grouting X9 mdash Facility failureExcessive cutter head torque X10 mdash Facility failureImproper control of face pressure X11 mdash Facility failureExcessive thrust X12 mdash Facility failureImproper control of excavation speed X13 mdash Facility failureTBM shutdown CE1 mdash Multiple failureGrouting in settlement area CE2 mdash Multiple failureBentonite injection to soil chamber and TBM shield CE3 mdash Multiple failure

14 Advances in Civil Engineering

Table 11 Probability of equipment fault

Event Surface settlementδmaxi (mm)

Permitted surfacesettlement δi (mm)

Value of TBMparameter

Occurrence rate(dminus1)

Occurrence probability(in 1 year)

X9 89 15 302 kPa 10675eminus 04 382eminus 02X10 84 10 2974 kNmiddotM 17792eminus 04 629eminus 02X11 86 15 143 kPa 71167eminus 05 256eminus 02X12 98 15 13100 kN 14233eminus 04 506eminus 02X13 120 15 41mmmin 28467eminus 04 987eminus 02All data were obtained from the operation log of the XWS

Table 12 Characteristics of experts participated in the occurrence probability evaluation

Expert Age Education Service (years) Professional position1 56 High school 25 Worker2 35 Master 10 Technician3 41 Master 15 Junior engineer4 47 Bachelor 20 Senior engineer5 50 PhD 18 Senior academic6 59 PhD 30 Senior engineer

0125 0125

01625 01625

020225

AgeEducationService

Professional positionWeighting

2 3 4 5 61Expert

0

005

01

015

02

025

Wei

ghtin

g

0

1

2

3

4

5

6

Wei

ghtin

g sc

ore

Figure 11 Distribution of each expert opinion weight

X1 X2 X3

M1

X5 X6 X7 X8

M2

X9 X11

M3

Excessive surface

settlement

X10 X12 X13X4

CE1 CE2 CE3

OE

Caus

esLE

CEC

onse

quen

ces

Figure 10 Bow-tie chart of excessive surface settlement

Advances in Civil Engineering 15

44 Identify Key Nodes and Provide Safety Measures Inorder to find the key nodes leading to excessive surfacesettlement the importance measure of each event was cal-culated via equations (E)ndash(G) in Figure 7 as shown inTable 15 Assume the number of events as ldquonrdquo e nor-malized weight Rlowast could be calculated from the importancemeasure Ii via the following equation

Rlowast

Ii

1113936ni1Ii

times 100 (17)

After the normalized weight Rlowast is calculated for eachimportance measure the total weight Rlowast could be calculatedvia equation (18) e total weight Rlowast of events was finally

ranked in descending order to find the key nodes as shownin Table 16

Rlowast R

lowastBM + R

lowastRAW + R

lowastFV (18)

It can be seen that X6 (seal failure at shield tail) X1(confined water) X2 (ground cavity or flow sand) X5 (ab-normal TBM shutdown) and X7 (excessive deviation fromaxis) have far higher weight than other events and are thusthe key nodes to accidents related to excessive surface set-tlement Measures can be taken to particularly ensure safetyat these nodes e occurrence probability of excessivesurface settlement can be reduced by 66 when X6 X1 X2X5 and X7 are ensured safe (Figure 13)

Table 13 Expert opinion on environmental failure operational error and multiple failures

Event Fuzzy numbers proposed by each expert

X1

Expert 1 Expert 2 Expert 3(02 03 04 05) (01 02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 02 03 05)

X2

Expert 1 Expert 2 Expert 3(01 02 03 05) (02 03 04) (01 02 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (02 03 05) (01 02 03 05)

X3

Expert 1 Expert 2 Expert 3(01 02 04 05) (01 02 03 05) (01 03 04)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03) (01 02 03)

X4

Expert 1 Expert 2 Expert 3(02 03 04 05) (01 02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(02 03 04) (02 03 05) (01 02 03 05)

X5

Expert 1 Expert 2 Expert 3(01 03 04) (01 02 03 05) (02 03 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (02 03 05) (01 02 03)

X6

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 03 05) (02 03 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (02 03 05) (01 02 04 05)

X7

Expert 1 Expert 2 Expert 3(01 02 04 05) (01 02 03 05) (02 03 04)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 03 05)

X8

Expert 1 Expert 2 Expert 3(01 03 04 05) (01 02 03 04) (02 03 04)

Expert 4 Expert 5 Expert 6(02 03 04) (01 02 03 05) (01 02 03)

CE1

Expert 1 Expert 2 Expert 3(02 03 04 05) (02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 02 04 05)

CE2

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 05) (02 03 04 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (01 02 03 05) (01 03 05)

CE3

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 03 05) (03 04 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (01 02 04 05) (01 02 03 05)

16 Advances in Civil Engineering

In accordance with the predictive and diagnosticanalysis results using the established model some safetymeasures for key nodes are displayed in time to reduce theexcessive surface settlement risk during the tunnelexcavation

(1) e nodes X5 (abnormal TBM shutdown) and X7(excessive deviation from the axis) mostly involveoperational error Safety management and supervi-sion need to be strengthened at the construction siteto eliminate such errors and ensure that the TBM isoperated properly Besides an advanced real-time

laser locator may help to alarm in the case of largeaxial deviation

(2) e nodes X1 (confined water) and X2 (ground cavityor flow sand) belong to environmental failure Inorder to reduce the influence of environmental failurecareful geological exploration should be carried outbefore tunneling to identify the poor geological and

Table 14 Calculation of FPS FFR and the occurrence probability of environmental failure operational error and multiple failures

Event Aggregated fuzzy numbers FPS FFR (dminus1) Failure probability (in 1 year)X1 (01288 02288 03288 04838) 02951 83969eminus 04 26402eminus 1X2 (01325 02325 03163 04713) 02909 80032eminus 04 25336eminus 1X3 (01000 02163 02700 03825) 02420 42986eminus 04 14518eminus 1X4 (00450 00900 01125 01800) 01082 22492eminus 05 81803eminus 3X5 (01363 02488 02775 04263) 02747 66022eminus 04 214155eminus 1X6 (01488 02488 03225 04713) 03004 89125eminus 04 27770eminus 1X7 (01163 02388 03125 04675) 02855 75157eminus 04 24002eminus 1X8 (01450 02538 02950 03100) 02463 45643eminus 04 15338eminus 1CE1 (01413 02413 03513 04838) 03058 94598eminus 04 29202eminus 1CE2 (01288 02513 03038 04713) 02916 80679eminus 04 25496eminus 1CE3 (01450 02450 03363 04713) 03010 89722eminus 04 27937eminus 1

08299

03155

01223 010800419

01301

00504 00445 00173

Occ

urre

nce p

roba

bilit

y (in

1 y

ear)

00

01

02

03

04

05

06

07

08

09

OE1 OE2 OE3 OE4 OE5 OE6 OE7 OE8LE

Figure 12 Occurrence probability of surface settlement and otheroutcome events

Table 15 Calculation of importance measure of influential factors

SymbolImportance measure

BM RAW FVX1 2311eminus 1 7352eminus 02 7352eminus 02X2 2279eminus 1 6958eminus 02 6958eminus 02X3 1990eminus 1 3481eminus 02 3481eminus 02X4 1716eminus 1 1691eminus 03 1691eminus 03X5 2165eminus 1 5587eminus 02 5587eminus 02X6 2356eminus 1 7884eminus 02 7884eminus 02X7 2239eminus 1 6476eminus 02 6476eminus 02X8 2010eminus 1 3715eminus 02 3715eminus 02X9 1370eminus 6 6306eminus 08 6306eminus 08X10 8300eminus 7 6291eminus 08 6291eminus 08X11 2040eminus 6 6293eminus 08 6293eminus 08X12 1030eminus 6 6280eminus 08 6280eminus 08X13 5300eminus 7 6303eminus 08 6303eminus 08

Table 16 Ranking results of the key events

Rank SymbolNormalization weighting (Rlowast) Total

weighting(Rlowast)

RlowastBM RlowastRAW RlowastFV

1 X6 13805 18942 18942 516892 X1 13541 17664 17664 488693 X2 13354 16717 16717 467884 X7 13120 15559 15559 442385 X5 12686 13423 13423 395326 X8 11778 8926 89255 296297 X3 11661 8363 8363 283878 X4 10055 0406 0406 108689 X11 00002 1512eminus 05 1512eminus 05 1498eminus 0410 X9 8028eminus 05 1515eminus 05 1515eminus 05 1106eminus 0411 X12 6035eminus 05 1509eminus 05 1509eminus 05 9053eminus 0512 X10 4863eminus 05 1511eminus 05 1511eminus 05 7886eminus 0513 X13 3106eminus 05 1514eminus 05 1514eminus 05 6134eminus 05Total 100 100 100 100

02822

01073

00416 0036700142

0044200172 00151 00059

Occ

urre

nce p

roba

bilit

y (in

1 y

ear)

000

005

010

015

020

025

030

OE1 OE2 OE3 OE4 OE5 OE6 OE7 OE8LE

Figure 13 Occurrence probability when safety is ensured at keynodes

Advances in Civil Engineering 17

hydrological conditions that may be encounteredDuring excavation the advanced geological pre-diction technologymay be employed to detect adversegeological and hydrological conditions ahead of theTBM in real time including confined water groundcavity and flow sand

(3) Node X6 (seal failure at shield tail) belongs tomultiple failures e quality of the tail brush needsto be enhanced and tail brush should promptly bereplaced when it is worn

By adopting corresponding safety measures in shieldtunnel excavation the occurrence probability of variousdegrees of surface collapse (OE3 OE4 OE6 OE7 and OE8)was significantly decreased (Figure 13) Finally the TBMssuccessfully passed through the left track of DCS on March3 2017 and the right track on June 11 2017 without anysurface collapse accident demonstrating the effectiveness ofour proposed hybrid method

5 Conclusions and Future Works

In this work we first defined the ldquonormal excavation phaserdquoof shield tunneling based on the fuzzy statistical test theoryData were extracted from the construction log of the XWS inthe Wuhan metro line 7 to determine the occurrenceprobability of facility fault and expert opinions were soli-cited to determine the occurrence probability of environ-mental failure operational error and multiple failuresProbabilistic safety assessment (PSA) of the normal shieldtunnel excavation system was then performed accordingly

We employed the bow-tie analysis to evaluate the oc-currence of excessive surface settlement during normaltunnel excavation e presence of emergency measurescould reduce the occurrence probability of surface collapsecaused by excessive surface settlement (OE3 OE4 OE6 OE7and OE8) but have limited effect on the prevention of ac-cidents of OE1 OE2 and OE5 It is essential to decrease theprobability of excessive surface settlement in order to pre-vent the resulting outcome events (OEs)

By mapping the bow-tie analysis to Bayesian networks(ie BT-BN analysis) we determined the key nodes thatcould cause excessive surface settlement (LE) e key nodesincluded the following X6 (seal failure at shield tail) X1(confined water) X2 (ground cavity or flow sand) X5 (ab-normal TBM shutdown) and X7 (excessive deviation fromthe axis) Effective safety measures at these nodes couldreduce the occurrence probability of excessive surface set-tlement (LE) by 66

To ensure safety careful geological exploration shouldbe carried out before the tunneling project During thetunneling safety management and supervision should bestrengthened at the construction site Advanced geo-logical prediction technology should be used to detectpoor geological and hydrological conditions ahead of theTBM in real time Advanced laser locator should be usedto monitor and alarm excessive axial deviation equality of the tail brush should be improved and tailbrush should be replaced timely when it becomes worn

e occurrence probability of excessive surface settlementwas decreased by adopting these safety measures and theoccurrence of the resulting surface collapse was sub-sequently decreased

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

e authors thank the workers foremen and safety co-ordinators of the main contractors for their participatione authors also wish to thank the engineers Yun Zhang andPeilun Tu for assistance in gathering field data

References

[1] T Zhao W Liu and Z Ye ldquoEffects of water inrush fromtunnel excavation face on the deformation and mechanicalperformance of shield tunnel segment jointsrdquo Advances inCivil Engineering vol 2017 Article ID 5913640 9 pages 2017

[2] W Liu T Zhao W Zhou and J Tang ldquoSafety risk factors ofmetro tunnel construction in China an integrated study withEFA and SEMrdquo Safety Science vol 105 pp 98ndash113 2018

[3] K Li ldquoHangzhou metro site collapse accidentrdquo 2008 httpnewssohucom20081115n260653551shtml

[4] S Liu ldquoConstruction of Nanchang metro line 2 constructionsection pavement collapsesrdquo 2017 httpnewssohucom20160514n449414512shtml

[5] R B Peck ldquoDeep excavations and tunneling in soft groundrdquo7th International Conference on Soil Mechanics and Foun-dation Engineering vol 7 no 3 pp 225ndash290 1969

[6] P B Attewell I W Farmer and N H Glossop ldquoGrounddeformation caused by tunnelling in a silty alluvial clayrdquoGround Engineering vol 11 no 8 pp 32ndash41 1978

[7] W J Rankin ldquoGround movements resulting from urbantunnelling predictions and effectsrdquo Geological Society Lon-don Engineering Geology Special Publications vol 5 no 1pp 79ndash92 1988

[8] P B Attewell and J P Woodman ldquoPredicting the dynamicsof ground settlement and its derivatives caused by tunnelingin soilrdquo Ground Engineering vol 15 no 8 pp 13ndash20 1982

[9] M P OrsquoReilly and B M New ldquoSettlement above tunnels inthe United Kingdommdashtheir magnitude and prediction intunnelling 82 proceedings of the 3rd international sympo-sium brighton 7ndash11 June 1982 P173ndash181 Publ LondonIMM 1982rdquo International Journal of Rock Mechanics ampMining Sciences amp Geomechanics Abstracts vol 20 no 1pp 1ndash18 1983

[10] R J Mair R N Taylor and A Bracegirdle ldquoSubsurfacesettlement profiles above tunnels in claysrdquo Geotechniquevol 45 no 2 pp 361-362 1995

[11] X L Yang and J MWang ldquoGroundmovement prediction fortunnels using simplified procedurerdquo Tunnelling and Un-derground Space Technology vol 26 no 3 pp 462ndash471 2011

18 Advances in Civil Engineering

To address the uncertainty regarding the events ofenvironmental failure operational error and multiplefailure six domain experts who participated in the con-struction of the Wuhan metro system including two seniorengineers one senior academic professor one technicalconsultant one junior engineer and one worker wereinvited to evaluate the occurrence probability of events thatcannot be readily derived from existing data (Table 12)eweights of their opinion were then calculated by usingequations (9) and (10) and the distribution of each opinionweight is shown in Figure 11

In addition Table 13 lists the expert opinions regardingthe events of environmental failure operational error andmultiple failures in the form of fuzzy numbers based onTable 8 e fuzzy numbers were aggregated via equations(12) and converted to FPS and FFR via equations (13)ndash(16)(Table 14) e occurrence probabilities were finally derivedfrom FFR (Table 14) Generally the expert knowledge isconsidered as a scarce resource which cannot provide

universal consultation or real-time guidance us there ismuch room to improve the data use efficiency

43 Update in Occurrence Probability of LE and OE eoccurrence probability of basic events is calculated as de-scribed in Section 42 including the occurrence probabilityof facility failure from the engineering log data of the XWS aswell as that of environmental failure operational error andmultiple failures derived from expert opinion e occur-rence probability of excessive surface settlement (LE) isdetermined via equations (A) and (B) by considering thelogical relationship between events in Figure 7 Finally theoccurrence probability of OEs including surface collapse canbe calculated via equation (C) in the figure by mapping theFT and ET analyses in the BTmodel to BN Figure 12 showsthe occurrence probabilities of the LE (ie excessive surfacesettlement) and that of the OEs

e above analysis shows that the occurrence probabilityof excessive surface settlement within one year is 08299(Figure 12) is occurrence probability of surface collapse(OE3 OE4 OE6 OE7 and OE8) may be decreased whenemergency measures are put in place including grouting insettlement area and bentonite injection to soil chamber andTBM shield However these measures cannot help to reduceminor accidents since the occurrence probability remains athigh levels for OE1 OE2 and OE5 Admittedly grouting andbentonite injection are necessary measures and they candecrease the effects of excessive surface settlement duringshield tunneling However the key point of avoiding outcomeevents including surface collapse to ensure project safety is toprevent the excessive surface settlement from occurring in thefirst place Hence we sought to determine the key nodesleading to excessive surface settlement via BT-BN analysis andpropose the corresponding preventive measures

Table 10 Analysis of event occurrence

Symbol EventOE1 Excessive surface settlement

OE2Grouted cutter head and shield excessive surface

settlement and minor property damageOE3 Minor surface collapse and property damage

OE4Moderate surface collapse major property damage

and minor casualtiesOE5 Excessive surface settlement

OE6Grouted cutter head and shield moderate surface

collapse and minor property damage

OE7Moderate surface collapse and major property

damage

OE8Severe surface collapse major property damage and

major casualties

Table 9 Details of bow-tie components in Figure 9

Event Symbol Logic link type Failure modelGround settlement Excessive surface settlement OR gate mdashCatastrophic geology M1 OR gate mdashUnforeseeable factors M2 OR gate mdashExcavation parameters M3 AND gate mdashConfined water X1 mdash Environmental failureGround cavity or flow sand X2 mdash Environmental failureObstacles X3 mdash Environmental failureSegment damage X4 mdash Operational errorAbnormal TBM shutdown X5 mdash Multiple failureSeal failure at shield tail X6 mdash Multiple failureExcessive deviation from axis X7 mdash Operational errorEquipment failure X8 mdash Multiple failureUntimely grouting X9 mdash Facility failureExcessive cutter head torque X10 mdash Facility failureImproper control of face pressure X11 mdash Facility failureExcessive thrust X12 mdash Facility failureImproper control of excavation speed X13 mdash Facility failureTBM shutdown CE1 mdash Multiple failureGrouting in settlement area CE2 mdash Multiple failureBentonite injection to soil chamber and TBM shield CE3 mdash Multiple failure

14 Advances in Civil Engineering

Table 11 Probability of equipment fault

Event Surface settlementδmaxi (mm)

Permitted surfacesettlement δi (mm)

Value of TBMparameter

Occurrence rate(dminus1)

Occurrence probability(in 1 year)

X9 89 15 302 kPa 10675eminus 04 382eminus 02X10 84 10 2974 kNmiddotM 17792eminus 04 629eminus 02X11 86 15 143 kPa 71167eminus 05 256eminus 02X12 98 15 13100 kN 14233eminus 04 506eminus 02X13 120 15 41mmmin 28467eminus 04 987eminus 02All data were obtained from the operation log of the XWS

Table 12 Characteristics of experts participated in the occurrence probability evaluation

Expert Age Education Service (years) Professional position1 56 High school 25 Worker2 35 Master 10 Technician3 41 Master 15 Junior engineer4 47 Bachelor 20 Senior engineer5 50 PhD 18 Senior academic6 59 PhD 30 Senior engineer

0125 0125

01625 01625

020225

AgeEducationService

Professional positionWeighting

2 3 4 5 61Expert

0

005

01

015

02

025

Wei

ghtin

g

0

1

2

3

4

5

6

Wei

ghtin

g sc

ore

Figure 11 Distribution of each expert opinion weight

X1 X2 X3

M1

X5 X6 X7 X8

M2

X9 X11

M3

Excessive surface

settlement

X10 X12 X13X4

CE1 CE2 CE3

OE

Caus

esLE

CEC

onse

quen

ces

Figure 10 Bow-tie chart of excessive surface settlement

Advances in Civil Engineering 15

44 Identify Key Nodes and Provide Safety Measures Inorder to find the key nodes leading to excessive surfacesettlement the importance measure of each event was cal-culated via equations (E)ndash(G) in Figure 7 as shown inTable 15 Assume the number of events as ldquonrdquo e nor-malized weight Rlowast could be calculated from the importancemeasure Ii via the following equation

Rlowast

Ii

1113936ni1Ii

times 100 (17)

After the normalized weight Rlowast is calculated for eachimportance measure the total weight Rlowast could be calculatedvia equation (18) e total weight Rlowast of events was finally

ranked in descending order to find the key nodes as shownin Table 16

Rlowast R

lowastBM + R

lowastRAW + R

lowastFV (18)

It can be seen that X6 (seal failure at shield tail) X1(confined water) X2 (ground cavity or flow sand) X5 (ab-normal TBM shutdown) and X7 (excessive deviation fromaxis) have far higher weight than other events and are thusthe key nodes to accidents related to excessive surface set-tlement Measures can be taken to particularly ensure safetyat these nodes e occurrence probability of excessivesurface settlement can be reduced by 66 when X6 X1 X2X5 and X7 are ensured safe (Figure 13)

Table 13 Expert opinion on environmental failure operational error and multiple failures

Event Fuzzy numbers proposed by each expert

X1

Expert 1 Expert 2 Expert 3(02 03 04 05) (01 02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 02 03 05)

X2

Expert 1 Expert 2 Expert 3(01 02 03 05) (02 03 04) (01 02 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (02 03 05) (01 02 03 05)

X3

Expert 1 Expert 2 Expert 3(01 02 04 05) (01 02 03 05) (01 03 04)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03) (01 02 03)

X4

Expert 1 Expert 2 Expert 3(02 03 04 05) (01 02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(02 03 04) (02 03 05) (01 02 03 05)

X5

Expert 1 Expert 2 Expert 3(01 03 04) (01 02 03 05) (02 03 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (02 03 05) (01 02 03)

X6

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 03 05) (02 03 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (02 03 05) (01 02 04 05)

X7

Expert 1 Expert 2 Expert 3(01 02 04 05) (01 02 03 05) (02 03 04)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 03 05)

X8

Expert 1 Expert 2 Expert 3(01 03 04 05) (01 02 03 04) (02 03 04)

Expert 4 Expert 5 Expert 6(02 03 04) (01 02 03 05) (01 02 03)

CE1

Expert 1 Expert 2 Expert 3(02 03 04 05) (02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 02 04 05)

CE2

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 05) (02 03 04 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (01 02 03 05) (01 03 05)

CE3

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 03 05) (03 04 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (01 02 04 05) (01 02 03 05)

16 Advances in Civil Engineering

In accordance with the predictive and diagnosticanalysis results using the established model some safetymeasures for key nodes are displayed in time to reduce theexcessive surface settlement risk during the tunnelexcavation

(1) e nodes X5 (abnormal TBM shutdown) and X7(excessive deviation from the axis) mostly involveoperational error Safety management and supervi-sion need to be strengthened at the construction siteto eliminate such errors and ensure that the TBM isoperated properly Besides an advanced real-time

laser locator may help to alarm in the case of largeaxial deviation

(2) e nodes X1 (confined water) and X2 (ground cavityor flow sand) belong to environmental failure Inorder to reduce the influence of environmental failurecareful geological exploration should be carried outbefore tunneling to identify the poor geological and

Table 14 Calculation of FPS FFR and the occurrence probability of environmental failure operational error and multiple failures

Event Aggregated fuzzy numbers FPS FFR (dminus1) Failure probability (in 1 year)X1 (01288 02288 03288 04838) 02951 83969eminus 04 26402eminus 1X2 (01325 02325 03163 04713) 02909 80032eminus 04 25336eminus 1X3 (01000 02163 02700 03825) 02420 42986eminus 04 14518eminus 1X4 (00450 00900 01125 01800) 01082 22492eminus 05 81803eminus 3X5 (01363 02488 02775 04263) 02747 66022eminus 04 214155eminus 1X6 (01488 02488 03225 04713) 03004 89125eminus 04 27770eminus 1X7 (01163 02388 03125 04675) 02855 75157eminus 04 24002eminus 1X8 (01450 02538 02950 03100) 02463 45643eminus 04 15338eminus 1CE1 (01413 02413 03513 04838) 03058 94598eminus 04 29202eminus 1CE2 (01288 02513 03038 04713) 02916 80679eminus 04 25496eminus 1CE3 (01450 02450 03363 04713) 03010 89722eminus 04 27937eminus 1

08299

03155

01223 010800419

01301

00504 00445 00173

Occ

urre

nce p

roba

bilit

y (in

1 y

ear)

00

01

02

03

04

05

06

07

08

09

OE1 OE2 OE3 OE4 OE5 OE6 OE7 OE8LE

Figure 12 Occurrence probability of surface settlement and otheroutcome events

Table 15 Calculation of importance measure of influential factors

SymbolImportance measure

BM RAW FVX1 2311eminus 1 7352eminus 02 7352eminus 02X2 2279eminus 1 6958eminus 02 6958eminus 02X3 1990eminus 1 3481eminus 02 3481eminus 02X4 1716eminus 1 1691eminus 03 1691eminus 03X5 2165eminus 1 5587eminus 02 5587eminus 02X6 2356eminus 1 7884eminus 02 7884eminus 02X7 2239eminus 1 6476eminus 02 6476eminus 02X8 2010eminus 1 3715eminus 02 3715eminus 02X9 1370eminus 6 6306eminus 08 6306eminus 08X10 8300eminus 7 6291eminus 08 6291eminus 08X11 2040eminus 6 6293eminus 08 6293eminus 08X12 1030eminus 6 6280eminus 08 6280eminus 08X13 5300eminus 7 6303eminus 08 6303eminus 08

Table 16 Ranking results of the key events

Rank SymbolNormalization weighting (Rlowast) Total

weighting(Rlowast)

RlowastBM RlowastRAW RlowastFV

1 X6 13805 18942 18942 516892 X1 13541 17664 17664 488693 X2 13354 16717 16717 467884 X7 13120 15559 15559 442385 X5 12686 13423 13423 395326 X8 11778 8926 89255 296297 X3 11661 8363 8363 283878 X4 10055 0406 0406 108689 X11 00002 1512eminus 05 1512eminus 05 1498eminus 0410 X9 8028eminus 05 1515eminus 05 1515eminus 05 1106eminus 0411 X12 6035eminus 05 1509eminus 05 1509eminus 05 9053eminus 0512 X10 4863eminus 05 1511eminus 05 1511eminus 05 7886eminus 0513 X13 3106eminus 05 1514eminus 05 1514eminus 05 6134eminus 05Total 100 100 100 100

02822

01073

00416 0036700142

0044200172 00151 00059

Occ

urre

nce p

roba

bilit

y (in

1 y

ear)

000

005

010

015

020

025

030

OE1 OE2 OE3 OE4 OE5 OE6 OE7 OE8LE

Figure 13 Occurrence probability when safety is ensured at keynodes

Advances in Civil Engineering 17

hydrological conditions that may be encounteredDuring excavation the advanced geological pre-diction technologymay be employed to detect adversegeological and hydrological conditions ahead of theTBM in real time including confined water groundcavity and flow sand

(3) Node X6 (seal failure at shield tail) belongs tomultiple failures e quality of the tail brush needsto be enhanced and tail brush should promptly bereplaced when it is worn

By adopting corresponding safety measures in shieldtunnel excavation the occurrence probability of variousdegrees of surface collapse (OE3 OE4 OE6 OE7 and OE8)was significantly decreased (Figure 13) Finally the TBMssuccessfully passed through the left track of DCS on March3 2017 and the right track on June 11 2017 without anysurface collapse accident demonstrating the effectiveness ofour proposed hybrid method

5 Conclusions and Future Works

In this work we first defined the ldquonormal excavation phaserdquoof shield tunneling based on the fuzzy statistical test theoryData were extracted from the construction log of the XWS inthe Wuhan metro line 7 to determine the occurrenceprobability of facility fault and expert opinions were soli-cited to determine the occurrence probability of environ-mental failure operational error and multiple failuresProbabilistic safety assessment (PSA) of the normal shieldtunnel excavation system was then performed accordingly

We employed the bow-tie analysis to evaluate the oc-currence of excessive surface settlement during normaltunnel excavation e presence of emergency measurescould reduce the occurrence probability of surface collapsecaused by excessive surface settlement (OE3 OE4 OE6 OE7and OE8) but have limited effect on the prevention of ac-cidents of OE1 OE2 and OE5 It is essential to decrease theprobability of excessive surface settlement in order to pre-vent the resulting outcome events (OEs)

By mapping the bow-tie analysis to Bayesian networks(ie BT-BN analysis) we determined the key nodes thatcould cause excessive surface settlement (LE) e key nodesincluded the following X6 (seal failure at shield tail) X1(confined water) X2 (ground cavity or flow sand) X5 (ab-normal TBM shutdown) and X7 (excessive deviation fromthe axis) Effective safety measures at these nodes couldreduce the occurrence probability of excessive surface set-tlement (LE) by 66

To ensure safety careful geological exploration shouldbe carried out before the tunneling project During thetunneling safety management and supervision should bestrengthened at the construction site Advanced geo-logical prediction technology should be used to detectpoor geological and hydrological conditions ahead of theTBM in real time Advanced laser locator should be usedto monitor and alarm excessive axial deviation equality of the tail brush should be improved and tailbrush should be replaced timely when it becomes worn

e occurrence probability of excessive surface settlementwas decreased by adopting these safety measures and theoccurrence of the resulting surface collapse was sub-sequently decreased

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

e authors thank the workers foremen and safety co-ordinators of the main contractors for their participatione authors also wish to thank the engineers Yun Zhang andPeilun Tu for assistance in gathering field data

References

[1] T Zhao W Liu and Z Ye ldquoEffects of water inrush fromtunnel excavation face on the deformation and mechanicalperformance of shield tunnel segment jointsrdquo Advances inCivil Engineering vol 2017 Article ID 5913640 9 pages 2017

[2] W Liu T Zhao W Zhou and J Tang ldquoSafety risk factors ofmetro tunnel construction in China an integrated study withEFA and SEMrdquo Safety Science vol 105 pp 98ndash113 2018

[3] K Li ldquoHangzhou metro site collapse accidentrdquo 2008 httpnewssohucom20081115n260653551shtml

[4] S Liu ldquoConstruction of Nanchang metro line 2 constructionsection pavement collapsesrdquo 2017 httpnewssohucom20160514n449414512shtml

[5] R B Peck ldquoDeep excavations and tunneling in soft groundrdquo7th International Conference on Soil Mechanics and Foun-dation Engineering vol 7 no 3 pp 225ndash290 1969

[6] P B Attewell I W Farmer and N H Glossop ldquoGrounddeformation caused by tunnelling in a silty alluvial clayrdquoGround Engineering vol 11 no 8 pp 32ndash41 1978

[7] W J Rankin ldquoGround movements resulting from urbantunnelling predictions and effectsrdquo Geological Society Lon-don Engineering Geology Special Publications vol 5 no 1pp 79ndash92 1988

[8] P B Attewell and J P Woodman ldquoPredicting the dynamicsof ground settlement and its derivatives caused by tunnelingin soilrdquo Ground Engineering vol 15 no 8 pp 13ndash20 1982

[9] M P OrsquoReilly and B M New ldquoSettlement above tunnels inthe United Kingdommdashtheir magnitude and prediction intunnelling 82 proceedings of the 3rd international sympo-sium brighton 7ndash11 June 1982 P173ndash181 Publ LondonIMM 1982rdquo International Journal of Rock Mechanics ampMining Sciences amp Geomechanics Abstracts vol 20 no 1pp 1ndash18 1983

[10] R J Mair R N Taylor and A Bracegirdle ldquoSubsurfacesettlement profiles above tunnels in claysrdquo Geotechniquevol 45 no 2 pp 361-362 1995

[11] X L Yang and J MWang ldquoGroundmovement prediction fortunnels using simplified procedurerdquo Tunnelling and Un-derground Space Technology vol 26 no 3 pp 462ndash471 2011

18 Advances in Civil Engineering

Table 11 Probability of equipment fault

Event Surface settlementδmaxi (mm)

Permitted surfacesettlement δi (mm)

Value of TBMparameter

Occurrence rate(dminus1)

Occurrence probability(in 1 year)

X9 89 15 302 kPa 10675eminus 04 382eminus 02X10 84 10 2974 kNmiddotM 17792eminus 04 629eminus 02X11 86 15 143 kPa 71167eminus 05 256eminus 02X12 98 15 13100 kN 14233eminus 04 506eminus 02X13 120 15 41mmmin 28467eminus 04 987eminus 02All data were obtained from the operation log of the XWS

Table 12 Characteristics of experts participated in the occurrence probability evaluation

Expert Age Education Service (years) Professional position1 56 High school 25 Worker2 35 Master 10 Technician3 41 Master 15 Junior engineer4 47 Bachelor 20 Senior engineer5 50 PhD 18 Senior academic6 59 PhD 30 Senior engineer

0125 0125

01625 01625

020225

AgeEducationService

Professional positionWeighting

2 3 4 5 61Expert

0

005

01

015

02

025

Wei

ghtin

g

0

1

2

3

4

5

6

Wei

ghtin

g sc

ore

Figure 11 Distribution of each expert opinion weight

X1 X2 X3

M1

X5 X6 X7 X8

M2

X9 X11

M3

Excessive surface

settlement

X10 X12 X13X4

CE1 CE2 CE3

OE

Caus

esLE

CEC

onse

quen

ces

Figure 10 Bow-tie chart of excessive surface settlement

Advances in Civil Engineering 15

44 Identify Key Nodes and Provide Safety Measures Inorder to find the key nodes leading to excessive surfacesettlement the importance measure of each event was cal-culated via equations (E)ndash(G) in Figure 7 as shown inTable 15 Assume the number of events as ldquonrdquo e nor-malized weight Rlowast could be calculated from the importancemeasure Ii via the following equation

Rlowast

Ii

1113936ni1Ii

times 100 (17)

After the normalized weight Rlowast is calculated for eachimportance measure the total weight Rlowast could be calculatedvia equation (18) e total weight Rlowast of events was finally

ranked in descending order to find the key nodes as shownin Table 16

Rlowast R

lowastBM + R

lowastRAW + R

lowastFV (18)

It can be seen that X6 (seal failure at shield tail) X1(confined water) X2 (ground cavity or flow sand) X5 (ab-normal TBM shutdown) and X7 (excessive deviation fromaxis) have far higher weight than other events and are thusthe key nodes to accidents related to excessive surface set-tlement Measures can be taken to particularly ensure safetyat these nodes e occurrence probability of excessivesurface settlement can be reduced by 66 when X6 X1 X2X5 and X7 are ensured safe (Figure 13)

Table 13 Expert opinion on environmental failure operational error and multiple failures

Event Fuzzy numbers proposed by each expert

X1

Expert 1 Expert 2 Expert 3(02 03 04 05) (01 02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 02 03 05)

X2

Expert 1 Expert 2 Expert 3(01 02 03 05) (02 03 04) (01 02 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (02 03 05) (01 02 03 05)

X3

Expert 1 Expert 2 Expert 3(01 02 04 05) (01 02 03 05) (01 03 04)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03) (01 02 03)

X4

Expert 1 Expert 2 Expert 3(02 03 04 05) (01 02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(02 03 04) (02 03 05) (01 02 03 05)

X5

Expert 1 Expert 2 Expert 3(01 03 04) (01 02 03 05) (02 03 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (02 03 05) (01 02 03)

X6

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 03 05) (02 03 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (02 03 05) (01 02 04 05)

X7

Expert 1 Expert 2 Expert 3(01 02 04 05) (01 02 03 05) (02 03 04)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 03 05)

X8

Expert 1 Expert 2 Expert 3(01 03 04 05) (01 02 03 04) (02 03 04)

Expert 4 Expert 5 Expert 6(02 03 04) (01 02 03 05) (01 02 03)

CE1

Expert 1 Expert 2 Expert 3(02 03 04 05) (02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 02 04 05)

CE2

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 05) (02 03 04 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (01 02 03 05) (01 03 05)

CE3

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 03 05) (03 04 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (01 02 04 05) (01 02 03 05)

16 Advances in Civil Engineering

In accordance with the predictive and diagnosticanalysis results using the established model some safetymeasures for key nodes are displayed in time to reduce theexcessive surface settlement risk during the tunnelexcavation

(1) e nodes X5 (abnormal TBM shutdown) and X7(excessive deviation from the axis) mostly involveoperational error Safety management and supervi-sion need to be strengthened at the construction siteto eliminate such errors and ensure that the TBM isoperated properly Besides an advanced real-time

laser locator may help to alarm in the case of largeaxial deviation

(2) e nodes X1 (confined water) and X2 (ground cavityor flow sand) belong to environmental failure Inorder to reduce the influence of environmental failurecareful geological exploration should be carried outbefore tunneling to identify the poor geological and

Table 14 Calculation of FPS FFR and the occurrence probability of environmental failure operational error and multiple failures

Event Aggregated fuzzy numbers FPS FFR (dminus1) Failure probability (in 1 year)X1 (01288 02288 03288 04838) 02951 83969eminus 04 26402eminus 1X2 (01325 02325 03163 04713) 02909 80032eminus 04 25336eminus 1X3 (01000 02163 02700 03825) 02420 42986eminus 04 14518eminus 1X4 (00450 00900 01125 01800) 01082 22492eminus 05 81803eminus 3X5 (01363 02488 02775 04263) 02747 66022eminus 04 214155eminus 1X6 (01488 02488 03225 04713) 03004 89125eminus 04 27770eminus 1X7 (01163 02388 03125 04675) 02855 75157eminus 04 24002eminus 1X8 (01450 02538 02950 03100) 02463 45643eminus 04 15338eminus 1CE1 (01413 02413 03513 04838) 03058 94598eminus 04 29202eminus 1CE2 (01288 02513 03038 04713) 02916 80679eminus 04 25496eminus 1CE3 (01450 02450 03363 04713) 03010 89722eminus 04 27937eminus 1

08299

03155

01223 010800419

01301

00504 00445 00173

Occ

urre

nce p

roba

bilit

y (in

1 y

ear)

00

01

02

03

04

05

06

07

08

09

OE1 OE2 OE3 OE4 OE5 OE6 OE7 OE8LE

Figure 12 Occurrence probability of surface settlement and otheroutcome events

Table 15 Calculation of importance measure of influential factors

SymbolImportance measure

BM RAW FVX1 2311eminus 1 7352eminus 02 7352eminus 02X2 2279eminus 1 6958eminus 02 6958eminus 02X3 1990eminus 1 3481eminus 02 3481eminus 02X4 1716eminus 1 1691eminus 03 1691eminus 03X5 2165eminus 1 5587eminus 02 5587eminus 02X6 2356eminus 1 7884eminus 02 7884eminus 02X7 2239eminus 1 6476eminus 02 6476eminus 02X8 2010eminus 1 3715eminus 02 3715eminus 02X9 1370eminus 6 6306eminus 08 6306eminus 08X10 8300eminus 7 6291eminus 08 6291eminus 08X11 2040eminus 6 6293eminus 08 6293eminus 08X12 1030eminus 6 6280eminus 08 6280eminus 08X13 5300eminus 7 6303eminus 08 6303eminus 08

Table 16 Ranking results of the key events

Rank SymbolNormalization weighting (Rlowast) Total

weighting(Rlowast)

RlowastBM RlowastRAW RlowastFV

1 X6 13805 18942 18942 516892 X1 13541 17664 17664 488693 X2 13354 16717 16717 467884 X7 13120 15559 15559 442385 X5 12686 13423 13423 395326 X8 11778 8926 89255 296297 X3 11661 8363 8363 283878 X4 10055 0406 0406 108689 X11 00002 1512eminus 05 1512eminus 05 1498eminus 0410 X9 8028eminus 05 1515eminus 05 1515eminus 05 1106eminus 0411 X12 6035eminus 05 1509eminus 05 1509eminus 05 9053eminus 0512 X10 4863eminus 05 1511eminus 05 1511eminus 05 7886eminus 0513 X13 3106eminus 05 1514eminus 05 1514eminus 05 6134eminus 05Total 100 100 100 100

02822

01073

00416 0036700142

0044200172 00151 00059

Occ

urre

nce p

roba

bilit

y (in

1 y

ear)

000

005

010

015

020

025

030

OE1 OE2 OE3 OE4 OE5 OE6 OE7 OE8LE

Figure 13 Occurrence probability when safety is ensured at keynodes

Advances in Civil Engineering 17

hydrological conditions that may be encounteredDuring excavation the advanced geological pre-diction technologymay be employed to detect adversegeological and hydrological conditions ahead of theTBM in real time including confined water groundcavity and flow sand

(3) Node X6 (seal failure at shield tail) belongs tomultiple failures e quality of the tail brush needsto be enhanced and tail brush should promptly bereplaced when it is worn

By adopting corresponding safety measures in shieldtunnel excavation the occurrence probability of variousdegrees of surface collapse (OE3 OE4 OE6 OE7 and OE8)was significantly decreased (Figure 13) Finally the TBMssuccessfully passed through the left track of DCS on March3 2017 and the right track on June 11 2017 without anysurface collapse accident demonstrating the effectiveness ofour proposed hybrid method

5 Conclusions and Future Works

In this work we first defined the ldquonormal excavation phaserdquoof shield tunneling based on the fuzzy statistical test theoryData were extracted from the construction log of the XWS inthe Wuhan metro line 7 to determine the occurrenceprobability of facility fault and expert opinions were soli-cited to determine the occurrence probability of environ-mental failure operational error and multiple failuresProbabilistic safety assessment (PSA) of the normal shieldtunnel excavation system was then performed accordingly

We employed the bow-tie analysis to evaluate the oc-currence of excessive surface settlement during normaltunnel excavation e presence of emergency measurescould reduce the occurrence probability of surface collapsecaused by excessive surface settlement (OE3 OE4 OE6 OE7and OE8) but have limited effect on the prevention of ac-cidents of OE1 OE2 and OE5 It is essential to decrease theprobability of excessive surface settlement in order to pre-vent the resulting outcome events (OEs)

By mapping the bow-tie analysis to Bayesian networks(ie BT-BN analysis) we determined the key nodes thatcould cause excessive surface settlement (LE) e key nodesincluded the following X6 (seal failure at shield tail) X1(confined water) X2 (ground cavity or flow sand) X5 (ab-normal TBM shutdown) and X7 (excessive deviation fromthe axis) Effective safety measures at these nodes couldreduce the occurrence probability of excessive surface set-tlement (LE) by 66

To ensure safety careful geological exploration shouldbe carried out before the tunneling project During thetunneling safety management and supervision should bestrengthened at the construction site Advanced geo-logical prediction technology should be used to detectpoor geological and hydrological conditions ahead of theTBM in real time Advanced laser locator should be usedto monitor and alarm excessive axial deviation equality of the tail brush should be improved and tailbrush should be replaced timely when it becomes worn

e occurrence probability of excessive surface settlementwas decreased by adopting these safety measures and theoccurrence of the resulting surface collapse was sub-sequently decreased

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

e authors thank the workers foremen and safety co-ordinators of the main contractors for their participatione authors also wish to thank the engineers Yun Zhang andPeilun Tu for assistance in gathering field data

References

[1] T Zhao W Liu and Z Ye ldquoEffects of water inrush fromtunnel excavation face on the deformation and mechanicalperformance of shield tunnel segment jointsrdquo Advances inCivil Engineering vol 2017 Article ID 5913640 9 pages 2017

[2] W Liu T Zhao W Zhou and J Tang ldquoSafety risk factors ofmetro tunnel construction in China an integrated study withEFA and SEMrdquo Safety Science vol 105 pp 98ndash113 2018

[3] K Li ldquoHangzhou metro site collapse accidentrdquo 2008 httpnewssohucom20081115n260653551shtml

[4] S Liu ldquoConstruction of Nanchang metro line 2 constructionsection pavement collapsesrdquo 2017 httpnewssohucom20160514n449414512shtml

[5] R B Peck ldquoDeep excavations and tunneling in soft groundrdquo7th International Conference on Soil Mechanics and Foun-dation Engineering vol 7 no 3 pp 225ndash290 1969

[6] P B Attewell I W Farmer and N H Glossop ldquoGrounddeformation caused by tunnelling in a silty alluvial clayrdquoGround Engineering vol 11 no 8 pp 32ndash41 1978

[7] W J Rankin ldquoGround movements resulting from urbantunnelling predictions and effectsrdquo Geological Society Lon-don Engineering Geology Special Publications vol 5 no 1pp 79ndash92 1988

[8] P B Attewell and J P Woodman ldquoPredicting the dynamicsof ground settlement and its derivatives caused by tunnelingin soilrdquo Ground Engineering vol 15 no 8 pp 13ndash20 1982

[9] M P OrsquoReilly and B M New ldquoSettlement above tunnels inthe United Kingdommdashtheir magnitude and prediction intunnelling 82 proceedings of the 3rd international sympo-sium brighton 7ndash11 June 1982 P173ndash181 Publ LondonIMM 1982rdquo International Journal of Rock Mechanics ampMining Sciences amp Geomechanics Abstracts vol 20 no 1pp 1ndash18 1983

[10] R J Mair R N Taylor and A Bracegirdle ldquoSubsurfacesettlement profiles above tunnels in claysrdquo Geotechniquevol 45 no 2 pp 361-362 1995

[11] X L Yang and J MWang ldquoGroundmovement prediction fortunnels using simplified procedurerdquo Tunnelling and Un-derground Space Technology vol 26 no 3 pp 462ndash471 2011

18 Advances in Civil Engineering

44 Identify Key Nodes and Provide Safety Measures Inorder to find the key nodes leading to excessive surfacesettlement the importance measure of each event was cal-culated via equations (E)ndash(G) in Figure 7 as shown inTable 15 Assume the number of events as ldquonrdquo e nor-malized weight Rlowast could be calculated from the importancemeasure Ii via the following equation

Rlowast

Ii

1113936ni1Ii

times 100 (17)

After the normalized weight Rlowast is calculated for eachimportance measure the total weight Rlowast could be calculatedvia equation (18) e total weight Rlowast of events was finally

ranked in descending order to find the key nodes as shownin Table 16

Rlowast R

lowastBM + R

lowastRAW + R

lowastFV (18)

It can be seen that X6 (seal failure at shield tail) X1(confined water) X2 (ground cavity or flow sand) X5 (ab-normal TBM shutdown) and X7 (excessive deviation fromaxis) have far higher weight than other events and are thusthe key nodes to accidents related to excessive surface set-tlement Measures can be taken to particularly ensure safetyat these nodes e occurrence probability of excessivesurface settlement can be reduced by 66 when X6 X1 X2X5 and X7 are ensured safe (Figure 13)

Table 13 Expert opinion on environmental failure operational error and multiple failures

Event Fuzzy numbers proposed by each expert

X1

Expert 1 Expert 2 Expert 3(02 03 04 05) (01 02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 02 03 05)

X2

Expert 1 Expert 2 Expert 3(01 02 03 05) (02 03 04) (01 02 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (02 03 05) (01 02 03 05)

X3

Expert 1 Expert 2 Expert 3(01 02 04 05) (01 02 03 05) (01 03 04)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03) (01 02 03)

X4

Expert 1 Expert 2 Expert 3(02 03 04 05) (01 02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(02 03 04) (02 03 05) (01 02 03 05)

X5

Expert 1 Expert 2 Expert 3(01 03 04) (01 02 03 05) (02 03 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (02 03 05) (01 02 03)

X6

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 03 05) (02 03 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (02 03 05) (01 02 04 05)

X7

Expert 1 Expert 2 Expert 3(01 02 04 05) (01 02 03 05) (02 03 04)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 03 05)

X8

Expert 1 Expert 2 Expert 3(01 03 04 05) (01 02 03 04) (02 03 04)

Expert 4 Expert 5 Expert 6(02 03 04) (01 02 03 05) (01 02 03)

CE1

Expert 1 Expert 2 Expert 3(02 03 04 05) (02 03 05) (02 03 04 05)

Expert 4 Expert 5 Expert 6(01 02 03 04) (01 02 03 05) (01 02 04 05)

CE2

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 05) (02 03 04 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (01 02 03 05) (01 03 05)

CE3

Expert 1 Expert 2 Expert 3(02 03 04) (01 02 03 05) (03 04 05)Expert 4 Expert 5 Expert 6

(01 02 03 04) (01 02 04 05) (01 02 03 05)

16 Advances in Civil Engineering

In accordance with the predictive and diagnosticanalysis results using the established model some safetymeasures for key nodes are displayed in time to reduce theexcessive surface settlement risk during the tunnelexcavation

(1) e nodes X5 (abnormal TBM shutdown) and X7(excessive deviation from the axis) mostly involveoperational error Safety management and supervi-sion need to be strengthened at the construction siteto eliminate such errors and ensure that the TBM isoperated properly Besides an advanced real-time

laser locator may help to alarm in the case of largeaxial deviation

(2) e nodes X1 (confined water) and X2 (ground cavityor flow sand) belong to environmental failure Inorder to reduce the influence of environmental failurecareful geological exploration should be carried outbefore tunneling to identify the poor geological and

Table 14 Calculation of FPS FFR and the occurrence probability of environmental failure operational error and multiple failures

Event Aggregated fuzzy numbers FPS FFR (dminus1) Failure probability (in 1 year)X1 (01288 02288 03288 04838) 02951 83969eminus 04 26402eminus 1X2 (01325 02325 03163 04713) 02909 80032eminus 04 25336eminus 1X3 (01000 02163 02700 03825) 02420 42986eminus 04 14518eminus 1X4 (00450 00900 01125 01800) 01082 22492eminus 05 81803eminus 3X5 (01363 02488 02775 04263) 02747 66022eminus 04 214155eminus 1X6 (01488 02488 03225 04713) 03004 89125eminus 04 27770eminus 1X7 (01163 02388 03125 04675) 02855 75157eminus 04 24002eminus 1X8 (01450 02538 02950 03100) 02463 45643eminus 04 15338eminus 1CE1 (01413 02413 03513 04838) 03058 94598eminus 04 29202eminus 1CE2 (01288 02513 03038 04713) 02916 80679eminus 04 25496eminus 1CE3 (01450 02450 03363 04713) 03010 89722eminus 04 27937eminus 1

08299

03155

01223 010800419

01301

00504 00445 00173

Occ

urre

nce p

roba

bilit

y (in

1 y

ear)

00

01

02

03

04

05

06

07

08

09

OE1 OE2 OE3 OE4 OE5 OE6 OE7 OE8LE

Figure 12 Occurrence probability of surface settlement and otheroutcome events

Table 15 Calculation of importance measure of influential factors

SymbolImportance measure

BM RAW FVX1 2311eminus 1 7352eminus 02 7352eminus 02X2 2279eminus 1 6958eminus 02 6958eminus 02X3 1990eminus 1 3481eminus 02 3481eminus 02X4 1716eminus 1 1691eminus 03 1691eminus 03X5 2165eminus 1 5587eminus 02 5587eminus 02X6 2356eminus 1 7884eminus 02 7884eminus 02X7 2239eminus 1 6476eminus 02 6476eminus 02X8 2010eminus 1 3715eminus 02 3715eminus 02X9 1370eminus 6 6306eminus 08 6306eminus 08X10 8300eminus 7 6291eminus 08 6291eminus 08X11 2040eminus 6 6293eminus 08 6293eminus 08X12 1030eminus 6 6280eminus 08 6280eminus 08X13 5300eminus 7 6303eminus 08 6303eminus 08

Table 16 Ranking results of the key events

Rank SymbolNormalization weighting (Rlowast) Total

weighting(Rlowast)

RlowastBM RlowastRAW RlowastFV

1 X6 13805 18942 18942 516892 X1 13541 17664 17664 488693 X2 13354 16717 16717 467884 X7 13120 15559 15559 442385 X5 12686 13423 13423 395326 X8 11778 8926 89255 296297 X3 11661 8363 8363 283878 X4 10055 0406 0406 108689 X11 00002 1512eminus 05 1512eminus 05 1498eminus 0410 X9 8028eminus 05 1515eminus 05 1515eminus 05 1106eminus 0411 X12 6035eminus 05 1509eminus 05 1509eminus 05 9053eminus 0512 X10 4863eminus 05 1511eminus 05 1511eminus 05 7886eminus 0513 X13 3106eminus 05 1514eminus 05 1514eminus 05 6134eminus 05Total 100 100 100 100

02822

01073

00416 0036700142

0044200172 00151 00059

Occ

urre

nce p

roba

bilit

y (in

1 y

ear)

000

005

010

015

020

025

030

OE1 OE2 OE3 OE4 OE5 OE6 OE7 OE8LE

Figure 13 Occurrence probability when safety is ensured at keynodes

Advances in Civil Engineering 17

hydrological conditions that may be encounteredDuring excavation the advanced geological pre-diction technologymay be employed to detect adversegeological and hydrological conditions ahead of theTBM in real time including confined water groundcavity and flow sand

(3) Node X6 (seal failure at shield tail) belongs tomultiple failures e quality of the tail brush needsto be enhanced and tail brush should promptly bereplaced when it is worn

By adopting corresponding safety measures in shieldtunnel excavation the occurrence probability of variousdegrees of surface collapse (OE3 OE4 OE6 OE7 and OE8)was significantly decreased (Figure 13) Finally the TBMssuccessfully passed through the left track of DCS on March3 2017 and the right track on June 11 2017 without anysurface collapse accident demonstrating the effectiveness ofour proposed hybrid method

5 Conclusions and Future Works

In this work we first defined the ldquonormal excavation phaserdquoof shield tunneling based on the fuzzy statistical test theoryData were extracted from the construction log of the XWS inthe Wuhan metro line 7 to determine the occurrenceprobability of facility fault and expert opinions were soli-cited to determine the occurrence probability of environ-mental failure operational error and multiple failuresProbabilistic safety assessment (PSA) of the normal shieldtunnel excavation system was then performed accordingly

We employed the bow-tie analysis to evaluate the oc-currence of excessive surface settlement during normaltunnel excavation e presence of emergency measurescould reduce the occurrence probability of surface collapsecaused by excessive surface settlement (OE3 OE4 OE6 OE7and OE8) but have limited effect on the prevention of ac-cidents of OE1 OE2 and OE5 It is essential to decrease theprobability of excessive surface settlement in order to pre-vent the resulting outcome events (OEs)

By mapping the bow-tie analysis to Bayesian networks(ie BT-BN analysis) we determined the key nodes thatcould cause excessive surface settlement (LE) e key nodesincluded the following X6 (seal failure at shield tail) X1(confined water) X2 (ground cavity or flow sand) X5 (ab-normal TBM shutdown) and X7 (excessive deviation fromthe axis) Effective safety measures at these nodes couldreduce the occurrence probability of excessive surface set-tlement (LE) by 66

To ensure safety careful geological exploration shouldbe carried out before the tunneling project During thetunneling safety management and supervision should bestrengthened at the construction site Advanced geo-logical prediction technology should be used to detectpoor geological and hydrological conditions ahead of theTBM in real time Advanced laser locator should be usedto monitor and alarm excessive axial deviation equality of the tail brush should be improved and tailbrush should be replaced timely when it becomes worn

e occurrence probability of excessive surface settlementwas decreased by adopting these safety measures and theoccurrence of the resulting surface collapse was sub-sequently decreased

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

e authors thank the workers foremen and safety co-ordinators of the main contractors for their participatione authors also wish to thank the engineers Yun Zhang andPeilun Tu for assistance in gathering field data

References

[1] T Zhao W Liu and Z Ye ldquoEffects of water inrush fromtunnel excavation face on the deformation and mechanicalperformance of shield tunnel segment jointsrdquo Advances inCivil Engineering vol 2017 Article ID 5913640 9 pages 2017

[2] W Liu T Zhao W Zhou and J Tang ldquoSafety risk factors ofmetro tunnel construction in China an integrated study withEFA and SEMrdquo Safety Science vol 105 pp 98ndash113 2018

[3] K Li ldquoHangzhou metro site collapse accidentrdquo 2008 httpnewssohucom20081115n260653551shtml

[4] S Liu ldquoConstruction of Nanchang metro line 2 constructionsection pavement collapsesrdquo 2017 httpnewssohucom20160514n449414512shtml

[5] R B Peck ldquoDeep excavations and tunneling in soft groundrdquo7th International Conference on Soil Mechanics and Foun-dation Engineering vol 7 no 3 pp 225ndash290 1969

[6] P B Attewell I W Farmer and N H Glossop ldquoGrounddeformation caused by tunnelling in a silty alluvial clayrdquoGround Engineering vol 11 no 8 pp 32ndash41 1978

[7] W J Rankin ldquoGround movements resulting from urbantunnelling predictions and effectsrdquo Geological Society Lon-don Engineering Geology Special Publications vol 5 no 1pp 79ndash92 1988

[8] P B Attewell and J P Woodman ldquoPredicting the dynamicsof ground settlement and its derivatives caused by tunnelingin soilrdquo Ground Engineering vol 15 no 8 pp 13ndash20 1982

[9] M P OrsquoReilly and B M New ldquoSettlement above tunnels inthe United Kingdommdashtheir magnitude and prediction intunnelling 82 proceedings of the 3rd international sympo-sium brighton 7ndash11 June 1982 P173ndash181 Publ LondonIMM 1982rdquo International Journal of Rock Mechanics ampMining Sciences amp Geomechanics Abstracts vol 20 no 1pp 1ndash18 1983

[10] R J Mair R N Taylor and A Bracegirdle ldquoSubsurfacesettlement profiles above tunnels in claysrdquo Geotechniquevol 45 no 2 pp 361-362 1995

[11] X L Yang and J MWang ldquoGroundmovement prediction fortunnels using simplified procedurerdquo Tunnelling and Un-derground Space Technology vol 26 no 3 pp 462ndash471 2011

18 Advances in Civil Engineering

In accordance with the predictive and diagnosticanalysis results using the established model some safetymeasures for key nodes are displayed in time to reduce theexcessive surface settlement risk during the tunnelexcavation

(1) e nodes X5 (abnormal TBM shutdown) and X7(excessive deviation from the axis) mostly involveoperational error Safety management and supervi-sion need to be strengthened at the construction siteto eliminate such errors and ensure that the TBM isoperated properly Besides an advanced real-time

laser locator may help to alarm in the case of largeaxial deviation

(2) e nodes X1 (confined water) and X2 (ground cavityor flow sand) belong to environmental failure Inorder to reduce the influence of environmental failurecareful geological exploration should be carried outbefore tunneling to identify the poor geological and

Table 14 Calculation of FPS FFR and the occurrence probability of environmental failure operational error and multiple failures

Event Aggregated fuzzy numbers FPS FFR (dminus1) Failure probability (in 1 year)X1 (01288 02288 03288 04838) 02951 83969eminus 04 26402eminus 1X2 (01325 02325 03163 04713) 02909 80032eminus 04 25336eminus 1X3 (01000 02163 02700 03825) 02420 42986eminus 04 14518eminus 1X4 (00450 00900 01125 01800) 01082 22492eminus 05 81803eminus 3X5 (01363 02488 02775 04263) 02747 66022eminus 04 214155eminus 1X6 (01488 02488 03225 04713) 03004 89125eminus 04 27770eminus 1X7 (01163 02388 03125 04675) 02855 75157eminus 04 24002eminus 1X8 (01450 02538 02950 03100) 02463 45643eminus 04 15338eminus 1CE1 (01413 02413 03513 04838) 03058 94598eminus 04 29202eminus 1CE2 (01288 02513 03038 04713) 02916 80679eminus 04 25496eminus 1CE3 (01450 02450 03363 04713) 03010 89722eminus 04 27937eminus 1

08299

03155

01223 010800419

01301

00504 00445 00173

Occ

urre

nce p

roba

bilit

y (in

1 y

ear)

00

01

02

03

04

05

06

07

08

09

OE1 OE2 OE3 OE4 OE5 OE6 OE7 OE8LE

Figure 12 Occurrence probability of surface settlement and otheroutcome events

Table 15 Calculation of importance measure of influential factors

SymbolImportance measure

BM RAW FVX1 2311eminus 1 7352eminus 02 7352eminus 02X2 2279eminus 1 6958eminus 02 6958eminus 02X3 1990eminus 1 3481eminus 02 3481eminus 02X4 1716eminus 1 1691eminus 03 1691eminus 03X5 2165eminus 1 5587eminus 02 5587eminus 02X6 2356eminus 1 7884eminus 02 7884eminus 02X7 2239eminus 1 6476eminus 02 6476eminus 02X8 2010eminus 1 3715eminus 02 3715eminus 02X9 1370eminus 6 6306eminus 08 6306eminus 08X10 8300eminus 7 6291eminus 08 6291eminus 08X11 2040eminus 6 6293eminus 08 6293eminus 08X12 1030eminus 6 6280eminus 08 6280eminus 08X13 5300eminus 7 6303eminus 08 6303eminus 08

Table 16 Ranking results of the key events

Rank SymbolNormalization weighting (Rlowast) Total

weighting(Rlowast)

RlowastBM RlowastRAW RlowastFV

1 X6 13805 18942 18942 516892 X1 13541 17664 17664 488693 X2 13354 16717 16717 467884 X7 13120 15559 15559 442385 X5 12686 13423 13423 395326 X8 11778 8926 89255 296297 X3 11661 8363 8363 283878 X4 10055 0406 0406 108689 X11 00002 1512eminus 05 1512eminus 05 1498eminus 0410 X9 8028eminus 05 1515eminus 05 1515eminus 05 1106eminus 0411 X12 6035eminus 05 1509eminus 05 1509eminus 05 9053eminus 0512 X10 4863eminus 05 1511eminus 05 1511eminus 05 7886eminus 0513 X13 3106eminus 05 1514eminus 05 1514eminus 05 6134eminus 05Total 100 100 100 100

02822

01073

00416 0036700142

0044200172 00151 00059

Occ

urre

nce p

roba

bilit

y (in

1 y

ear)

000

005

010

015

020

025

030

OE1 OE2 OE3 OE4 OE5 OE6 OE7 OE8LE

Figure 13 Occurrence probability when safety is ensured at keynodes

Advances in Civil Engineering 17

hydrological conditions that may be encounteredDuring excavation the advanced geological pre-diction technologymay be employed to detect adversegeological and hydrological conditions ahead of theTBM in real time including confined water groundcavity and flow sand

(3) Node X6 (seal failure at shield tail) belongs tomultiple failures e quality of the tail brush needsto be enhanced and tail brush should promptly bereplaced when it is worn

By adopting corresponding safety measures in shieldtunnel excavation the occurrence probability of variousdegrees of surface collapse (OE3 OE4 OE6 OE7 and OE8)was significantly decreased (Figure 13) Finally the TBMssuccessfully passed through the left track of DCS on March3 2017 and the right track on June 11 2017 without anysurface collapse accident demonstrating the effectiveness ofour proposed hybrid method

5 Conclusions and Future Works

In this work we first defined the ldquonormal excavation phaserdquoof shield tunneling based on the fuzzy statistical test theoryData were extracted from the construction log of the XWS inthe Wuhan metro line 7 to determine the occurrenceprobability of facility fault and expert opinions were soli-cited to determine the occurrence probability of environ-mental failure operational error and multiple failuresProbabilistic safety assessment (PSA) of the normal shieldtunnel excavation system was then performed accordingly

We employed the bow-tie analysis to evaluate the oc-currence of excessive surface settlement during normaltunnel excavation e presence of emergency measurescould reduce the occurrence probability of surface collapsecaused by excessive surface settlement (OE3 OE4 OE6 OE7and OE8) but have limited effect on the prevention of ac-cidents of OE1 OE2 and OE5 It is essential to decrease theprobability of excessive surface settlement in order to pre-vent the resulting outcome events (OEs)

By mapping the bow-tie analysis to Bayesian networks(ie BT-BN analysis) we determined the key nodes thatcould cause excessive surface settlement (LE) e key nodesincluded the following X6 (seal failure at shield tail) X1(confined water) X2 (ground cavity or flow sand) X5 (ab-normal TBM shutdown) and X7 (excessive deviation fromthe axis) Effective safety measures at these nodes couldreduce the occurrence probability of excessive surface set-tlement (LE) by 66

To ensure safety careful geological exploration shouldbe carried out before the tunneling project During thetunneling safety management and supervision should bestrengthened at the construction site Advanced geo-logical prediction technology should be used to detectpoor geological and hydrological conditions ahead of theTBM in real time Advanced laser locator should be usedto monitor and alarm excessive axial deviation equality of the tail brush should be improved and tailbrush should be replaced timely when it becomes worn

e occurrence probability of excessive surface settlementwas decreased by adopting these safety measures and theoccurrence of the resulting surface collapse was sub-sequently decreased

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

e authors thank the workers foremen and safety co-ordinators of the main contractors for their participatione authors also wish to thank the engineers Yun Zhang andPeilun Tu for assistance in gathering field data

References

[1] T Zhao W Liu and Z Ye ldquoEffects of water inrush fromtunnel excavation face on the deformation and mechanicalperformance of shield tunnel segment jointsrdquo Advances inCivil Engineering vol 2017 Article ID 5913640 9 pages 2017

[2] W Liu T Zhao W Zhou and J Tang ldquoSafety risk factors ofmetro tunnel construction in China an integrated study withEFA and SEMrdquo Safety Science vol 105 pp 98ndash113 2018

[3] K Li ldquoHangzhou metro site collapse accidentrdquo 2008 httpnewssohucom20081115n260653551shtml

[4] S Liu ldquoConstruction of Nanchang metro line 2 constructionsection pavement collapsesrdquo 2017 httpnewssohucom20160514n449414512shtml

[5] R B Peck ldquoDeep excavations and tunneling in soft groundrdquo7th International Conference on Soil Mechanics and Foun-dation Engineering vol 7 no 3 pp 225ndash290 1969

[6] P B Attewell I W Farmer and N H Glossop ldquoGrounddeformation caused by tunnelling in a silty alluvial clayrdquoGround Engineering vol 11 no 8 pp 32ndash41 1978

[7] W J Rankin ldquoGround movements resulting from urbantunnelling predictions and effectsrdquo Geological Society Lon-don Engineering Geology Special Publications vol 5 no 1pp 79ndash92 1988

[8] P B Attewell and J P Woodman ldquoPredicting the dynamicsof ground settlement and its derivatives caused by tunnelingin soilrdquo Ground Engineering vol 15 no 8 pp 13ndash20 1982

[9] M P OrsquoReilly and B M New ldquoSettlement above tunnels inthe United Kingdommdashtheir magnitude and prediction intunnelling 82 proceedings of the 3rd international sympo-sium brighton 7ndash11 June 1982 P173ndash181 Publ LondonIMM 1982rdquo International Journal of Rock Mechanics ampMining Sciences amp Geomechanics Abstracts vol 20 no 1pp 1ndash18 1983

[10] R J Mair R N Taylor and A Bracegirdle ldquoSubsurfacesettlement profiles above tunnels in claysrdquo Geotechniquevol 45 no 2 pp 361-362 1995

[11] X L Yang and J MWang ldquoGroundmovement prediction fortunnels using simplified procedurerdquo Tunnelling and Un-derground Space Technology vol 26 no 3 pp 462ndash471 2011

18 Advances in Civil Engineering

hydrological conditions that may be encounteredDuring excavation the advanced geological pre-diction technologymay be employed to detect adversegeological and hydrological conditions ahead of theTBM in real time including confined water groundcavity and flow sand

(3) Node X6 (seal failure at shield tail) belongs tomultiple failures e quality of the tail brush needsto be enhanced and tail brush should promptly bereplaced when it is worn

By adopting corresponding safety measures in shieldtunnel excavation the occurrence probability of variousdegrees of surface collapse (OE3 OE4 OE6 OE7 and OE8)was significantly decreased (Figure 13) Finally the TBMssuccessfully passed through the left track of DCS on March3 2017 and the right track on June 11 2017 without anysurface collapse accident demonstrating the effectiveness ofour proposed hybrid method

5 Conclusions and Future Works

In this work we first defined the ldquonormal excavation phaserdquoof shield tunneling based on the fuzzy statistical test theoryData were extracted from the construction log of the XWS inthe Wuhan metro line 7 to determine the occurrenceprobability of facility fault and expert opinions were soli-cited to determine the occurrence probability of environ-mental failure operational error and multiple failuresProbabilistic safety assessment (PSA) of the normal shieldtunnel excavation system was then performed accordingly

We employed the bow-tie analysis to evaluate the oc-currence of excessive surface settlement during normaltunnel excavation e presence of emergency measurescould reduce the occurrence probability of surface collapsecaused by excessive surface settlement (OE3 OE4 OE6 OE7and OE8) but have limited effect on the prevention of ac-cidents of OE1 OE2 and OE5 It is essential to decrease theprobability of excessive surface settlement in order to pre-vent the resulting outcome events (OEs)

By mapping the bow-tie analysis to Bayesian networks(ie BT-BN analysis) we determined the key nodes thatcould cause excessive surface settlement (LE) e key nodesincluded the following X6 (seal failure at shield tail) X1(confined water) X2 (ground cavity or flow sand) X5 (ab-normal TBM shutdown) and X7 (excessive deviation fromthe axis) Effective safety measures at these nodes couldreduce the occurrence probability of excessive surface set-tlement (LE) by 66

To ensure safety careful geological exploration shouldbe carried out before the tunneling project During thetunneling safety management and supervision should bestrengthened at the construction site Advanced geo-logical prediction technology should be used to detectpoor geological and hydrological conditions ahead of theTBM in real time Advanced laser locator should be usedto monitor and alarm excessive axial deviation equality of the tail brush should be improved and tailbrush should be replaced timely when it becomes worn

e occurrence probability of excessive surface settlementwas decreased by adopting these safety measures and theoccurrence of the resulting surface collapse was sub-sequently decreased

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

e authors thank the workers foremen and safety co-ordinators of the main contractors for their participatione authors also wish to thank the engineers Yun Zhang andPeilun Tu for assistance in gathering field data

References

[1] T Zhao W Liu and Z Ye ldquoEffects of water inrush fromtunnel excavation face on the deformation and mechanicalperformance of shield tunnel segment jointsrdquo Advances inCivil Engineering vol 2017 Article ID 5913640 9 pages 2017

[2] W Liu T Zhao W Zhou and J Tang ldquoSafety risk factors ofmetro tunnel construction in China an integrated study withEFA and SEMrdquo Safety Science vol 105 pp 98ndash113 2018

[3] K Li ldquoHangzhou metro site collapse accidentrdquo 2008 httpnewssohucom20081115n260653551shtml

[4] S Liu ldquoConstruction of Nanchang metro line 2 constructionsection pavement collapsesrdquo 2017 httpnewssohucom20160514n449414512shtml

[5] R B Peck ldquoDeep excavations and tunneling in soft groundrdquo7th International Conference on Soil Mechanics and Foun-dation Engineering vol 7 no 3 pp 225ndash290 1969

[6] P B Attewell I W Farmer and N H Glossop ldquoGrounddeformation caused by tunnelling in a silty alluvial clayrdquoGround Engineering vol 11 no 8 pp 32ndash41 1978

[7] W J Rankin ldquoGround movements resulting from urbantunnelling predictions and effectsrdquo Geological Society Lon-don Engineering Geology Special Publications vol 5 no 1pp 79ndash92 1988

[8] P B Attewell and J P Woodman ldquoPredicting the dynamicsof ground settlement and its derivatives caused by tunnelingin soilrdquo Ground Engineering vol 15 no 8 pp 13ndash20 1982

[9] M P OrsquoReilly and B M New ldquoSettlement above tunnels inthe United Kingdommdashtheir magnitude and prediction intunnelling 82 proceedings of the 3rd international sympo-sium brighton 7ndash11 June 1982 P173ndash181 Publ LondonIMM 1982rdquo International Journal of Rock Mechanics ampMining Sciences amp Geomechanics Abstracts vol 20 no 1pp 1ndash18 1983

[10] R J Mair R N Taylor and A Bracegirdle ldquoSubsurfacesettlement profiles above tunnels in claysrdquo Geotechniquevol 45 no 2 pp 361-362 1995

[11] X L Yang and J MWang ldquoGroundmovement prediction fortunnels using simplified procedurerdquo Tunnelling and Un-derground Space Technology vol 26 no 3 pp 462ndash471 2011

18 Advances in Civil Engineering

[12] B Zeng and D Huang ldquoSoil deformation induced by Double-O-tube shield tunneling with rolling based on stochasticmedium theoryrdquo Tunnelling and Underground Space Tech-nology vol 60 pp 165ndash177 2016

[13] C Shi C Cao and M Lei ldquoAn analysis of the ground de-formation caused by shield tunnel construction combining anelastic half-space model and stochastic medium theoryrdquoKSCE Journal of Civil Engineering vol 21 no 5 pp 1933ndash1944 2017

[14] T Hagiwara R J Grant M Calvello and R N Taylor ldquoeeffect of overlying strata on the distribution of groundmovements induced by tunnelling in clayrdquo Soils amp Foun-dations vol 39 no 3 pp 63ndash73 1999

[15] V Fargnoli D Boldini and A Amorosi ldquoTBM tunnelling-induced settlements in coarse-grained soils the case of thenew Milan underground line 5rdquo Tunnelling and UndergroundSpace Technology vol 38 no 3 pp 336ndash347 2013

[16] V Fargnoli C G Gragnano D Boldini and A Amorosi ldquo3Dnumerical modelling of soil-structure interaction during EPBtunnellingrdquo Geotechnique vol 65 no 1 pp 23ndash37 2015

[17] GB 50911-2013 Code for Monitoring Measurement of UrbanRail Transit Engineering China Construction Industry PressBeijing China 2014

[18] S Suwansawat and H H Einstein ldquoArtificial neural networksfor predicting the maximum surface settlement caused by EPBshield tunnelingrdquo Tunnelling and Underground Space Tech-nology vol 21 no 2 pp 133ndash150 2006

[19] J Sun J Zhou X Gong and M Zhang ldquoeory of soilenvironment stability and deformation control under influ-ence of construction disturbancerdquo Journal of Tongji Univer-sity vol 32 no 10 pp 1261ndash1269 2004

[20] C Jacinto C Silva P Swuste T Koukoulaki andA Targoutzidis ldquoA semi-quantitative assessment of occu-pational risks using bow-tie representationrdquo Safety Sciencevol 48 no 8 pp 973ndash979 2010

[21] P Cherubin S Pellino and A Petrone ldquoBaseline risk as-sessment tool a comprehensive risk management tool forprocess safetyrdquo Process Safety Progress vol 30 no 3pp 251ndash260 2011

[22] A Targoutzidis ldquoIncorporating human factors into a sim-plified ldquobow-tierdquo approach for workplace risk assessmentrdquoSafety Science vol 48 no 2 pp 145ndash156 2010

[23] A S Markowski and A Kotynia ldquoldquoBow-tierdquo model in layer ofprotection analysisrdquo Process Safety and Environmental Pro-tection vol 89 no 4 pp 205ndash213 2011

[24] R Ferdous F Khan R Sadiq P Amyotte and B VeitchldquoAnalyzing system safety and risks under uncertainty using abow-tie diagram an innovative approachrdquo Process Safety andEnvironmental Protection vol 91 no 1-2 pp 1ndash18 2013

[25] L Purton R Clothier and K Kourousis ldquoAssessment oftechnical airworthiness in military aviation implementationand further advancement of the bow-tie modelrdquo ProcediaEngineering vol 80 no 17 pp 529ndash544 2014

[26] A Badreddine and N B Amor ldquoA Bayesian approach toconstruct bow tie diagrams for risk evaluationrdquo Process Safetyamp Environmental Protection vol 91 no 3 pp 159ndash171 2013

[27] N Khakzad F Khan and P Amyotte ldquoDynamic risk analysisusing bow-tie approachrdquo Reliability Engineering amp SystemSafety vol 104 pp 36ndash44 2012

[28] Z Bilal K Mohammed and H Brahim ldquoBayesian networkand bow tie to analyze the risk of fire and explosion ofpipelinesrdquo Process Safety Progress vol 36 no 2 pp 202ndash2122016

[29] M Abimbola F Khan and N Khakzad ldquoRisk-based safetyanalysis of well integrity operationsrdquo Safety Science vol 84pp 149ndash160 2016

[30] M V D Borst and H Schoonakker ldquoAn overview of PSAimportance measuresrdquo Reliability Engineering amp SystemSafety vol 72 no 3 pp 241ndash245 2001

[31] L A Zadeh ldquoProbability measures of fuzzy eventsrdquo Journal ofMathematical Analysis and Applications vol 23 no 2pp 421ndash427 1968

[32] E Leca ldquoSettlements induced by tunneling in soft groundrdquoTunnelling amp Underground Space Technology vol 22 no 2pp 119ndash149 2007

[33] R J Mair ldquoTunnelling and geotechnics new horizonsrdquoGeotechnique vol 58 no 9 pp 695ndash736 2008

[34] Y Fang K Xu X Yao and Y Li ldquoFuzzy Bayesian network-bow-tie analysis of gas leakage during biomass gasificationrdquoPLoS One vol 11 no 7 Article ID e0160045 2016

[35] H M Hsu and C T Chen ldquoAggregation of fuzzy opinionsunder group decision makingrdquo Fuzzy Sets amp Systems vol 79no 3 pp 279ndash285 1996

[36] S-J Chen and S-M Chen ldquoFuzzy risk analysis based on theranking of generalized trapezoidal fuzzy numbersrdquo AppliedIntelligence vol 26 no 1 pp 1ndash11 2007

[37] T Onisawa ldquoAn approach to human reliability in man-machine systems using error possibilityrdquo Fuzzy Sets andSystems vol 27 no 2 pp 87ndash103 1988

[38] S D Eskesen P Tengborg J Kampmann andT H Veicherts ldquoGuidelines for tunnelling risk managementinternational tunnelling association working group no 2rdquoTunnelling amp Underground Space Technology vol 19 no 3pp 217ndash237 2004

Advances in Civil Engineering 19

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