A Methodology for Assessing Geotechnical Hazards for TBM Tun

International Journal of Rock Mechanics & Mining Sciences 41 (2004) 987–999

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*Correspondi

2107722156.

E-mail addre

1365-1609/$ - see

doi:10.1016/j.ijrm

A methodology for assessing geotechnical hazards for TBMtunnelling—illustrated by the Athens Metro, Greece

A.G. Benardos*, D.C. Kaliampakos

School of Mining and Metallurgical Engineering, National Technical University of Athens, 9 Iroon Polytechneiou Str., GR 15780 Athens, Greece

Accepted 28 March 2004

Abstract

Unexpected ground conditions have always been a major problem for the tunnelling industry. As demand for the development of

new underground structures, regardless of the ground conditions, has increased, safety and risk considerations have become even

more important. The methodology presented in this paper aims at the identification of risk-prone areas, incorporating, at the same

time, the uncertainty of ground conditions. It is focused on TBM tunnelling and can be implemented in the early stages of the

project. The methodology assesses the hazards by introducing the concept of a vulnerability index, which is based on the principles

of rock engineering systems, to identify the weighting of the parameters, and on probabilistic modelling to address the uncertainty in

the parameters’ values. The proposed model is illustrated via the Athens Metro case study, used also for validating its performance

under actual construction conditions.

r 2004 Elsevier Ltd. All rights reserved.

Keywords: Hazard assessment; TBM tunnelling; Vulnerability index

1. Introduction

Underground construction projects many times findthemselves entrapped in the areas where unexpectedground conditions threaten the achievement of cost andschedule milestones. The utilisation of advanced in-vestigation techniques and numerical methods hasassisted in a more comprehensive analysis of thesubsurface; however, the projects that are not able tosuccessfully overcome such ‘‘emergency-events’’ haveprobably been the majority of cases [1]. Thus, the mainquestion nowadays concerning underground construc-tion has shifted, from ‘‘whether can it be constructed’’ to‘‘which is the most suitable construction method to beadopted and what will be the consequences of such adecision’’ [2].The setting up of an underground infrastructure

within the urban environment poses new challenges totunnel engineers. High profile works should not onlyovercome restrictions arising from existing city func-

ng author. Tel.: +30-2107722182; fax: +30-

ss: [email protected] (A.G. Benardos).

front matter r 2004 Elsevier Ltd. All rights reserved.

ms.2004.03.007

tions, but also deal with the fact that the error marginfor inflicting damage on other infrastructure or propertymay be extremely small. Furthermore, the use oftunnelling boring machines (TBM), that, on the onehand provide increased advance rates but on the otherfind it hard to bypass ground conditions other thanthose originally expected [3,4], increase the stakes. Ifeverything goes according to plan, everybody can claimsuccess; however, in the case where serious problems areencountered, the blame can be passed from one toanother. To avoid such unfortunate situations, it iscrucial to assess the possible areas that may pose athreat to the tunnelling operation and to identify themagnitude of such problems.Even though the above issue has been investigated by

many researchers, it still concerns the tunnelling society.Amongst other researchers, the efforts of Einstein [5–7]introducing the decision aids in tunnelling—DAT,should be noted. DAT simulates tunnel constructionand studies the effects of different methods on theconstruction cost and time schedule. Marinos et al. [8]uses geological criteria and, in particular, the relativeoccurrence of geological classes, from investigationboreholes, to the overall tunnel profile—so as to

ARTICLE IN PRESSA.G. Benardos, D.C. Kaliampakos / International Journal of Rock Mechanics & Mining Sciences 41 (2004) 987–999988

characterise the anticipated conditions in terms of‘‘friendliness’’ to tunnel construction. Alvarez Grimaet al. [9] uses a different approach that incorporates aneuro-fuzzy model to assess TBM performance for anew project, based on a database of 640 tunnellingprojects with explicit records of geological and machinecharacteristics. Finally, Barton [10] presented the Qtbm;an index adapted from the Q-system and key machineparameters, attempting a direct link between the groundproperties and TBM performance (advance rate—AR;penetration rate—PR; utilisation—U).It is clear that there is substantial on-going research

attempting to illuminate and formulate answers cover-ing all aspects of possible tunnelling induced risks. Inlike fashion, this paper is concerned with the manage-ment of the uncertainty regarding the subsurface groundconditions, mainly focusing on the first stages of theproject. These initial phases are critical to the project’ssuccess [11] as, at that time, the construction guidelinesand final decisions are brought into shape; therefore, itis essential to have a clearer view of the undergroundconditions so as to tune the construction system andachieve a more efficient meeting of the site-specificdemands. Nevertheless, during that period the mainobstacle that has to be overcome is the uncertainty ofthe input data.The aim of this paper is to establish an overall

assessment index of the problems that might beencountered during the TBM tunnelling operation,incorporating in the analysis the uncertainty andvariability related to the geologic medium. Thus, aproactive assessment, focusing on potential problematicareas and the magnitude of the hazards encounteredthere, can be made possible via a common referencescale. In such manner, the advice given by Sir AlastairMorton [12] is invoked, that the primary challenge forthe tunnel engineers is to address and manage the riskfactors in tunnelling.

2. Athens Metro problems

The problems that can be encountered during theTBM excavation differ in relation to the prevailinggeological environments. For example, in hard rockprojects it is not unusual to experience increased cutterwear and delays because of the frequent replacement ofthe cutters; in squeezing ground, the major problem isthe large-scale tunnel deformation that can even resultin the blocking of the machine [13].In the case of the Athens Metro, the problems were

mainly related to the presence of soft ground that causedinstabilities and overbreaks. Also, the erratic behaviourof the Athens schist and the surface loading of thebuildings caused many similar problems, even surfacecollapses. These made a negative impression of the

project’s profile and gave rise to adverse comments fromthe engineering community [14,15]. Tunnelling in softground environments, as in the case of Athens, is morecomplex because the variability of ground conditionscan significantly affect the tunnel’s advance and causeconsiderable variations in the boring rate—even, some-times, making unavoidable the use of systematic groundpre-treatment in an attempt to overcome such ‘difficult’areas.The proposed methodology mainly targets problems

encountered during the TBM tunnel construction in softground environments. Accordingly, the major riskconditions encountered are:

* face instabilities/collapses and overbreaks;* surface settlements; and* water inflows.

3. Development of the vulnerability index (VI)

methodology

For the identification of vulnerable areas that maypose problems to the tunnelling operation, two mainissues should be taken into account. The first issue is toidentify the parameters that are responsible for theoccurrence of risk events, analyse their behaviour andevaluate the significance that each one has in the overallrisk conditions. Not only understanding the relativeimportance of each one is of essence, but also theassessment of their interaction mechanisms should beintegrated in the analysis, because potential threats tothe construction might be originated through criticalinter-connections between the parameters. The secondissue is to take into account the uncertainty andvariability in the parameters’ values. Consequently,relying only on the mean values of the collected datais not a prudent approach, as it could well be moreimportant to investigate the likelihood of occurrence ofextreme values, low or high, that might disrupt thenormal tunnelling sequence.In order to accommodate the above issues into the

proposed methodology, two approaches have beenemployed. The first approach makes use of the rockengineering systems (RES) principles, as illustrated byHudson [16,17], concentrating on the interaction be-tween the different variables and components of therock mass, in an attempt to take all aspects into account.In this approach, the basic device used for describingand analysing the principal parameters and theirinteractive mechanisms is an interaction matrix.Through this matrix, the interaction intensity of theparameters can be evaluated and their relative weightingin the system, as a whole can be assessed.The second approach, the management and evalua-

tion of the uncertainty, is achieved by selecting a

ARTICLE IN PRESSA.G. Benardos, D.C. Kaliampakos / International Journal of Rock Mechanics & Mining Sciences 41 (2004) 987–999 989

probabilistic approach to the data values, makingpossible the systematic expression of the uncertainaspects in quantitative terms [18]. As Hoek [19] notes,uncertainties associated with the properties of geotech-nical materials and the great care that has to be taken inselecting appropriate values for analysis has promptedseveral authors, including himself, to suggest that thetraditional deterministic methods of geotechnical ana-lysis should be replaced by probabilistic methods. Morespecifically, the Monte-Carlo technique that appliesrandom numbers to samples from known input prob-ability distributions and determines specific outcomes isused [20].Additionally, the system platform is a GIS application

that facilitates the mapping and management of theinput data. Furthermore, the GIS model is used for thespatial modelling of the data and the final visualisationand classification of the areas under evaluation.The basic steps of the proposed methodology (Fig. 1)

are:

* Identification of the principal parameters and ratingassignments for their different value classes.

* Definition of statistical distributions that model theparameters’ behaviour and probabilistic modellingusing Monte-Carlo simulation.

* Analysis and aggregation of the effect that theselected parameters have on the tunnelling process,through the generation of the interaction matrix.

* Vulnerability index estimation.

In order to estimate the model’s performance, thefinal stage includes the model validation with respect tothe actual conditions encountered during the tunnellingperiod. The model applies to the interval between theKatehaki and Panormou stations (Fig. 2), having a total

PARAMETERS'IDENTIFICATION

PARAMETERS' RATIN

HISTOGRAMS,STATISTICAL DISTRIBUT

PROBABILISTIC MODEL

VULNERABILITYINDEX ASSESSMENT

ASSESSMENT OFPARAMETERS'

WEIGHTING

OBJECTIVE OF THE STU

GENERATION OF THEINTERACTION MATRIX

Fig. 1. Flowchart of the proposed vuln

length of 1129.36m and an excavation diameter of closeto 9.5m [21]. The section examined in the model covers1077.05m, i.e. excluding the first 53m as, in that length,the details and adjustments for the machine operationwere finalised. Therefore, this learning curve period isnot representative of the tunnelling process and wasexcluded from further processing. The tunnel lengthunder consideration is divided in 11 control areas(segments), in which the vulnerability index assessmentis performed. Each segment represents an investigationarea 100� 100m, following the TBM chainage (ch.),starting from ch. 11+100 to ch. 10+023. Every segmenttracks 100m of tunnelling length, except for the last one(segment 11) that is limited to only 77m. In addition, theanalysis is made in a 12m thick layer, followingthe tunnelling depth, ranging along the chainage, fromthe level of +120m to the level of +156m.

3.1. Selection of principal parameters

The selection of the principal parameters for theanalysis is made bearing in mind the most useful andcredible representation of the ground conditions, i.e. thegeological, geotechnical and hydrogeological environ-mental properties, as well as other data related to sitespecific conditions (i.e. external loading by buildings,etc.). In doing so, one can find numerous factors, eachone influencing the overall behaviour of the rock mass.However, the parameters given below represent themost important ones, and also the most easilyobtainable without having to resort to special siteinvestigation techniques. Also, as Benardos et al. note[22], the majority of these parameters have beenproposed by researchers as essential indicators for

SPATIAL MODELLING

G

IONS

LING

PROBABILISTIC ASSESSMENT OF GEOLOGICAFORMATIONS' CHARACTERISTICS

DY

RMR, RQD, Overburden, Hydrogeology,Geological Formations

Intact Strength, Permeability, Weathering

erability assessment methodology.

ARTICLE IN PRESS

Fig. 2. 3D model of the examined tunnel. The tunnel alignment, the investigation boreholes, as well as the buildings in that area are shown.

A.G. Benardos, D.C. Kaliampakos / International Journal of Rock Mechanics & Mining Sciences 41 (2004) 987–999990

assessing the TBM’s tunnelling performance. Theseparameters are:

* Rock mass fracture degree as represented by RQD—(P1).

* Weathering degree of the rock mass—(P2).* Overload factor—stability factor (N)—(P3).* Rock mass quality represented by RMR classifica-tion—(P4).

* Uniaxial compressive strength of the rock—(P5).* Overburden—construction depth—(P6).* Hydrogeological conditions represented by the water-table surface relative to the tunnel depth—(P7).

* Rock mass permeability—(P8).

Ideally, the selected parameters should be indepen-dent of each other, avoiding any double counting thatmight bias the final outcome. However, some of theparameters listed above do have a degree of inter-connection between them (e.g. RQD with RMR,because RQD is included in the RMR constituentparameters). Nevertheless, this is not considered to be adifficulty as each parameter is used to describe a specificissue relating to possible problems. For example, RQDvalues are used to describe the fracturing degree of therock mass; whereas, RMR denotes the quality of therock mass and can be used as an assessment indicator ofthe excavation’s stand-up time. Thus, the option ofincluding such information can further enhance thediscerning capability of the model, not only for use as anoverall hazard index, but also to assist in indicating thepossible associated problem or failure mode. For

instance, even when there are cases with same overallRMR values, where similar behaviour is expected,differences in the fractures and the joint network inthose cases could lead to different stability conditions.The next step is the rating of the parameters’ values

with respect to their effect in the vulnerability condi-tions. The rating is made using an interval scaleapproach, with a total of 4 classes, from 0 to 3, where0 denotes the worst case (most unfavourable) and 3 thebest (most favourable condition). The limits set in everyclass are representative of the specific site conditions andthe machine characteristics. In the case of the AthensMetro, the tunnel is constructed at a relative low depthand, in general, in soft ground conditions with a doubleshield TBM machine. The rating of each parameter ispresented in Table 1. Special focus is given on the lowerrange of the values so as to cover the most critical casesand to enhance the analysis resolution in those classes.

3.2. Definition of statistical distributions that model the

behaviour of the parameters

The definition of the statistical distribution describinga parameter’s behaviour is used in order to proceed withthe probabilistic modelling. Two basic groups can bediscerned between the parameters: the first group iscomprised of parameters that are associated with thegeological formations (lithology), such as intactstrength, permeability, etc.; whereas, parameters in thesecond group are characterised only their relativeposition (spatial data), such as fracture degree, con-struction depth, etc.

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Table 1

Proposed rating of the principal parameters

Value class Rating

Rock mass fracture degree—RQD

o10 0

10–30 1

30–60 2

>60 3

Overload factor (N)

>5 0

3–5 1

1.25–3 2

o1.25 3

UCS (MPa)

o2 0

2–15 1

15–40 2

>40 3

Water table surface (m)

>10 0

5–10 1

0–5 2

o0 3

Rock mass weathering

Compl. weath.-CW 0

High weath.-HW 1

Med. weath.-MW 2

SW, fresh 3

Rock mass rating—RMR

o10 0

10–30 1

30–60 2

>60 3

Overburden (m)

o7.5 0

7.5–12.5 1

12.5–17.5 2

>17.5 3

Permeability (m/s)

o10�4 0

10�4–10�6 1

10�6–10�8 2

>10�8 3

A.G. Benardos, D.C. Kaliampakos / International Journal of Rock Mechanics & Mining Sciences 41 (2004) 987–999 991

The lithology is not selected as a primary parameter,despite its great importance, because establishing itsvaluation in quantitative terms is not easy, bearing inmind the variations occurring in each formation. Incontrast, modelling its properties (e.g. strength) can be amuch safer and simpler task. Thus, the value of theparameter associated with the geological formations, fora specific area, is calculated as the product of thecombined probability of the parameter value for eachgeological formation multiplied by the probability of

occurrence of the geological formations in that specificarea.For example, consider k geological formations,

namely G1;G2; y; Gk; having a probability of occur-rence, in a specific area, P½G1�;P½G2�; y; P½Gk�: Also,denote w1 and w2; as parameter values, having aprobability of occurrence PG1½w1�; PG1½w2�; PG2½w1�;PG2½w2�; y; PGk½w1�; PGk½w2�; for each geologicalformation, respectively. What is in question is to assessthe probability of having the values w1 and w2 in thatspecific area. This is possible through the followingformulae:

P½w1� ¼Xk

i¼1

P½Gi�PGi½w1�;

P½w2� ¼Xk

i¼1

P½Gi�PGi½w2� whereXk

i¼1

P½Gi� ¼ 1:

In the proposed model, the probability of occurrence ofa geological formation is considered as spatial data. Theprobability distributions describing the parameters’values are taken from the site investigation findings, oreven assessed according to engineering judgements andrelevant literature studies, in cases where missing orincomplete data are encountered.The main geological units found in the area under

investigation were: sandstone -S, siltstone -s, breccia-b,limestone-L and conglomerate-Cg. For all units, thespatial modelling regarding their probability of occur-rence is performed, followed by the modelling focusingon all other spatial parameters. This analysis is based onthe spatial modelling capabilities of the GIS applicationhaving as input the data gathered from approximately16 boreholes. In Fig. 3, for example, the spatialmodelling of the RQD values is presented, coveringthe wider area of the Katehaki–Panormou metro tunnel.The distributions describing the values of all involved

parameters are found through such spatial modelling. Ineach of the 11 segments, the spatial behaviour for everyparameter is identified and transformed to a respectivestatistical distribution. For example, the statistical datarelating to the geological formation’s probability ofoccurrence found in segment 10 (ch. 10+200 to ch.10+100), is presented in Table 2. Breccia (b), sandstone(S) and siltstone (s) are the dominant geological unitsfound there and their statistics and correlation data areclearly indicated.The probabilistic modelling is performed having as

inputs the distribution of each parameter. The results,also in distribution form, are transformed into a discreteprobability structure, after applying the ratings—fromTable 1—to each parameter. This is presented graphi-cally in Fig. 4 for all of the involved parameters inthe 11 analysis segments. Looking into the data shownthere, one can see important variations in the para-meter’s values, across the segments—thus having a first

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Fig. 3. Spatial modelling of the RQD values in the wider area of the examined tunnel.

Table 2

Statistical data regarding the probability of occurrence for the

geological formations (S, s, b) found in segment 10

Univariate statistics Min Max Mean St. dev

S 0.24404 0.370042 0.338905 0.0345332

s 0.130531 0.318397 0.245878 0.0529392

b 0.351724 0.470959 0.407728 0.0285298

Correlation matrix S s b

S 1 �0.961347 0.692604

s �0.961347 1 �0.864377b 0.692604 �0.864377 1


indication of the rock mass behaviour with respect tothe tunnelling operation.

3.3. Generation of the interaction matrix and associated

parameter values

The generation of the interaction matrix can assist inassessing the weighting of the parameters within therock mass system as a whole. The principal parameters(Pi) are listed along the leading diagonal of the matrixand the interactions are placed on the off-diagonal cells.These interaction mechanisms between the parametersare identified and their intensity is evaluated using theESQ (Expert Semi-Quantitative) coding as proposed byHudson [17]. According to this coding technique, theinteraction intensity is denoted by integral values from 0to 4, from ‘‘no interaction’’ to ‘‘critical interaction’’, asshown in Table 3.The matrix for the examined metro case is presented

in Table 4, where the interactions between all theprincipal parameters are evaluated and coded. Theprincipal parameters are listed along the leading

diagonal of the matrix from top left to bottom right;then the interactions are represented by the off-diagonalboxes using a clockwise convention. For example, thefracturing degree of the rock mass (P1) has a criticalinfluence on the weathering (P2)—as represented by thevalue 4 in the second box of the top row in Table 4—andon RMR (P4) and hydrogeology (P7), while having astrong interaction with permeability (P8). Similarly, thepermeability has no interaction with overburden depth(P6) and can only slightly influence the compressivestrength (P5).Thus, the matrix describes the ‘Cause’ (C) and ‘Effect’

(E) of the parameters on one another using theclockwise convention. More specifically, the sum of thecoding values, each value being Iij ; in the row passingthrough Pi; represents the influence of Pi on all the otherparameters in the system—i.e. the ‘Cause’ value.Conversely, the sum of the coding values in the columnthrough Pi represents the influence of the otherparameters, i.e. the rest of the system, on Pi—the‘Effect’ [17].Thus, the following are evaluated:

CPi ¼Xn

j¼1

Iij

extent to which the parameter affects the system;

EPj ¼Xn

i¼1

Iij

extent to which the parameter is affected by the system:

The interactive intensity value of each parameter isdenoted as the sum of the C and E values (C þ E) and isused as an indicator of the parameter’s significance inthe system. The C þ E histograms for the selected caseare presented in Fig. 5. It can be seen that the values, forthe case under investigation, are not widely spread

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Permeability Rating

0%

20%

40%

60%

80%

100%

1 2 3 4 5 6 7 8 9 10 11

3

2

1

0

Overburden Rating

0%

20%

40%

60%

80%

100%

1 2 3 4 5 6 7 8 9 10 11

3

2

1

0

RMR Rating

0%

20%

40%

60%

80%

100%

1 2 3 4 5 6 7 8 9 10 11

3

2

1

0

Weathering Rating

0%

20%

40%

60%

80%

100%

1 2 3 4 5 6 7 8 9 10 11

3

2

1

0

UCS Rating

0%

20%

40%

60%

80%

100%

1 2 3 4 5 6 7 8 9 10 11

3

2

1

0

RQD Rating

0%

20%

40%

60%

80%

100%

1 2 3 4 5 6 7 8 9 10 11

3

2

1

0

Water-Table Rating

0%

20%

40%

60%

80%

100%

1 2 3 4 5 6 7 8 9 10 11

3

2

1

0

Overload factor Rating

0%

20%

40%

60%

80%

100%

1 2 3 4 5 6 7 8 9 10 11

3

2

1

0

Fig. 4. Rating of the principal parameters for each of the examined segments.

Table 3

ESQ-coding of the parameters’ interaction intensity used in the model

Coding Description

0 No interaction

1 Weak interaction

2 Medium interaction

3 Strong interaction

4 Critical interaction


indicating that there are no major differences in theimportances of the parameters; nevertheless, the mostinteractive parameters are the rock mass rating, the

fracture degree and the hydrogeological conditions,whereas the least interactive is the overburden.In conclusion, the percentage value of (C þ E) is used

as the parameter’s weighting factor (ai), (Table 5)according to the following expression:

ai ¼ðCi þ EiÞPi Ci þ

Pi Ei

� � ð%Þ;

where Ci: cause of the ith parameter, Ei: effect of the ithparameter, i: number of principal parameters.

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Table 4

Interaction matrix coding for the Athens Metro case

Fracture degree 4 1 4 1 1 4 3

2 Weathering 1 4 4 1 2 4

3 1 Overload Factor 2 2 3 0 2

1 2 2 Rock Mass Rating 3 0 2 4

3 1 3 4 UCS 2 0 1

3 1 4 2 1 Overburden 3 1

4 4 2 4 3 1 Hydrogeology 2

1 2 3 2 1 0 3 Permeability

0

5

10

15

20

25

30

35

40

Fractu

re D

egre

e

Wea

therin

g

Overlo

ad F

actor

Rockm

ass R

ating

UCS

Constr

. Dep

th

Hydro

geolo

gical

Permea

bility

C+E

val

ue

Fig. 5. C þ E values of the principal parameters, as calculated from the interaction matrix.

Table 5

Final weighting of the principal parameters

Principal parameter ai (%)

Fracture degree—RQD 14.11

Rockmass weathering 13.31

Overload factor—N 11.69

Rockmass rating—RMR 14.52

UCS 11.69

Overburden—construction depth 9.27

Hydrogeological conditions 13.71

Permeability 11.69


3.4. Vulnerability index estimation

The final stage includes the estimation of thevulnerability index—VI [23]. As noted, VI can be usedas an overall indicator of the potential problemsencountered (instabilities/settlements/inflows) in thearea under investigation during the tunnel constructionphase. It is expressed as the linear combination of theparameter’s weighting (ai) and its respective rating (Pi)

as given by the discrete probability distribution,summed over the n parameters.The probabilistic modelling approach is also used in

estimating VI, as Pi is expressed in a discrete probabilityform, where the values (class rating 0, 1, 2 and 3)correspond to a certain probability of occurrence, asillustrated in Fig. 4. Thus, VI is also in the form of aprobabilistic distribution and is calculated using thefollowing formula:

VI ¼ 100�Xn

i¼1

aiPi

Pmax

!;

where ai is the weighting of the ith parameter in thesystem, Pi the value (rating) of the ith parameter, andPmax the maximum value a parameter can take (normal-isation factor).The term Pmax; used as the denominator in the

summation formula above, is added so as to normalisethe vulnerability index to a 0–100 scale. In the caseexamined, Pmax ¼ 3; the maximum rating value for allthe involved parameters.

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Frequency Chart

0.000

0.033

0.067

0.100

0.133

0

33.25

66.50

99.75

133

32.88 39.31 46.10 52.89 59.68

1.000 Trials 1.000 Displayed

Forecast: VI Segm8

Pro

bab

ility

Freq

uen

cy

Certainty is 99.00% from 32.88 to 59.68

Fig. 7. VI estimation in segment 8, as output of the probabilistic

modelling.


In this way, the VI is calculating the combined totalresult of the parameters taking values in a percent scale(0–100), ranging from the more favourable conditions(low vulnerability) to the more adverse ones (highvulnerability). With respect to the parameter rating from0 to 3, three main vulnerability classes can be discerned,namely [0, 33), (33, 66) and (66, 100], as seen in Fig. 6.Moreover, each class can be divided in two sub-classesso as to improve resolution for the interpretation of theresults.The VI calculation for segment 8 (ch. 10+400 to ch.

10+300) is shown in Fig. 7, as output from the Monte-Carlo probabilistic modelling method. The VI values arepresented there (x-axis), in relation to their probabilityof occurrence, after 1000 iterations. It can be clearlyseen that, with a certainty level of 99.8%, the VI rangesfrom 32.88 to 59.68.The histograms of the VI values for all the examined

segments are presented in Fig. 8. On the x-axis, theVulnerability Index in 5 point interval classes, truncatedto a 25–80 scale, is shown, while the frequencies forthese specific classes are presented on the y-axis.Additionally, the complete VI statistics are given inTable 6.The interpretation of the results should not rely only

on the mean values reading. The VI histograms can alsobe used in a risk assessment approach, as they canprovide data for the probability of encountering acertain vulnerability type (consequence) that affects thetunnelling. Also, the certainty degree of the estimatescan be assessed, as illustrated in Fig. 9. In this graph, thevulnerability index values are given using three certaintylevels of 25%, 50% and 90%.For the case investigated, with respect to the VI

findings, the following can be concluded:

* The VI ranges from 28 to 79, having an overall meanvalue of about 50, characterising the tunnellingenvironment as medium to highly vulnerable.

* The average VI values for all segments range from 44to 59, thus having a relative difference in the order of40%.

* The control segments can be discerned in two majorgroups, having a gap of about 9 units in their meanvalues.

Fig. 6. Proposed

In particular, the first group covers the first 4segments (ch. 11+100 to ch. 10+700), where theirmean VI values are approximately 56, but their uppervulnerability limits reach an average value of 75. On theother hand, the second group consists of the remainingseven segments (ch. 10+700 to ch. 10+023), havinglower mean values in the range of 47, but moreimportantly, their upper limits are in the range of 62.Furthermore, it can be deduced that the area expected toencounter the most significant problems is found insegment 1 (ch. 11+100 to ch. 11+000); whereas themost risk-free area is found in segment 7 (ch. 10+500 toch. 10+400).In a more explicit manner, four major hazard

categories can be identified:Category 1: high to medium vulnerability—its main

portion is in the IIb category, but caution should be paidto the 15–20% found in IIIa category. Certainindividual regions that might cause several difficultiesduring the excavation process must be taken intoaccount (segments: 1,2; ch. 11+100 to ch. 10+900).

Category 2: relatively medium to high vulnerability—as it is mainly found in II category (approximately 40%in IIa and 60% in IIb) although it tends towardsincreased vulnerability. The problematic regions thatmust be taken into account are fewer with respect to theprevious category (segments: 3,4; ch. 10+900 toch.10+700).

VI scale.

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Fig. 8. VI histograms for each segment (truncated to a 25–80 scale).


Category 3: medium vulnerable—and its values arefound in IIa category (65–70%), while the rest arelocated to more vulnerable categories. In general, theproblems that may be encountered are not of particular

difficulty (segments: 5,6,8,9,10,11; ch. 10+700 to ch.10+500 and ch. 10+400 to ch. 10+023).

Category 4: medium to low vulnerability—small-scaleproblems are expected that cannot significantly affect

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Table 6

VI estimation in each of the tunnel segments

Statistics Vun Seg1 Vun Seg2 Vun Seg3 Vun Seg4 Vun Seg5 Vun Seg6 Vun Seg7 Vun Seg8 Vun Seg9 Vun Seg10 Vun Seg11

Mean 59.72 57.69 54.05 53.79 48.11 48.70 44.13 46.85 48.86 47.80 46.65

Median 58.20 58.06 54.57 54.17 48.92 47.98 44.89 46.51 49.87 46.77 45.97

Mode 61.29 58.06 54.70 51.34 45.03 51.08 40.99 49.60 49.87 45.97 45.30

St. dev 6.04 6.47 6.36 4.51 4.68 4.81 4.51 5.17 4.79 4.90 4.49

Minimum 41.80 40.19 36.83 39.65 35.08 31.05 28.76 33.33 32.66 33.06 33.06

Maximum 77.96 79.44 72.31 68.82 61.16 61.16 59.01 62.77 62.90 62.90 62.90

Range 36.16 39.25 35.48 29.17 26.08 30.11 30.24 29.44 30.24 29.84 29.84

Std. error 0.19 0.20 0.20 0.14 0.15 0.15 0.14 0.16 0.15 0.16 0.14

25.00

38.75

52.50

66.25

80.00

Vun S

eg1

Vun S

eg2

Vun S

eg3

Vun S

eg4

Vun S

eg5

Vun S

eg6

Vun S

eg7

Vun S

eg8

Vun S

eg9

Vun S

eg10

Vun S

eg11

90%

50%

25%

Trend Chart

Fig. 9. VI assessment, for each segment, in relation to the certainty degree of the estimate.


the excavation process. Approximately 80% is found inIIa, and a 15% is in Ib category (segment: 7; ch.10+500 to ch. 10+400).

4. Model validation

The validation of the vulnerability index methodologyis based on the actual construction records [24] of theselected inter-station tunnel. The direct approach is toanalyse the problems experienced in each one of theexamined segments in relation to the vulnerability indexclasses. An indirect, but more quantitative, assessmentcan be made possible by examining the tunnellingadvance rate (AR) in each segment, as problems relatingto geological conditions result in unplanned downtimeand delays in the tunnelling operations.

Examining the construction records revealed that themajor problems were encountered in the boring of thefirst 4 segments, from which the most intense werelocated in segment 1. These problems consisted ofoverbreaks, where a ground treatment program (mostlygrouting) had to be implemented so as to overcome suchconditions, ground water inflows and finally occurrenceof extensive surface settlements mainly in areas ofsegment 1, in which records showed a maximumdisplacement value of about 110mm.More illuminating can be the linkage between the

vulnerability index and the advance rate achieved in theanalysed segments. It should be noted that all delaysresulting from external causes (e.g. strikes, maintenance,etc.) were excluded.In Fig. 10 the cumulative advance of the TBM in each

of the 11 segments is presented, while the averagemaximum and minimum tunnelling advance rates are

ARTICLE IN PRESS

0

20

40

60

80

100

120

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26Days

Cu

mu

lati

ve P

rog

ress

(m

)

Seg 1

Seg 2

Seg 3

Seg 4

Seg 5

Seg 6Seg 7

Seg 8

Seg 9

Seg 10

Seg 11

Seg 7 Seg 8

Seg 10 Seg 9

Seg 3Seg 2

Seg 4

Seg 1

Seg 6

Seg 5

Seg 11

Fig. 10. Tunnelling cumulative progress in each segment.

Table 7

Tunnelling advance rate data in each of the tunnel segments

Segment Average AR

(m/day)

Max AR

(m/day)

Min AR

(m/day)

1 4.00 8.8 0.0

2 4.54 8.8 0.0

3 6.25 10.4 2.8

4 4.35 13.5 0.0

5 9.82 12.1 0.5

6 9.09 13.7 7.3

7 16.67 21.0 14.7

8 11.11 18.3 4.4

9 10.85 17.0 6.1

10 12.50 17.3 1.6

11 14.07 14.8 10.4Seg 1

Seg 2Seg 4

Seg 3

Seg 5

Seg 6

Seg 8

Seg 9

Seg 6

Seg 11

Seg 7

2

4

6

8

10

12

14

16

18

35 40 45 50 55 60 65

Average Vulnerability Index

Ave

rag

e A

dva

nce

Rat

e (m

/day

)

Correl = -0.925

Fig. 11. Relation between average VI and AR values for each segment.


given in Table 7. With the help of these data, theconstruction history of the tunnel can be observed. Forexample, looking at Fig. 10, the steepest the cumulativeadvance line is, the faster the boring is made. Accord-ingly, flat areas indicate that problems were experiencedthere, resulting in delays. Also, the advance ratestatistics (Table 7) can indicate the segments in whichinterruptions in the boring process have taken place andfurthermore present the consistency of the achievedboring rate in the various segments.It is evident that the VI results are consistent with the

analysis findings, as in the first four segments, andparticularly in segments 1, 2 and 4, the lowest TBMadvance rates have been measured. The boring time foreach of these segments (1–4) was more than 16 days,reaching a maximum of 25. In all others (segments 5–11), the tunnelling was completed in a maximum of 12days, having an average advance rate of about 10–12m/day. Furthermore, in segments 7 and 11, the best resultswere recorded (average AR of about 15m/day), while

having at the same time a remarkable consistencyregarding the achieved AR; throughout the tunnellingperiod.Accordingly, the mean values of VI and AR (Fig. 11)

for all the examined tunnel segments have a highnegative correlation coefficient, about �0.92, signifyingthe coherent behaviour of the proposed vulnerabilityindex methodology. The relation between thetwo variables for this case study is approximatelyAR ¼ �0:78VI þ 49:Apart from the mean values, the spread in both the

VI and AR values is important as well. The model’sconsistency is also of value there, as the VI limits, withrespect to their probability of occurrence, can beconsidered as an indicator of the expected tunnelling

ARTICLE IN PRESSA.G. Benardos, D.C. Kaliampakos / International Journal of Rock Mechanics & Mining Sciences 41 (2004) 987–999 999

performance, providing information regarding theseverity of the problems and the extent of the proble-matic areas.

5. Conclusions

The identification of vulnerable areas that mightcause problems in tunnelling, in a proactive context, isvital to the project’s final success. The approach adoptedin this paper aims at providing a quantitative estimationregarding the possible hazards encountered in TBMtunnelling, with special focus on the uncertaintyprevailing in the early stages of the project. Theintroduction of the vulnerability index provides aneffective way of estimating the anticipated conditionsthrough a common scale of reference. The case studyillustrated its importance in identifying risk-prone areasallowing the engineers to:

* focus the site investigation program on selected areasthat will allow clarification of the prevailing condi-tions;

* assess the possible dangers (consequences) inducedfrom tunnelling operations and define the acceptablerisk limits for the project;

* change or adjust the tunnelling specifications inorder to successfully deal with the possible problems;and

* introduce measures towards the improvement of thegeotechnical characteristics of the subsurface in aproactive approach.

Another aspect of the methodology is the ability toassist in a prediction of the TBM’s advance rate, aparameter crucial to the project success. Even though inthe case example illustrated here, the model wascalibrated to the specific site conditions and machinecharacteristics, it can be easily adapted to other cases aswell. Its flexible form allows it to be implemented inapplications where the parameters and their importanceto the tunnelling system varies.

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Documents

A Methodology for Assessing Geotechnical Hazards for TBM Tun