TBM Performance Rock Mass Rating

International Journal of Rock Mechanics & Mining Sciences 39 (2002) 771788

TBM performance estimation using rock mass classifications

M. Sapignia, M. Bertib,*, E. Bethazc, A. Busillod, G. Cardonee

aEnelpower S.p.A., Via Torino 16, 30172 Venezia-Mestre, ItalybDipartimento di Scienze della Terra e Geologico-Ambientali, Universit "a di Bologna, Via Zambonii 67, 40126 Bologna, Italy

cEnelpower S.p.A., Ciso Regina Margherita 267, 10143 Torino, ItalydSELI S.p.A., Viale America 93, 00144, Roma, Italy

eSOGIN S.p.A., Via Torino 6, 00184, Italy

Accepted 1 June 2002

Abstract

Three tunnels for hydraulic purposes were excavated by tunnel-boring machines (TBM) in mostly hard metamorphic rocks inNorthern Italy. A total of 14 km of tunnel was surveyed almost continually, yielding over 700 sets of data featuring rock masscharacteristics and TBM performance. The empirical relations between rock mass rating and penetration rate clearly show thatTBM performance reaches a maximum in the rock mass rating (RMR) range 4070 while slower penetration is experienced in bothtoo bad and too good rock masses. However, as different rocks gives different penetrations for the same RMR, the use ofBieniawskis classification for predictive purpose is only possible provided one uses a normalized RMR index with reference to thebasic factors affecting TBM tunneling. Comparison of actual penetrations with those predicted by the Innaurato and Barton modelsshows poor agreement, thus highlighting the difficulties involved in TBM performance prediction.r 2002 Elsevier Science Ltd. All rights reserved.

1. Introduction

Since James S. Robbins built his tunnel-boringmachine (TBM) in 1954, the TBM designs haveimproved greatly, in an effort to tackle ever-widerranges of rock conditions at higher advance rates.Todays TBMs can reach extremes of 1000m/month [1]but advance rates of less than 50m/month may beexperienced in adverse geologic conditions or whensupport measures fail to maintain tunnel stability untilthe final lining [2].A reliable estimation of excavation rates is needed for

time planning, cost control and choice of excavationmethod in order to make tunnel boring economic incomparison with the classical drill and blasting method.As a consequence, great efforts have been made tocorrelate TBM performance with rock mass andmachine parameters, either through empirical approachor physically based theories [37].

Performance prediction of TBM drives requires theestimation of both penetration rate (PR) and advancerate (AR). Penetration rate is defined as the distanceexcavated divided by the operating time during acontinuous excavation phase, while advance rate is theactual distance mined and supported divided by thetotal time and it includes downtimes for TBM main-tenance, machine breakdown, and tunnel failure [8].Even in stable rock, the rate of advance AR isconsiderably lower than the net rate of penetrationPR; and utilization coefficients (U AR=PR) in theorder of 3050% have been reported by many authorsmainly due to TBM daily maintenance [911]. In low-quality rock, the penetration rate can be potentially veryhigh but the support needs, rock jams and gripperbearing failure result in slow advance rate, withutilization coefficients as low as 510% or less [2].Simple performance correlations have been developed

from data on conventional rock strength testing at thelaboratory scale. These equations relate the penetrationrate with intact rock parameters like the uniaxialcompressive strength [12,13], the rock tensile strength[14] or the rock fracture toughness [15], showinggood predictive ability in the case of homogenous

*Corresponding author. Tel.: +39-051-209-4546; fax: +39-051-209-45-22.

E-mail address: [email protected] (M. Berti).

1365-1609/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved.PII: S 1 3 6 5 - 1 6 0 9 ( 0 2 ) 0 0 0 6 9 - 2

low-fractured rocks. Belonging to these is the predictivemodel proposed by the Colorado School of Mines [16],in which TBM penetration and utilization are computedby means of a force equilibrium approach on the basisof cutter geometry and uniaxial and tensile strength ofintact rock.In jointed rocks the presence of discontinuities

reduces the rock mass strength increasing the rate ofpenetration for a given TBM thrust [1719]. Predictiveequations should be based on rock mass propertiesrather than intact rock strength, for example, relatingTBM performance with rock mass strength derived bystandard geomechanical classifications [2024].Barton [23,24] made the most progress in this

direction. He proposed an expanded version of hiswell-known Q-system [25] in which additional rockmachinerock mass interaction parameters were intro-duced in order to take into account both the rockconditions and the reaction of TBM to the conditions.QTBM allows one to estimate TBM penetration andadvance rate in a wide range of rock conditions even if,as pointed out by the same author, improvements andcorrections are possible by testing new case records.As far as we know, less attention has been paid to the

correlation between TBM performance and Rock MassRating [26], despite the wide use of this geomechanicalclassification in daily practice [10,2729]. The basicfeatures of the correlation with rock mass rating (RMR)are presented in this paper, referring to three tunnelsexcavated in the Italian Alps in medium to hardmetamorphic rocks. Fourteen kilometer of TBM tunnelswere classified and analyzed, yielding over 700 sets ofdata featuring rock mass quality, TBM penetration,thrust and utilization coefficient.

2. Case studies

2.1. Sites characteristics

Data for TBM-performance analysis have beenobtained from three tunnels excavated in metamorphicrocks for hydraulic purposes. The three tunnels (Fig. 1)are located in the northwestern Alps (Italy) and consistof one inclined tunnel for the installation of a penstock(Maen) and two horizontal diversion tunnels (Pieve andVarzo). Descriptive information on the tunnel projectsand tunneling equipment are summarized in Table 1while Table 2 reports the main strength and drillabilityparameters determined through laboratory tests onintact rock samples.

2.1.1. MaenThe area rock units consist of meta-ophiolites

(serpentinite, metagabbro, metabasite, chlorite schist,talc schist) and meta-sediments (calc schist and silicate

marble) belonging to the Zermatt-Saas Zone of thePennidic Domain [30,31]. The parent rocks werecarbonate pelagic sequences and mafic crystalline rocksthat underwent high-pressure low-temperature meta-morphism during the early phases of the alpineorogenesis. Schists and serpentinite show a foliatedtexture while metagabbro and metabasite are generallyweakly foliated. The attitude of rock units is moreor less uniform throughout the tunnel, at N2202701E/35451 (dip direction/dip), so that the longitudinal axisof the inclined tunnel (plunging direction N1281E) isalmost normal to the schistosity.A major shear zone, 20m in thickness, is encountered

within the tunnel. It is composed of massive blocks ofserpentinite and metagabbro (0.51.5m3) embedded in asheared matrix of talc and chlorite schists associatedwith cataclastic bands. Even if the fault zone was clearlyrecognized by the geological investigations, as soon asthe excavation reached the adverse stretch, massiveblocks jammed the TBM cutterhead. In the attempt tomove back the TBM, a large face and roof collapseoccurred involving an estimated volume of 150200m3

of loosened rocks. The accident caused 4 monthsstoppage over the 14 months total construction timeand it required an extensive grouting of the failed massto be undertaken [32,33].Dataset for performance analysis consists of 330

records featuring TBM parameters (head thrust, netboring time, total boring time) and rock mass classifica-tion indexes (RMR and Q). The open-type TBMallowed continuous surveying of the rock mass all overthe tunnel length: RMR and Q were independentlylogged by surveying adjacent tunnel sections 5m inlength; penetration rate and advance rate were com-puted dividing the length of the surveyed section (5m)by the net boring time and the total boring time,respectively.

2.1.2. Pieve vergonteMost of the Pieve Vergonte tunnel is located in the

Sesia-Lanzo Zone of the Austroalpine Domain [3436].Excavated rocks consist of two metamorphic complexesmade up of gneiss and micaschists separated by ametadiorite intrusive body with minor masses of meta-quartzdiorite and metagabbro. The first upstream reach(1.5 km) crosses the metagranite belonging to thePennidic Domain (M. Rosa tectonic unit) and, for ashort reach approximately 100m in length, chlorite andamphibole schists which separate the Austroalpine fromthe Pennidic Domain. Micaschists, chlorite schists andamphibole schists are characterized by a foliated texture,gneiss and metamorphic rocks of the intrusive complexare non-foliated or weakly foliated.The geological structure is complicated by multiple

folding associated with shear zones and brittle faultzones, but the general attitude of rock units forms a

M. Sapigni et al. / International Journal of Rock Mechanics & Mining Sciences 39 (2002) 771788772

Fig. 1. Geological sections along the three tunnels.

M. Sapigni et al. / International Journal of Rock Mechanics & Mining Sciences 39 (2002) 771788 773

monocline dipping at N1401801E/30601 (dip direction/dip), so that the longitudinal axis of the tunnel (directionN070050E) is mainly parallel to the schistosity.Due to the continuous segmental lining, rock mass

survey was possible only during the daily maintenanceof the boring machine, accessing the excavationface beyond the TBM cutterhead. We then had toassume that the rock mass surveyed in the short reach

between the rock face and the cutterhead (1m) wasrepresentative of the whole section bored over a workingday (17m on average); a rather hard assumption that itwas finally accepted, given the homogeneity of the rockmass and the high surveying frequency.The dataset consists of 301 daily records describing

rock mass quality, mean head thrust, net boring time,and excavated length for the first 6.4 km of the tunnel.RMR was logged in all the surveyed sections, Q in only44 sections regularly spaced along the tunnel axis (15%of the dataset). Penetration rate and advance rate werecomputed by dividing the daily excavated length by thenet boring time and the total boring time (24 h),respectively.

2.1.3. VarzoThe Varzo tunnel is excavated entirely in the

Antigorio Gneiss Formation, a massive or weaklyfoliated rock generated by high-grade metamorphismof granite and granodiorite rocks [37,38]. Metaapliteand metabasite dikes locally traverse the tunnel axis, butthe area may be considered essentially homogenous.The geological structure is a monocline gently dipping

(10201) in a southerly direction, slightly complicated byfolds and minor fault zones related to the Sempione-Centovalli fault, a major tectonic structure located 2 kmto the south [39]. In general, the schistosity follows theattitude of the overall structure and, is therefore, mainlyparallel to the longitudinal axis of the tunnel (plungingdirection N080EN070E).

Table 1Summary description of tunnel projects and tunneling equipment

Maen Pieve Varzo

Total tunnel length (m) 1750 9600 6600Total excavation time(days)

413 809 468

Surveyed sectionlength (m)

1750 6400 5800

Excavated diameter (m) 4.20 4.05 4.05Tunnel slope (1) 2435 D0 D0TBM model Wirth 340/

420 ERobbins11112343

Robbins1214240/1

TBM type Open Doubleshield

Doubleshield

Number of cutters 36 27 27Cutter spacing (mm) 66 75 75Cutter diameter (in) 1700 1700 1700

Maximum thrust (kN) 7920 4602 8827Boring stroke (m) 1.5 0.63 0.63Cutterhead curvature Domed Flat FlatCutterhead rotationrate (rpm)

5.511 11.3 4.58.9

Table 2Main characteristics of excavated rocks

Tunnel Rock type Uniaxialcompressivestrength(MPa)

Tensilestrength(MPa)

HardnessIndenter(u.c.)

Knoophardness(GPa)

Drillability(mm"1)

TangentYoungsmodulus(GPa)

Maen Serpentinite 124 (64174)

Metabasite 180 15 26 6.2 0.040.10 65(104289) (929) (1340) (4.38.3) (3794)

Chloriteschist

17

(0.939)Metagabbro 138 1012 13 5.1 39

(113163)Calc schist 75

(29134)

Pieve Micaschist 124215 59 7.59.7 5.28.5 0.110.22 28Metadiorite 171221 813 11 6.27.0 0.030.05 46100Metagranite 146296 0.77 7.17.4 710 0.060.09 2438

Varzo Gneiss > Schist. 161 16 3.7 (90260) 9 (924) (2.24.8)

//Schist. 115 (613) 17 3.8 (82217) (725) (2.53.3)


Also, in this latter case, the use of double shield TBMwith segmental lining prevented a continuous surveyingof excavated rocks. Geomechanical classification wasthen performed during the maintenance downtimes(almost every day), and the surveyed quality was ex-tended to the whole section bored in that day asdescribed for Varzo. Resulting dataset consists of 103daily records featuring rock mass quality (RMR=allsections; Q 16 sectionsE16% of the dataset), meanhead thrust, net boring time, and daily excavated length(15m on average).

2.2. Rock mass classification

Most of the excavated rock masses exhibited goodstrength and a relatively low degree of fracturing. Rarelymore than three discontinuity sets were encountered,and usually only two were found at any location,typically characterized by planar, smooth and tight,unweathered or slightly weathered joint walls.The general good quality of the rock masses is evident

by the frequency distributions of rock mass ratingdepicted in Fig. 2. RMR values are based on the 1989version of the classification [26] taking into account theadjustment factor for discontinuity orientation. Fre-

quency distributions are negatively skewed (relativelyfewer frequencies at low RMR values) with most of thevalues falling in the good-quality classes (I and II RMRclasses). Low quality reaches (IVV RMR class) arerelated to fault zones, composed of highly fracturedrocks, softened chlorite and talc schists and ground-water dripping from major planes.RMR is well correlated with Q (Fig. 3) and

the experimental distribution follows very closelythe correlation line proposed by Bieniawski [26] fortunnels.

3. Empirical relationships

3.1. Penetration rate

3.1.1. Testing the regression modelTypical relation between PR and RMR is depicted in

Fig. 4. As can be seen the scatter is rather wide, leadingto uncertainties about which regression model, forexample quadratic or linear, is appropriate to fitexperimental data. Published works typically show thatempirical relations seem to follow a bell-shaped curvemore than a linear trend, with maximum performance

Fig. 2. Frequency distributions of the excavated rocks in the three tunnels.


for medium-quality rock masses and lower penetrationfor poor and very hard rock masses [3,8,10,40].In order to attain a significant regression model of

performance data, a statistical analysis of variance wasperformed [41]. The analysis consists of a set of three Ftests aimed to verify: (i) the significance of the linear fit;(ii) the significance of the quadratic fit; (iii) thesignificance of increase of quadratic over linear fit.If the computed F value for each of the three tests

falls in the critical region, that is if it exceeds the critical

value of F (Fcrit) at the selected level of significance (forexample, a 0:05; see [41]), we conclude that our modelis correct. On the other hand, if FoFcrit we must acceptthe null hypothesis stating that the variance about theregression is no different to the variance in theobservations, and conclude that our model is notcorrect. In the example of Fig. 4, all the three tests giveF > Fcrit; so we can state that: (i) the linear regression issignificant; (ii) the quadratic regression is also signifi-cant; (iii) the quadratic term is making a significant

Fig. 3. Correlation between RMR and Q values logged in the three tunnels. Dotted lines include 80% of the 111 case histories analyzed byBieniawski [26].

Fig. 4. A statistical analysis of variance was performed in order to attain a significant regression models of performance data. Example refers toMaen tunnel.


contribution to the regression model and should beretained. This means that the quadratic equation fitsperformance data more closely than a straight line does.If performance data were linearly distributed with

RMR; we would obtain a significant regression(F > Fcrit) both for the linear and the quadratic model(a quadratic equation may also fit a linear distribution),but the third test on the contribution of the quadraticmodel over the linear one would have given negativeresponse (FoFcrit). It was then suggested that we adoptthe linear regression model.In the right chart of Fig. 4, data have been grouped in

10 RMR classes and plotted as bar charts, the centralpoint of each bar indicating the mean and the length twotimes the standard deviation of the values falling in eachclass. This simple averaging technique allows the trendto be seen more clearly, and it will be used throughoutthe paper to enhance charts readability. However,statistical analyses and correlation coefficients willalways refer to unaveraged values.

3.1.2. Empirical relations for different rocksThe analysis of variance has been performed for the

predominant rock types encountered in the three tunnelsand both for RMR and Q classification methods. Fig. 5summarizes the results obtained for RMR system.In general, the penetration rate increases with

decreasing rock mass quality until RMR values of about5070. The performance drop below that range reflectsbad boreability in adverse rock masses, where muckingproblems and face instability reduce the potentially highpenetration rate. On the contrary, low PR recorded invery good rock masses (RMR>8090) depend on thehigh strength of the intact rock and by the lowdiscontinuity frequency in the rock mass, which reducethe ability of roller cutter indentation and chipsformation by a fracture mechanism. An approximatequadratic trend also characterizes the correlationbetween penetration rate and Q (Maen only) on alogarithmic scale, with maximum performance in therange Q 5215 and slower penetration for both higherand lower Q-values.In most cases, the curvilinear regression model fits

performance data better than the linear one, with theonly exceptions of mostly bad (Chlorite and TalcSchistsMaen Tunnel) or good rocks (MetadioritePieve Tunnel) characterized by a range of RMR valuestoo narrow to depict the whole curvilinear trend. Themore or less quadratic relation between penetration rateand RMR is seen despite the steady linear increase ofTBM thrust with rock mass strength (Fig. 6), indicatingthat the observed trend does not imitate the appliedforce but that it is the result of the TBMrock massinteraction. A similar trend of decreasing penetrationwith increasing thrust has been observed by Grandoriet al. [22] for Hong Kong granites, in which the available

thrust per cutter was insufficient because of the verystrong rock.

3.1.3. Average trendPerformance data for all the excavated rocks in the

three tunnels are summarized in Fig. 7 (upper) as afunction of Rock Mass Rating. Once again, a quadraticrelation between PR and RMR is suggested, both forsingle tunnels and the cumulative dataset. The correla-tions are significant from the statistical point of view,and almost identical results have been obtainedcorrelating the penetration rate with the basic RMRindex, that is RMR unadjusted for discontinuityorientations [26].However, the high dispersion of recorded data should

be noted (shaded area in Fig. 7). Although some of thescatter is obviously due to the cumulative analysis ofdifferent rocks excavated by different machines, webelieve the dispersion is an intrinsic feature of penetra-tion data, and that it mostly arises from the difficulty inmaintaining a constant thrust. In fact, similar scattermay be also seen considering individual rock types(Fig. 5) or normalizing the penetration rate according tothe net thrust per cutter and rpm of a specific TBMmachine (Fig. 7 lower). Relevance of data scatter toperformance prediction will be discussed in Section 5.As regards, the applicability of our results to other

TBM projects, correlations depicted in Fig. 7 areprobably significant in terms of shape (best performancein medium-quality rocks) but not for numerical predic-tion. The RMR-system, in fact, does not account forrockmachine interaction parameters, so any empiricalrelation based on this system is inevitably limited to therockmachine combinations considered in the originaldataset.

3.2. Utilization coefficient

The fraction of total construction time that the TBMhas been utilized for boring (utilization coefficient, U) isgiven by the ratio of AR and PR: As pointed out byBarton [24] the advance rate declines with timefollowing a rather uniform logarithmic trend, so thatdeclining utilization is seen as the unit of time (day,week, month) increase (see also [11]). The trend isdescribed by the equation U Tm; where T is expressedin hours and the negative gradient m is a function ofrock and machine parameters (see Section 4.2), and itindicates the increasing likelihood that unfavorableextreme conditions (both exceptionally poor and ex-ceptionally good) are encountered as tunnel lengthprogresses.In our case, TBM utilization has been derived from

daily data (T 24) and mean values for the threetunnels are depicted in Fig. 8 as a function of RockMass Rating. The three lines show that even in


favorable conditions the utilization coefficient is lessthan 55% and that values as low as 510% may beexperienced in bad conditions. The corresponding meanadvance rate ranges from 0.7 to 1.0m/h in good rocksand from 0.2 to 0.3m/h in highly jointed faulted rocks.

These values are well in the range of published dailyutilizations [9,10,40], although the average gradients mback-calculated in the three cases (Maen="0.43;Pieve="0.30; Varzo="0.33) are lower than the typicalgradient m "0:20 indicated by Barton. That is to say

Fig. 5. Relationships between RMR and penetration rate for the predominant rock types encountered in the three tunnels. The small table in thecorner of each plot summarizes the results of the analysis of variance: F > Fcrit states that the model is correct (the null hypothesis must be accepted(A); FoFcrit states that the model is not correct (the null hypothesis must be rejected (R).


that we experienced slower performance compared to atypical project. Rather low-utilization coefficients mightbe due to the non-optimal cutter spacing and the severe

cutter wear from abrasive rocks at Pieve and Varzo, andto the steeply inclined excavation at Maen.

4. Comparison with existing predictive models

Actual penetrations may be compared with thosepredicted by the empirical equations proposed byInnaurato et al. [3,21] and Barton [23,24], which relateTBM performance with rock classification indexes.Purpose of the comparison is to test the predictivecapabilities of these models when detailed data, closelysurveyed at the excavation face, are available. To someextent we are dealing with ideal conditions, so we expectgood predictions.

4.1. Penetration rate

4.1.1. The RSR modelInnaurato et al. [3,21] found a strong correlation

between PR; rock structure rating (RSR) [42] anduniaxial compressive strength (UCS) of intact rock:

PR 40:41UCS"0:44 0:047RSR 3:15; 1

where PR is in mm/round and UCS in MPa. For a givenrock with constant UCS the relation predicts penetra-tion as a linear function of RSR; faster boring beingexpected in low-quality rock masses. The database usedby Innaurato consists of five tunnels (totallengthD19 km) excavated in igneous, sedimentary, andmetamorphic rocks with average UCS in the range50150MPa.The RSR is related to RMR by the following [26]:

RSR 0:77RMR 12:4 2

Fig. 8. Utilization coefficient derived from daily average data.

Fig. 6. Mean TBM thrust linearly increase with Rock Mass Rating forindividual rocks (Maen tunnel).

Fig. 7. Relation between TBM penetration and Rock Mass Rating.Excavated rocks include serpentinite, metabasite, chlorite schist, talcschist, calc schist, metagabbro, mica schist, metadiorite, metagranite,and gneiss, involving a total length of about 14 km.


which has been used by Innaurato to derive RSR whennot available.Using Eq. (1) and the mean UCS values listed in

Table 2, the theoretical penetrations for Maen, Pieveand Varzo have been computed and compared with therecorded ones. The comparison is shown in Fig. 9 interms of difference between simulated and measuredpenetrations (DPR) as a function of RMR: As can beseen, predicted penetrations are consistently higher thanthe measured ones, the difference increasing in poorrock where the mean error rises up to 100% of the realvalue.It is likely that the poor agreement is due to the

absence of any TBM-related factor in the predictivemodel, which limits the applicability of Eq. (1) to rockmachine combinations similar to those considered in theoriginal database. This is especially true in poor rock,where the TBMrock mass interaction is of paramountimportance.

4.1.2. The QTBM modelThe method recently proposed by Barton [23] is based

on an expanded Q-system of rock mass classification, inwhich the average cutter force, abrasive nature of therock, and rock stress level is accounted for. The newparameter QTBM is a function of 20 basic parameters,many of which can be simply estimated by anexperienced engineering geologist:

QTBM RQD0Jn

JrJa

JwSFR

SIGMA

F10=20920

CLI

q

20

sy5; 3

where RQD0 is the conventional RQD interpreted in thetunneling direction; Jn; Jw; and SFR are unchanged fromconventional Q; Jr and Ja are also unchanged but theyshould refer to the joint set that most assists (or hinders)boring; SIGMA is the rock mass strength (MPa); F is

the average cutter load (tnf); CLI is the cutter life index;q is the quartz content (on percentage); sy is the averagebiaxial stress on tunnel face (MPa).From the analysis of numerous projects (145 cases),

Barton derived a simple relationship between penetra-tion rate and QTBM:

PR 5QTBM"0:2 4

which predicts a power increase of penetration withdecreasing of QTBM: As clearly stated by the author (see[24], pp. 73 and 99), the relation gives meaningful resultsonly for QTBM > 1; as in very poor rock masses theoperator would usually reduce the penetration rate dueto the bad rock conditions.At the time of the construction of the tunnels (from

early 1998 to middle 2000) we were not aware of the newmethod developed by Barton, therefore geomechanicaldata were collected according to conventional RMR andQ systems (see Section 2). The problem behind a late-in-the-project QTBM analysis is that the new term QTBM hasadditional rockmachinerock mass interaction para-meters that should be explicitly evaluated for TBMtunneling, while conventional classification procedures arefocused on tunnel stability and support measurements.In our case, however, at least for Maen tunnel in

which conventional Q-values were continuously logged,the available dataset seems adequate for a posteriorievaluation of QTBM: This belief is supported as follows:

* Jn; Jw; SFR are unchanged from conventional Q:* RQD0 coincides with conventional RQD, since

scanlines for spacing measurements were orientedalong tunnel alignment.

* Jr and Ja; are essentially unknown, but the errorrelated to the use of conventional joint factors can beestimated.

Fig. 9. Difference between recorded and computed penetration rate as a function of RMR. Predictions are based on the empirical equationsproposed by Innaurato et al. [21] and Barton [23].


In principle, the use of conventional Jr and Javalues is a potential source of large error in a late-in-the-project QTBM analysis. Logged values for con-ventional Q; in fact, refer to the joint set that mostinfluence tunnel stability, which is usually the setwhose strike is parallel to the tunnel axis, while QTBMdraws the attention to the joint set that mostinfluence boring, which is typically a dominantjointing or anisotropic structure parallel to the tunnelface [24,43].Based on our geomechanical surveys, the worst

scenario we could have faced in Maen is that, at agiven tunnel section, the difference in Jr=Ja ratiobetween the joint set critical for stability (logged) andthat critical for boring (required by QTBM) was veryhigh, let us say Jr=Ja 5 for the first and Jr=Ja 0:13 for the latter. This unfavorable combinationwould have caused QTBM to be modified by a factorup to 40.Reanalyzing the original data sheets we have

estimated that such a large error should not affectmore than 10% of the dataset, while it should rangefrom 0 to 20 in a further 20%, and it is almostnegligible in the remaining 70%, both because onlyone set or a dominant set were present (55%) andbecause the rock mass was so highly fractured thataverage logged values were suitable both for boringand stability analysis (15%).

* SIGMA was estimated on the basis of Q0 (theconventional Q with oriented RQD0) and rockdensity as proposed by Barton [24] (Table 3).

* F was continuously recorded during excavation.* CLI values were defined with reference to the typical

values published by NTH for 12 different rock types[18]. Obviously, the NTH table does not deal with agreat variety of rocks texture and composition, so thechoice of appropriate values was sometimes ambig-

uous. To overcome this problem and in order toreduce subjectivity, an estimate of CLI was sup-ported by petrographic analyses and laboratory testsperformed on numerous rock samples collected at thetunnel face during excavation.In particular, mean Mohs hardness and rock

abrasivity were useful for this purpose. The firstwas estimated by determining the proportional ofeach mineral in the rock and then multiplying thehardness value assigned to that mineral by the Mohsscale [44]; the latter from the relation between meanMohs hardness and steel point abrasiveness testvalue [44].Estimated hardness and abrasivity values are listed

in Table 3 with corresponding CLI : As can be seen,the maximum uncertainty range of CLI is about 40(serpentinite and calc schist), which might causeQTBM to be modified by a factor of 2. Relevance ofthis uncertainty to QTBM predictions has beeninvestigated with a sensitivity analysis.

* The quartz content q was obtained from petrographicanalysis. Values are less than 2030% for most of theexcavated rocks, as they result from metamorphismof igneous and sedimentary rocks with low quartzcontent. However, severe cutters wear was observedin garnet-rich rocks (metabasite) and in rockscontaining more than 6070% amphiboles andolivine (metagabbro), suggesting that an equivalentquartz content would be more suitable for ourpurposes.Three different values of q were then considered for

each lithotype: (i) the true quartz content; (ii) theequivalent quartz content, computed on the basis ofthe quartz-equivalence of the rock-forming minerals[45]; (iii) the percentage of minerals with Mohshardness grade higher than 7, which is the nominalhardness of quartz. Computed values are summarized

Table 3Relevant parameters for QTBM analysis. Italic values are those giving the best agreement between recorded and computed penetrations fromsensitivity analyses. (1)(3) refer to the three methods for estimating the quartz-content described in the text

Tunnel Rock type SIGMA(MPa)

Mean Mohshardness

Abrasiveness(1/10mm)

CLI q (%)

(1) (2) (3)

Maen Serpentinite 41716 3.6 1.9 3070 5 28 5Metabasite 72731 6.2 5.0 1020 8 63 26Talc and chlorite schists 874 2.8 1.0 6090 5 23 5Metagabbro 75727 6.0 4.8 1525 5 56 5Calc schist 42712 3.6 1.9 3070 20 37 20

Pieve Micaschist 50718 4.1 2.5 1570 30 51 30Metadiorite 65723 5.1 3.7 1540 5 53 5Meta quartzdiorite 68724 6.4 5.2 15 15 80 15Metagranite and metaaplite 56724 6.6 5.5 10 40 85 40

Varzo Gneiss 48726 5.8 4.5 1525 40 75 40


in Table 3 and have been used as inputs for asensitivity analysis.

The comments above apply to Pieve and Varzo aswell, but with three important differences: (i) conven-tional Q was not logged except in a few sections (seeSection 2); (ii) RQD0 was derived from joints spacingmeasurements at the tunnel face; (iii) due to continuoussegmental lining, the rock mass is known with lessaccuracy than in Maen.Of these three, the first is the most important

limitation, since we should derive Q (Q0) from RMR(RMR0) [26] in order to compute QTBM; and althoughRMR and Q are well correlated (Fig. 3) the procedure isquestionable and results cannot be used for testingmodel capabilities. However, QTBM was computed in thecases of Pieve and Varzo as well, with the purpose ofevaluating model response when the available dataset isneither comprehensive nor tailored for performanceanalysis. It is logical to expect the model would performworse than in the case of Maen.A first series of sensitivity analyses was done on CLI ;

q and Jr=Ja: The results showed that, over the selectedranges, QTBM is only slightly influenced by CLI and q;while it is very sensitive to Jr=Ja changes. We thendecided to use single values for CLI and q (chosen toobtain best predictions; see Table 3) and error bars onthe graphs to help capture the uncertainty in Jr=Ja ratio.The difference between predicted and measured

penetrations at Maen is plotted in Fig. 9 as a functionof RMR: Unlike the Innaurato model, QTBM apparentlygives good results, the difference in penetration ratevarying around zero on the average. However, when wecompare actual and theoretical penetrations as afunction of QTBM (Fig. 10 upper) the apparent goodmatch disappears into statistical noise: measured pointselongate over an almost horizontal axis, indicating lowsensitivity of QTBM:We can explain this different outcome looking at the

term SIGMA=F 10=209 of Eq. (3). Following Barton[24], this ratio should allow QTBM to predict PR in poorrocks, expressing the possibility of reduced penetration(high QTBM values) with decreased rock mass strength(SIGMA) if cutter force (F ) decreases more consistently.From this point of view, the ratio performed well in ourcase: much higher values were obtained in poor rocks(up to 105) than in hard rocks (102 and lower), with aprogressive decrease of the ratio for increasing QTBM:However, an unwelcome reduction in QTBM sensitivity

was observed, as it is evident by plotting mean Q andQTBM values as a function of RMR (Fig. 11). The slopeof the QTBM2RMR correlation line, in fact, is remark-ably higher than the slope of the conventional relationbetween Q and RMR [26], with the result that a widerange of our RMR values (10oRMRo70) falls into anarrow range of QTBM indexes (100oQTBMo700). In

this narrow range, the theoretical curve in Fig. 10 cutsthe experimental distribution close to its mean axis,which is why the model seems to predict the mean PR inFig. 9 well.It may be tempting to explain these unsatisfactory

results with the uncertainties inherent in our late-in-the-project analysis, but we must remember that the error isprobably negligible at least for 70% of the Maen dataset(single points in Fig. 10); we probably could not domuch better even logging QTBM during tunnel excava-tion. On the other hand, the new Barton model is basedon data from 145 TBM projects and its reliability cannotbe judged by an individual case. A short discussion onthis point will be given later in the paper.

4.2. Advance rate

The QTBM-system also allows the estimate of advancerate (AR) as follows [24]:

AR PRTm; 5

where T is the time in hours and m is a negative gradientwhich express the decelerating average advance rate asthe unit of time increase. The gradient m is a function ofcutter life index (CLI), quartz content (q), porosity ofthe rock (n), tunnel diameter (D) and of a parameter(m1) tabulated as a function of Q [24]:

m m120

CLI

! "0:15 q20

# $0:10 n2

# $0:05: 6

From his case record analysis, Barton obtained a typicalvalue m "0:20 and an approximate ranges from"0.15 to "0.45, the least negative value referring togood rock conditions. In the case of Maen, the meanvalue is m 20:17 and 95% of the computed gradientsfall between "0.30 and "0.10; similar results have beenobtained for Pieve and Varzo, the mean gradients being0.18 and 0.22, respectively.As expected given the data in Fig. 10 for PR; the

correlation between QTBM and daily AR (T 24 h) isunsatisfactory as well, the experimental points spreadingparallel to the abscissa without a significant trend(Fig. 12). Moreover, the majority of experimental pointsfall below the two theoretical curves computed using theextreme values of the gradient m; thus the predictedadvance rate is somehow overestimated. However, it isvery probable that our data are not suitable for thiscomparison because of the non-optimal design of themachines (Pieve and Varzo) and the steeply inclinedexcavation (Maen) already mentioned for explaining thelow-utilization coefficients (Section 3.2).

4.3. Specific penetration

Alber [28] proposed an interesting correlation be-tween uniaxial rock mass strength, derived from RMR


using the Hoek-Brown failure criterion, and the specificpenetration SP, which is more suitable than thepenetration rate for comparing different TBM projects.The correlation is based on the analysis of 55 km TBMtunneling involving five different TBMs (1700 disc size)and may be used for a probabilistic estimate of projecteconomics. Unfortunately, the comparison of recordedand predicted penetrations is rather unsatisfactory,actual data falling below the correlation line of the10% percentile (Fig. 1, [28]). The presence of highabrasive rocks and the non-optimal cutter spacing may

possibly explain lower penetration velocities experiencedin our cases.

5. Discussion

As previously described, empirical relations betweenmean penetration rate and rock mass rating clearlyreveals the strong dependence of TBM performance onrock type (Fig. 5). Even considering the same TBMmachine and the same RMR class, lower penetration

Fig. 10. Comparison of recorded penetrations in the three tunnels (Maen, upper; Pieve and Varzo, lower) with predictive equation proposed byBarton [23]. Classes indicate relative difficulty of ground for TBM use.


rates are experienced in stronger rocks, as shown, forexample, by the comparison of the two predominantrock types encountered in Maen and Pieve tunnels(Fig. 13). Reductions in mean penetration rate are seendespite the increased thrusts that were utilized forstronger rocks, suggesting that rock-related factors(joint spacing, tensile strength, joint or fabric orienta-tion) may dominate the mechanism of rock crushing andchip formation in hard rock.Based on this simple observation we can conclude that

the conventional RMR system is inadequate for TBMperformance prediction, which is not surprising if weconsider that rock mass rating, like most of the

geomechanical classifications used in daily practice, hasbeen developed to provide support guidelines for under-ground openings excavated with drill-and-blast method.A logical development would be to define a normal-

ized RMR index with reference to the basic factorsaffecting penetration rate, for example, uniaxial com-pressive strength, tensile strength, brittleness, abrasion,or rock hardness, that is factors controlling rockresistance to cutter penetration and fracture propaga-tion: ideally, different rocks would depict a unique curveon a PR-normalized RMR plot. Our data do not allowus to define a suitable normalization factor but someindications can be given.

Fig. 11. Relationship between Q; QTBM and RMR for Maen tunnel.

Fig. 12. Comparison of advance rate in the three tunnels with predictive equation proposed by Barton [23].


Fig. 14 compares the difference of mean penetrationrates recorded for predominant rock types in Maen atthe same RMR value (RMR 60) with the difference inUCS and mean Mohs hardness (Section 4.1). Interest-ingly, the variation of mean penetration rate is muchbetter correlated with mean Mohs hardness (r 0:81)than with UCS (r 0:16), and in the former case theregression line passes close to zero indicating that tworocks with same mean Mohs hardness should ideallygive the same penetration rate (for the same RMR).Similar results have been obtained for RMR values inthe range 4090 and by normalizing UCS and Mohshardness with reference to the mean TBM thrust, F :Mohs hardness scale, however, is neither linear, nor

do the minerals selected provide a uniform scale of

hardness increase when the minerals are evaluated usingmodern hardness testing instruments, so Mohs hard-ness is not really the ideal candidate for RMR normal-ization. Beside the most logical choice of using somemeasurable drillability parameter, for example, theDrilling Rate Index [46], the Rock Drillability Index[47], or the Stamp Test [48], also quantitative measure ofrock texture describing grain shape, orientation, inter-locking and relative proportions with matrix (e.g. theTexture Coefficient proposed by Howarth and Row-lands [49,50]) are worthy of attention. As stated bySanio [43] these parameters can be linked to the fracturepropagation mechanism caused by the TBM rollingcutters, which is strongly dependent on rock fabricorientation. Numerous rock samples collected during

Fig. 13. Different penetrations are experienced in different rocks for the same RMR. Examples refer to the two predominant rock types in Maen andPieve tunnel.

Fig. 14. The variation of mean penetration rate (DPR) is much better correlated with mean Mohs hardness than with uniaxial compressive strengthof the intact rock (UCS). The ten data points plotted in each chart derive from the one-by-one comparison of the five rock types encountered in Maentunnel (serpentinite, metabasite, chlorite and talc schists, calc schist, metagabbro).


tunnels excavations are freely available to everyonewishing to start a collaborative research on this topic.The last point of discussion concerns the large scatter

showed by recorded penetrations. As said above, webelieve this scatter mostly depends on the difficulty inmaintaining a constant thrust during excavation, whichcauses the net penetration to vary up to 50% of themean values for the same rock type and the same RMRvalue (Fig. 4, 5 and 7; see also [51]). In Maen, forexample, the 50m tunnel section from 1+100 to1+150m is characterized by a low-fractured, homo-genous serpentine rock mass in which 10 identical RMRvalues have been logged (RMR 89; continuoussurveying with 5m steps), but despite this apparenthomogeneity, the mean thrust averaged over the 5msteps (nominal data recorded every 0.2m) varies from4500 to 6000 kN, and the penetration rate from 2.0 to2.6m/h (note that the variation of TBM thrust is toolarge to be explained by an unnoticed variation of rockmass quality; see Fig. 6). Operator sensitivity and hard-to-capture interactions between rock mass and TBMcutterhead are the possible source of data scatter, whichseems to be unavoidable even for an experienced team.In fact, similar dispersions have been obtained in manydifferent tunneling projects [22,52,53], apparently in theform of a random error superimposed to a simple trend.Assuming the scatter is normally distributed around

the mean, performance prediction might be focused onthe mean trend, neglecting the complicated pattern ofreal data. But if we just deal with a rough estimate of theaverage penetration, do we really need a large number ofparameters in our prediction models?Table 4 gives a preliminary answer to this question.

Following the approach recently proposed by Sundaramet al. [53], the table summarizes TBM performance dataand corresponding correlation levels with main geome-chanical classifications and basic rock mass and intactrock properties. As can be seen, even if the strongestcorrelation coefficients are those related with rock massconditions (RMR; Q; rock mass uniaxial strength)rather good correlation is also shown by a basicparameter like the uniaxial compressive strength of theintact rock.A large number of parameters is probably essential

when the relative importance of discontinuities overintact rock properties is high, but we should consider thedifficulties involved when many rock mass parametersare involved. The correlation coefficient of QTBM; forexample, which contains factors of special relevance toTBM penetration, is even slightly lower than conven-tional Q: As the objective of the prediction (penetrationrate) exhibits such a large random scatter, simpleparameters probably give similar or even better resultsthan comprehensive indexes.This conclusion agrees with the results presented by

Morgan et al. [56] on the TBM construction of the

Kielder tunnel, where it was found that Schmidthammer rebounds were much better correlated withTBM performance than conventional classificationindexes, and that better correlations emerge using anaveraging method over geological lengths of the tunnel,a way to smooth out the inherent scatter of penetrationdata.

6. Conclusions

Data from the three tunnels excavated in predomi-nately hard metamorphic rocks support the followingconclusions:

(1) The correlation between penetration rate and RockMass Rating is significant from a statistical point ofview and can be approximated by a second-degreepolynomial curve. Best performances have beenrecorded in fair rock (RMR 40270) whilst slowerpenetrations were experienced both in too bad(RMRo30" 40) or too good (RMR > 70" 80)rock masses, as a consequence of thrust reductionin the former case and reduced ability of cutterindentation and chips formation in the latter.

(2) Despite the significant correlation, empirical rela-tions are of very limited use in terms of predictingmachine performance, even for a specific rockmachine combination. The scatter about the meantrend is in fact remarkably high, the penetrationrate varying up to 50% of mean value for a givenRMR: Literature review confirms this scatter is nota limitation of our dataset; rather, it is a commonfeature in many TBM projects, and it is probablyrelated to the difficulty in maintaining a constantthrust during excavation.

(3) Several improvements should be made to theconventional RMR-system if it is to predict TBMperformance. Different penetrations have beenobtained in different rocks for the same RMRvalue, suggesting the need of RMR normalization

Table 4Correlation values (r) of machine parameters with average intact rock(UCS) and rock mass properties

Machine parameters UCS UCSRMa UCSRM

b

Penetration rate 0.36 0.46 0.44Field penetration index 0.40 0.48 0.40

Machine parameters RMR Log(Q) Log(QTBM)

Penetration rate 0.42 0.41 0.37Field penetration index 0.44 0.50 0.26

aRock mass uniaxial compressive strength following Hoek andBrown [54].

bRock mass uniaxial compressive strength following Singh [55].


with reference to parameters of special relevance tobored tunnels. As regard rock properties, simpleanalyses of our data showed that rock hardnesscould be suitable for this purpose.

(4) Comparison of actual penetrations with thosepredicted by the Innaurato [21] and Barton [23]model showed poor agreement. As regards theInnaurato model, the mismatch is probably due tothe absence of machine-related factors, which limitsits application to rockmachine combinationssimilar to those considered by the author. In thecase of the Barton model the poor result is muchmore difficult to explain, as the new term QTBM hasadditional rockmachine interaction parameters ofspecial relevance for TBM applications. In parti-cular, QTBM shows low sensitivity to penetrationrate, and the correlation coefficient with recordeddata is even worse than conventional Q or otherbasic parameters like the uniaxial compressivestrength of the intact rock. Obviously, the reliabilityof the Barton model cannot be judged by anindividual case, but the mismatch underlines thedifficulties involved in performance prediction whenso many factors (rock mass condition, machine andmuck removal system characteristics, human ex-perience) are involved.

Finally, it is important to note that empirical relationsdiscussed above are based on rock mass surveyingduring the excavation, that is considering the rock massconditions at depth. At the design stage instead,especially for deep tunnel, performance predictionmostly deal with geomechanical surveys of outcroppingrocks, whose characteristics may be significantly worseas a consequence of superficial weathering and stressremoval effects [57]. A preliminary analysis involvingmore than 20 km of TBM tunnels has shown that anincrease of rock mass quality is experienced both interms of Q and RMR: For example, an increase up to1520 RMR points may be expected at depth, the entityof the variation being a function of the RMR valueitself. The detailed analysis of this effect is still inprogress and it will be the topic of a future paper.In order to promote refinements of existing predictive

models and to facilitate the comparison with otherexperiences, the authors are happy to place the data setused in this paper at everyones disposal. Data files maybe downloaded from our web page: www.geomin.uni-bo.it/ORGV/geoappl/TBM Performance.htm.

Acknowledgements

Authors wish to thank the colleagues of Maen, PieveVergonte, and Varzo sites for their help in the collectionof machine performance data and their support in

fieldwork. We are also grateful to the reviewers for theircareful reading of our manuscript and their manyhelpful comments.

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TBM performance estimation using rock mass classificationsIntroductionCase studiesSites characteristicsMaenPieve vergonteVarzo

Rock mass classification

Empirical relationshipsPenetration rateTesting the regression modelEmpirical relations for different rocksAverage trend

Utilization coefficient

Comparison with existing predictive modelsPenetration rateThe RSR modelThe QTBM model

Advance rateSpecific penetration

DiscussionConclusionsAcknowledgementsReferences

TBM Performance Rock Mass Rating

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