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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
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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
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Fig. 1. Geological sections along the three tunnels.
M. Sapigni et al. / International Journal of Rock Mechanics
& Mining Sciences 39 (2002) 771788 773
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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)
M. Sapigni et al. / International Journal of Rock Mechanics
& Mining Sciences 39 (2002) 771788774
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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.
M. Sapigni et al. / International Journal of Rock Mechanics
& Mining Sciences 39 (2002) 771788 775
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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.
M. Sapigni et al. / International Journal of Rock Mechanics
& Mining Sciences 39 (2002) 771788776
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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
M. Sapigni et al. / International Journal of Rock Mechanics
& Mining Sciences 39 (2002) 771788 777
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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).
M. Sapigni et al. / International Journal of Rock Mechanics
& Mining Sciences 39 (2002) 771788778
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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.
M. Sapigni et al. / International Journal of Rock Mechanics
& Mining Sciences 39 (2002) 771788 779
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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].
M. Sapigni et al. / International Journal of Rock Mechanics
& Mining Sciences 39 (2002) 771788780
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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
M. Sapigni et al. / International Journal of Rock Mechanics
& Mining Sciences 39 (2002) 771788 781
-
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
M. Sapigni et al. / International Journal of Rock Mechanics
& Mining Sciences 39 (2002) 771788782
-
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.
M. Sapigni et al. / International Journal of Rock Mechanics
& Mining Sciences 39 (2002) 771788 783
-
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].
M. Sapigni et al. / International Journal of Rock Mechanics
& Mining Sciences 39 (2002) 771788784
-
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).
M. Sapigni et al. / International Journal of Rock Mechanics
& Mining Sciences 39 (2002) 771788 785
-
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].
M. Sapigni et al. / International Journal of Rock Mechanics
& Mining Sciences 39 (2002) 771788786
-
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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M. Sapigni et al. / International Journal of Rock Mechanics
& Mining Sciences 39 (2002) 771788788
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