FOCUS ON TBMS
Empl mploying ying the QTBM progn og nosis os is model odel D r Ni ck Ba r ton, of Ni ck Ba r ton & Ass Associates, ociates, an d geolog geolog ist Ricar do A Abr Abr ah ão, of Fu nd ação d e Ciência s Aplicad as e Tecnolog Tecnolog ia Espaciai s (FU NCATE NCATE ), ex ex pla in the w or k in gs of the Q T BM t u n n e l l i n g pr ognosis m odel, odel, using using a va r iety iety of geologi geologi cal cond ition s that g ive big ra nges of tunn elli ng per per form an ce. ce. Their Their m ai n ex ex am ple r ein forces forces the idea of hybri d tun nelli nelli ng w hen hen gr eat contra sts of condition s ar e found (se (see com pan ion ar ticle in T&TI, June 2003) 2003)
I
n a previous article by the first author, entitled ‘TB ‘TB M or Dril Drilll and B las t’ (T&TI , J une 2003), 2003), mention mention w as mad e of the QTBM QTBM prognosis mod el. This is is a time sa ving ving Exce l program, developed by co-author Ricardo Abrahão, for es timating the co nse q uence s of TBM TBM tunnelling tunnelling in in the differing geological and rock mechanics properties of a site. The The input for this this mod el are a variety of eng ineering neering geological parameters that are commonly collected during during projec projec t feas ibility bility and d es ign pha se s. The The output are estimates of penetration rates (PR), and actual advance rates (AR) over calculated periods of time, as ea ch zone (or ge ologica l/structural/roc k mec ha nics domain) of given length are penetrated, and supported as neces sa ry. The program c a lcula lcula tes (and g raphs ) the overa ll performance, performance, and estimated time time of tunnel completion. completion. We w ill show va rious exa mples, mples, and discuss both strengths and weaknesses, and areas where industry input from from new TBM des igns needs to b e incorporated incorporated now, and of course in the future.
Basic elements of QTBM There here a re thos e w ho think think that the s tand ard Q-system for describing rock masses has too many parameters, and others that feel it is already too much of a simplifica tion. tion. The fact is, that w e a ll need de sign as sistanc e – whe ther from from a life-ti life-time me o f experienc experienc e, ha lf a life ife time, or from from mo de ls, or from from truste d ‘rules-of-thumb’. ‘rules-of-thumb’. The QTBM model has a lot of pa rameters, for which no a pology is m ad e. The The rock-mac hine hine interact ion in TB M tunnelling is very complex after all. But with its founda tion in in the a na lysis lysis o f 140 140 TBM ca se rec ords [1], and freq freq uent app lica tion tion s ince then, a certain feeli feeling for its s trengths trengths and wea knesses has been ac quir quired. Two importa nt diag rams for a rapid understa nding of the principles need to be reproduced here for ready reference. They They ha ve bee n see n before by T&TI ’s ’s readers. Figure 1 shows an example of the basic model with PR and AR on left and right axes, and the ‘logarithmic’ scale of QTBM defined along the bottom axis. Figure Figure 2 shows log P R a nd log AR AR on left and right right axes and log TIME along the b ottom a xis, xis, s howing 1 da y, 1 wee k, 1 month, etc. Top: Fig 1 - Some principles and definitions of the Q TBM model, that are now incorporated
Deceleration
in the numerical version of QTBM
The c la ss ic e q uation rela rela ting P R a nd AR via via utilisation utilisation (U) is refined as follows in the QTBM model, to allow for the important fac tor of time (a (a nd tunne l leng leng th): th):
Above: Fig 2 - The (usual) law of deceleration as time increases. Typical gradients of decline are m = -0.1 5 to 0.2 5, except in fault zones where (m) (m) is steeper, steeper, when Q is <0.1
20
T u n n e l s & T u n n e l l i n g I n t er er n a t i o n a l DECEMBER 2003
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FOCUS ON TBMS =PRxU A R
m
AR=PRxT
m
U = T
The ba sic TBM TBM ope rations a re to cut a nd provide provide s uppo rt for a t unnel. This mea ns 100% utili utiliss a tion wh ile ile boring one stroke, or 100% utilisation while continuously boring until cutter change (pushing off the PC lining while re-setting the grippers), must inevitably fall when changing the cutters, when performing maintenance, (or when placing neces sa ry support support when not us ing a do uble-shield–and–li uble-shield–and–lini ning ng opera tion). tion). Even with these impressive semi-automated techniques, such as used by all four machines at the current current G uad a rram rram a Tunnels in Spa in, the utilisat utilisat ion is lower over monthly periods, than the 100% used to define the ma gnitude gnitude of P R. Neverthel Nevertheless ess , it is is reported that well in excess of 40% utilisation per month has been achieved while driving the four faces at Guadarrama, a combined total of about 25km by the time this a rticle rticle is p rinte rinte d. This utilisa utilisa tion of 40% or more, gives a remarkably shallow gradient (-m ) of deceleration (see Figure 2), which we can express from the above as:
=log U / log T m With 1 month expressed as a continuous 720 hours, and the assumed U expressed as a fraction 0.40, the gradient (-)m of deceleration is found to be less than (-) 0.14. This is a remarkable result in in view o f the ha rdness of the rock, and the reported need for quite frequent cutter changes .
Time (h)
) h / m ( e t a r
) h / m ( e t a r
Be st G o oo d o d
n o i t a r t e n e P
e c n a v d A
F ai r P o oo r
Zone 1 Zone 2
E x xt r e m me l ly p o y o or r
Zone 3 Zone 4 Overall
Hand-worked example and Excel result A major planned project in Brazil, the San Francisco River Wa ter Trans fer P rojec rojec t - to a rid rid reg ions in the NE path compared to the above, and in a few minutes of Top: Fig 3 - The last ‘keyof Brazil - had a 16km long tunnel in an earlier stage of carefully applied input data, on four separated ‘key- board’ board’ for the 12km- 16km planning (this (this ha s now bee n a ltered a little) little).. The The longe r boards’ (the last of which is shown in Figure 3), supplies zone of the tunnel tunnel is a convenient project for illustrating the QTBM both the full tabulated calculations in Excel, and the model, as it had almost equal lengths of km in hard graphic output shown in Figure 4. Above: Above: Fig 4 - The log-log massive sandstones, jointed phyllites, jointed mica plot of PR and AR and TIME. T a ckling varia bility sc hists hists and hard ma ss ive granites, respectively. respectively. These The phyllite and mica schist gave contrasting tunnel-speed prognoses, suggesting a In a second example we demonstrate what variable show the best result, while hybrid hybrid (TBM + dril drill and blas t) so lution, ution, a pos sible cond itions tions m ay d o to TBM TBM progress progress , a s mo delled delled b y the massive sandstone and solution solution d isc usse d in B arton, 2003 2003[3], for ma inta ining ining the the QTBM model. For purposes of illustration, we granite show the worst good reputation of both tunnelling methods, when contrasting conditions Table 2: Basic calculation are found in the sa me project. project. Zone Lithology Stability oriented Rock mass strength Q Gradient A worked example of this 16km long Q Q 0 Q c Q T S I G M A m CM SIGMATM SIGMA TBM tunnel shows the successive stages of 1 f a ult 3 E -3 3 E -3 1 . 6 E -4 3 . 9 E -5 0 . 59 0. 3 7 0 . 37 0. 09 -0 . 6 9 (hand) calculation, and the equations 2 s a n d s t o n e 3 . 3 0 2 . 2 0 1 . 1 0 2 . 2 0 1 2 . 9 0 1 6 . 2 6 1 2 . 9 0 6 3 . 0 1 0. 19 used at each stage of calculation (see 3 g ra n it e 30 0 . 0 0 30 0 . 0 0 7 50 . 00 1 , 12 5. 0 0 12 7. 2 0 1 4 5 . 6 1 1 2 7 . 2 0 2 , 4 5 8 . 4 1 -0 . 2 4 Ta b les A to H, p 22). 22). 4 f a ult 1 . 00 1 . 00 0 . 10 0. 1 3 5 . 11 5. 5 0 5 . 11 2 6 1. 4 1 -0 . 3 7 Due to decimal rounding, the Q TBM 5 t uff 2 . 50 2 . 00 1. 00 1. 2 5 11. 00 1 1. 8 5 11. 00 0. 07 -0 . 1 8 Excel program follows an abbreviated 6 0. 00 0. 0 0 7 8 9 10 11
Right and below: Reproduced ‘Input data’ and ‘Basic calculation’ tables; for the first 0.5km of a tunnel with widely different conditions for each 100m
0. 00 0. 00 0. 00 0. 00 0. 00
0. 0 0 0. 0 0 0. 0 0 0. 0 0 0. 0 0
Table 1: Input data Zone Lithology
RQD
Jn
J r
J a
J w
SRF
m1 RQ RQD D0
γ
ß
σc
I50
F
CLI
q
σe
D
n
L
Vp
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FOCUS ON TBMS a) Stability (and gradient m1) Jr
RQ D
Zo n e Sandstones P hyllites hyllites Mica schists Granites
J w
1 Q= 2 S RF Jn Ja s 3 (s = leas t favourable favourable for stability) 4
m1
R Q D /J n J r/J a 100/9 2/1 2/1 35/9 1. 5/1 5/1 50/9 1. 0/1 0/1 100/6 2/1 2/1
J w /S R F Q 0.5/1 11.1 1.0/1 5.8 0.66/1 3.7 0.66/1 22.0
Deg (º) R Q D o /J n (J r/J a )o Zo n e Sandstones 20/70 100/9 2/1 2/1 P hyllites hyllites 60 30/9 1. 5/1 5/1 Mica schists 60 45/9 1. 0/1 0/1 Granites 10/80 100/6 2/1 2/1
J w /S R F Q o 0.5/1 11.1 1.0/1 5.0 0. 66/ 66 /1 3.3 0. 66/ 66 /1 22.0
-0.17 -0.19 -0.20 -0.18
b) Oriented Qo (in tunnelling direction) Jr
RQ D o
J w
1 Q o = S RF 2 Jn Ja c 3 (c = most affecti affecting ng cutters) 4
c) Rock mass strength (SIGMA) 1/3 1/3
Zone
SIGMAcm = 5 Q c
1/3
1 2 3 4
SIGMAtm = 5 Q t Q c = Q o
C
100
Q t = Q o
I50 4
Qc
c
Sandstones P hyllites hyllites Mica schists Granites
2.5 2.6 2.6 2.7 (
SIGMAcm I50 (MPa)
125 13.9 75 3.8 150 5.0 200 44.0 or (
30.1 20.2 22.2 47.7
5 1 4 8 ( or
Qt
SIGMAtm (MPa)
13.9 1.25 3.3 44.0
30.05 14.0 19.35 47.66
(
d) QTB TBM M Q TBM = Q o
S IG MA F
10
F=mean cutter cutter force CLI= cutt er life life Index (NTNU) q= % quartz = biaxi biaxial al stress (5 MPa/ 100m depth
20
20
9
C LI
q 20
9
(
5
20 F
10
= 0.0054 with 25tnf/ 25tnf/cutte cutte r)
Zo ne
Qo
SIGMA SIGMA cm (MP a ) (MPa)
1 Sandstones 2 P hyllites hyllites 3 Mica schists
11.1 5.0 3.3
30.05 14.00 19.35
F (tnf) 25 25 25
4 Granites
22.0
47.66
25
C LI
q (%)
10 20 15
70 20 20
10
35
(MP a ) Q TBM (MPa) 8 20.07 8 0.60 8 0.73
12
44.28
e) Gradient (-)m
m = m1
D 5
0.20
0.15
20 C LI
q 20
0.10
n 2
0.05
1 2 3 4
Zone Sandstones P hyllites hyllites Mica schists Granites
m1 D n (%) -0.17 15 ø -0.19 5 10.7 -0.20 2 (m) -0.18 1
m -0.28 -0.23 -0.24 -0.24
f) Penetration rate -0.2
PR 5 (Q TBM ) AR PRxT =
m
1 2 3 4
Zone Sandstones P hyllites hyllites Mica schists Granites
Q TBM 20.07 0.60 0.73 447.28
P R (m/hr) (m/hr) 2.74 5.54 5.32 2.31
AR (m/hr) 0.17 0.76 0.63 0.23
g) Time to advance length L Zone
1
T=
L PR
1+ m
1 2 3 4
Sandstones P hyllites hyllites Mica schists Granites
L (m)
(m)
4000 4000 4000 4000
-0.28 -0.23 -0.24 -0.24
1 1+ m 1.39 1.30 1.32 1.32
T (hr) 23,204 5,256 6,307 17,656
T AR Assume max. = L* 8736 hrs/yr hrs/yr 4000 4000 4000 4000
2.66 yrs 0.60 yrs 0.72 yrs 2.02yrs
(m) (hrs ) = (6.00 yrs) ∑L= 16000 (m) ∑T= 52,42 3 (hrs *rough c heck o f AR AR x T= T= L(err L(errors ors w ill ill occ ur ifif dec imal places are rounded )
h) Overall performance P R,AR R,AR (we (we ighted me an),∑L
L
T
consider fi ve 100m 100m long, c onsec utive utive do mains, ma king king the fi rst 0.5km of a tunne l. The fi ve ‘key-boards ’ of input data are recorded at the top of the Excel three-part ta ble, reproduc reproduc ed a s Ta bles 1 to 3. Ta ble 2 show s the basic calculations of extremely variable QTB M values (min = 0.07; ma x = 2,458) 2,458). Note a lso the va riab riab le fi na l gradients of deceleration (-)m (derived from the ‘fine‘fi netuning’ tuning ’ s een in Ta ble E of our ha nd-ca lculation for the 16km tunnel). Figure Figure 5 shows the variab variab ility of these doma ins mo st clea rly. rly. Time of c ompletion om pletion for this fi rst 0.5km is predicted to be six months, due to the big initial delay in a serious fault zone, which was penetrated ‘too fast’ fast ’ (PR too high due to unnecessarily high F). A blocked cutter-head or local collapse would be the likely result. The ne ed for pre-tr pre-trea ea tment (from from t he s urfa urfa ce? ) or avoidanc e, is very clear, clear, a s the fault spoils spoils the sc hedule hedule completely, pulling down the overall gradient.
Discussion In the above example of 0.5km of variability, we have two fault fault zones, one of w hich hich wa s ‘de fi ned ’ by seismic velocity. Care should be taken to allow for the compacting effect of signifi signifi cant tunnel depth when using using P -wave velocity velocity[2]. We We ha ve expe rienc rienc e of d eeply buried fault zones with unexpectedly high (seismictomography-determined) velocities, yet very low Qvalues, c a using six months delay to the TB TB M tunnell tunnelling. The co ntras ting effect of wea k, jointed jointed tuff, compa red to hard massive granite is well illustrated by the contrasting values of QTBM in Ta ble 2. The The s a me c utter force of 25t was selected for each, just for illustration. As will will be s een in the eq uations ta bulated bulated in our handcalculation sheets, the QTBM value can be backcalculated from the PR results at a tunnel project. In our exa mple P R differs differs from from 1.05m/hr in in the ha rd ma ss ive ive granite (QTBM = 2,458) to 8.57m/hr in in the med ium strength, jointed tuff (QTBM = 0.07) 0.07).. As As w e ha ve see n, the effective gradient of deceleration (-)m can also be backcalculated from the utilisation being achieved in an existing project, but when, and only when, the time period period is clea rly rly de fi ned. From recent, highly successful semi-automated double-shield– double-shield–a nd– nd –lining projects, we note that the effective gradient is reduced compared to projects where a cheaper lining is selected, as the re-setting of the grippers is one of the utilisation delays when there is no lining to take the thrust while the grippers are re-set. So far during the development of QTBM, we have found that the initial gradient (-)m of deceleration is strongly linked to the conventional Q-value of rock mas s qua lity, ty, a s per the ta ble below. The The s trong trong linkag nkag e to Q is weakened however, when the rock is of high quality. If the effective gradients of deceleration (-)m derived from utilisation records can be as low as (-)0.12 to (-)0.13 by the extra investment in doubleshield– shield –a nd– nd –lining methods, the question needs to be raised: “ how far into the low Q-value area will this apply?” apply? ” Can many untreated faults be penetrated with few delays, using such techniques?
Q
0 001 0 01 0 1 1 0
10
100 1000
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FOCUS ON TBMS and squeezing ground. It may be so that collapses are more diffi diffi cult to recover from when the support technique is semi-automated and ‘easier’ easier’ with an open TBM, b eca use of rela rela tively tively ‘easier’ easier’ access for ‘ conventional’ conventional’ reinforcement and grouting equipment. We need at any rate, to be aw are of the potentiall potentially (25%-30% or more?) reduced deceleration gradient (-)m 1 over presumably a quite wide range of conditions (or Q-values), if the extra investment in a doubleshield– shield –a nd– nd –lining tunnelling system is to be used. It would be of great value if the industry would report more widely on utilisation rates over specifi specifi ed time intervals intervals for the d ifferent ifferent TBM s olutions olutions tha t a re presently available. An all-important additional data set would be the approximate Q-value (or RMR) ranges of rock quality. We ma y also no te tha t effective Q-values Q-values (and RMR values) can be improved by pre-injection (e.g. Barton, 2002[2]), although from behind a cutterhead, this process is usually incomplete, e.g. 10 o’ o ’clock to 2 o ’clock only, but perhaps enough to improve arch T& T stability.
Time (h) 10
) h / m ( e t a r
1
10
1 0. 000
10 0. 000 10 5 4 3 2
1
Be st 1
Zone 1
0.1
Zone 3
0.05 0.04 0.03 0.02
Zone 4
G o oo d o d 0.5 0.4 F ai r 0.3 0.2 P
Zone 2
o oo r o r
0.1
E x xt r e m e l ly p o y oo r o r 0.05
) h / m ( e t a r e c n a v d A
0.04 0.03 0.02
Zone 5 Overall
0.01
1 da y
1 w e ek
1 m o nt h
1 yea r
5 y e a rs
0.01
Above: Above: Fig 5 - The log PR, log AR and time prognoses for the 0.5 km of variable conditions. Each domain is is 100m long Below: Reproduced ‘Performance’ table
Table 3: Performance Zone
Lithography
REFERENCES 1. N Ba rton, 2000. 2000. “ TBM tunne lling lling in jointed jointed a nd fa ulted rock” rock” 173p, Balkema, Rotterdam. 2. N Ba rton, 2002. 2002. “ Some new Q-value correlations to assist in site chara cterisa cterisa tion tion a nd tunnel design” design ” Int. J. Rock Mech. &Min. &Min. S ci. Vol. 3 9/2. 3. Ba rton, 2003. 2003. “ TBM o r drill drill and blas t ” Tunnels &Tunnelling Interna tiona l, Vol. Vol. 35/6. 4. R G rand ori, M Ja ege r, F Antonini Antonini &L &L Vigl, Vigl, 1995. Evinos Evinos Mornos Tunnel Tunnel - Greece . “ Cons truction truction of a 30km 30km long hydraulic draulic tunnel in in less tha n three years under the mos t a dverse geologica l conditions conditions ” P roc. RETC, S an Francisco , CA.
1. 000
5 4 3 2
0.5 0.4 0.3 0.2
n o i t a r t e n e P
10 0
1 2 3 4 5 6 7 8 9 10 11
fa ult s a nd s t o ne g ra n it e fa ult t uf f
Penetration PR
AR
8 . 18 2 . 18 1 . 05 1 . 64 8 . 57 0 . 00 0 . 00 0 . 00 0 . 00 0 . 00 0 . 00
0. 0 3 0. 8 8 0. 2 6 0. 1 4 4. 9 1 0. 0 0 0. 0 0 0. 0 0 0. 0 0 0. 0 0 0. 0 0
Time to Overall performance advance T check ∑L ∑T 3 , 1 3 4. 1 2 1 1 4. 1 2 3 8 7. 3 9 7 0 3. 1 6 2 0. 3 7 0. 0 0 0. 0 0 0. 0 0 0. 0 0 0. 0 0 0. 0 0
1 00 . 00 1 00 . 00 1 00 . 00 5 0 0. 0 0 4 , 3 5 9. 1 5 1 00 . 00 m h 1 00 . 00 0 . 00 0 . 00 0 . 00 0. 50 6 . 00 5 0 . 00 km m o nt h 0 . 00 0 . 00
P R L(a v ) 4 . 33
AR T(a v )
0 . 11
