TBM tunnelling may give extremes of 15km/year and 15m/year, sometimes even less. The expectation of fast tunnelling places great responsibility on those evaluating the geology and hydrogeolgy along a planned tunnel route. When rock conditions are reasonably good, a TBM may be two to four times faster than drill+blast. The problems lie in the extremes of rock mass quality, which can be both too bad, as in Fig 1, and too good (no joints), where alternatives to TBM methods may be faster.
There has been a long-standing challenge to develop a link between rock mass characterisation and essential machine characteristics such as cutter load and cutter wear, so that surprising rates of advance (or slowness) become the expected rates. Even from a 1967 TBM tunnel Robbins7 could report 7.5km of advance in shale during four record breaking months. Yet, earlier in the same project, 270m of unexpected glacial debris had taken nearly seven months. Advance rates (AR) of 2.5m/h that can decline to 0.05m/h in the same project need to be explained by a quantitative rock mass classification.
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A penetration rate (PR) pushing 10m/h for short periods is so different from an advance rate through a major regional fault zone as slow as 0.005 m/h that a large range of quality seems to be required. The new parameter QTBM can range over 12 orders of magnitude but each end of the scale is exceptionally unfavourable for progress and project economy.
Q and QTBM
The Q-system was developed in 1974 from drill+blast tunnel case records and now totals 1250 cases4. By good fortune, Q-values already stretch over six orders of magnitude of rock mass quality. Continuous zones of squeezing rock and clay may have Q = 0.001, while virtually unjointed hard massive rock may have Q = 1000. Both conditions are usually extremely unfavourable for TBM advance, one stopping the machine for extended periods and requiring heavy pre-treatment and support, the other perhaps slowing average progress to 0.2m/h over many months due to multiple daily cutter shifts.
The general trends for PR with uninterrupted boring, and actual AR measured over longer periods is shown in Fig 2. The Q-value goes a long way to explain the different magnitudes of PR and AR but it is not sufficient without modification and the addition of some machine-rock interaction parameters.
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By GlobalDataRecently, a new method has been developed for estimating both PR and AR using both the Q-value and a new term: QTBM1. This is strongly based on the familiar ‘Q’ parameters but has additional rock-machine-rock mass interaction parameters. Together, these give a potential 12 orders of magnitude range of QTBM. The exact value depends on the cutter force.
Fig 3 can be used to illustrate four basic classes of rock tunnelling conditions that need to be described in some quantitative way:
1. Jointed, porous rock, easy to bore, some rock support
2. Hard, massive rock, tough to bore, frequent cutter change, no support
3. Overstressed rock, squeezing, stuck machine, needs over-boring, heavy support
4. Faulted rock, overbreak, erosion of fines, long delays for drainage, grouting, temporary steel support, back-filling.
The new term QTBM incorporates parameters that take account of such rock conditions and the all important reaction of the TBM to the conditions.
The conventional Q-value, together with the cutter life index5 and quartz content help to explain some of the delays involved. The Q-value can also be used to help select support once differences between drill+blast logging and TBM logging are correctly quantified in the ‘central threshold’ area of the Q-diagram1.
A definition of QTBM is given in Fig 4, and some adjectives at the top of the figure suggest the ease or difficulty of boring. (Note the difference to the Q-value adjectives used in Fig 2, which describe rock mass stability and need of tunnel support.) The components of QTBM are as follows:
QTBM=(RQD0 / Jn) x (Jr / Ja) x (Jw / SRF) x (SIGMA / (F10 / 200)) x (20 / CLI) x (q / 20) x (σθ / 5) (1)
Where RQD0 = RQD (%) interpreted in the tunnelling direction. RQD0 is also used when evaluating the Q-value for rock mass strength estimation (equations 2 and 3).
Jn, Jr, Ja, Jw and SRF ratings are unchanged, except that Jr and Ja should refer to the joint set that most assists (or hinders) boring.
F = average cutter load (tnf) through the same zone, normalised by 20 tnf (the reason for the high power terms will be seen later)
SIGMA = rock mass strength estimate (MPa) in the same zone.
CLI = cutter life index (e.g. 4 for quartzite, 90 for limestone)5.
q = quartz content in percentage terms
σθ = induced biaxial stress on tunnel face (approx. MPa) in the same zone, normalised to an approximate depth of 100m.
The statistics for each parameter, or best estimates, should be assembled on a geological/structural longitudinal section of the planned (or progressing) tunnel.
The rock mass strength estimate (SIGMA) incorporates the Q-value (but with oriented RQD0), together with the rock density (from an idea by Singh8). The Q-value is normalised by uniaxial strengths (σc) different from 100MPa (typical hard rock) and is normalised by point load strengths (I50) different from 4MPa. A simplified (σc)/I50 conversion of 25 is assumed. Relevant I50 anisotropy in relation to the direction of tunnelling should be quantified by point load tests in the case of strongly foliated or schistose rocks. The choice between SIGMAcm and SIGMAtm will depend on orientation1.
SIGMAcm = 5.γ Qc1/3 (2)
SIGMAtm = 5.γ Qt1/3 (3)
Where: Qc = Q.σc/100; Qt = Q.I50/4; and γ = density (gm/cm3).
Example: Slate Q ≈ 2 (poor stability); . σc ≈ 50MPa; I50 ≈ 0.5MPa; γ = 2.8gm/cm3; Qc = 1; and Qt = 0.25. Therefore, SIGMAcm ≈ 14MPa and SIGMAtm ≈ 8.8MPa.
The slate is bored in a favourable direction and RQD0 = 15 (i.e. < RQD). Assume that average cutter force = 15 tnf; CLI = 20; q = 20%; and σθ = 15MPa (approx. 200m depth). The cleavage joints have Jr /Ja = 1/1 (smooth, planar, unaltered). The estimate of QTBM is as follows:
QTBM = (15 / 6) x ( 1 / 1) x ( 0.66 / 1) x (8.8 / (1510 / 209)) x (20 / 20) x (20 / 20) x (15 / 5) ≈ 39
According to Fig 4, QTBM ≈ 39 should give fair penetration rates (about 2.4m/h). If average cutter force were doubled to 30 tnf, QTBM would reduce to a much more favourable 0.04 and PR would increase by a factor 22 = 4 to a potential 9.6m/h. However, the real advance rate would depend on tunnel support needs and on conveyor capacity.
Case record analysis
Fig 5 is a log – log plot of PR and AR as one progresses from average PR for 1h of boring through average AR per day, per week, per month and, in some cases, per year. In each case, rates have been expressed as m/h. The figure is based on data from 145 TBM tunnels totalling more than 1000km, and includes hard rock, soft rock, faulted rock and many exceptional cases1.
The usual relationship between AR and PR is via the utilisation factor U, where:
AR = PR.U (4)
The decelerating trend of all the data can be expressed in an alternative and more useful format:
AR = PR. Tm (5)
where the negative gradient (m) which has units LT-2 (deceleration) has the following values, and T is time in hours. (Numbers 1 to 4 refer to trend lines in Fig 5.)
WR (best performances) m ≈ -0.13 to -0.17 (variable)
1 (good) m ≈ -0.17
2 (fair) m ≈ -0.19
3 (poor) m ≈ -0.21
4 (excep. poor) m ≈ -0.25
The value of (-)m has a weak relationship with the Q-value when rock conditions are good and a strong relationship with the Q-value when rock conditions are bad. The approximate Q-values: 0.1 = very poor; 0.01 = extremely poor; and 0.001 = exceptionally poor are shown among ‘unexpected events’ in Fig 5. Table 1 shows approximate values of (-) m in relation to Q-values. These can be refined in the future when it becomes more normal to log Q-values during TBM tunnelling progress.
Cutter wear
The final gradient (-) m will be modified by the abrasiveness of the rock, which is based on a normalised value of CLI, the cutter life index5. Values less than 20 give rapidly reducing cutter life, and values over 20 tend to give longer life. A typical value for quartzite might be 4 and for shale, 80. Because of the additional influence of quartz content (q %) and porosity (n %), both of which may accentuate cutter wear, these are also included to give ‘fine tuning’ of the gradient.
Finally, one must consider tunnel size and support needs. Although large tunnels can be driven almost as fast as (or even faster than) small tunnels in similar good rock conditions10, more support-related delays occur if the rock is consistently poor in the larger tunnel. Therefore, a normalised tunnel diameter (D) of 5m is used to slightly modify the gradient (m). (QTBM is already ‘adjusted’ for tunnel size by the use of average rated cutter force.)
The ‘fine tuned’ gradient (-) m is estimated as follows:
m ≈ m1 (D / 5)0.20 (20 / CLI)0.15 (q / 20)0.10 (n / 2)0.05 (6)
To give a feel for the influence of (-) m on utilisation and on the declining advance rate, an example is given in Table 2.
Sometimes, PR becomes too fast for the logistics and muck handling. There will then be a local increase in gradient from 1h to 1 day as a more rapid fall in AR occurs11.
Penetration and advance rate in relation to QTBM
Development of a workable relationship between penetration rate PR and QTBM was based on a process of trial and error using case records1. Striving for a simple relationship, and rounding decimal places, the following was obtained:
PR ≈ 5 (QTBM)-0.2 (7)
From Equation 5 we can therefore also estimate AR as follows:
AR ≈ 5 (QTBM)-0.2.Tm (8)
We can also check the ‘operative’ QTBM value by back calculation from penetration rate:
QTBM ≈ (5/PR)5 (9)
An idea of the big numerical range of QTBM is given by the values in Table 3 on p34.
We can also back calculate QTBM from advance rate if the deceleration gradient (-) m is estimated from Table 1 and Equation 6. A weighted mean Q-value for the relevant stretch of tunnel should be adequate for this estimate.
QTBM ≈ (5.Tm/AR)5 (10)
For example: if the weekly average is 220m, where 1 week = 110h, this will give AR = 2m/h, and T = 110h. With m = (-) 0.2, Tm (= U) would then be 0.39, and QTBM would be about 0.9, i.e. mid-range and quite ideal for rapid penetration rate, in this case PR ≈ 5.1m/h. This almost follows line 1 in Fig 5.
It will be noticed that dotted lines have been used for PR and AR estimates in Fig 4 wherever QTBM < 1.0. This is due to uncertainty as to what operator practices will be and also to the destabilising nature of fault zones, where wrong decisions or non-optimal machines may enhance problems.
The large gradients of (-)m in major fault zones will tend to stop TBM according to Equation 8. Pre-treatment (or post-treatment) to increase the effective Q-value to reduce (-)m and to increase stand-up time will each be needed before TBM progress can be resumed1.
Estimating times for completion
The time (T) taken to penetrate a length of tunnel (L) with an average advance rate of AR is obviously L/AR. From Equation 5 we can therefore derive the following:
T = (L / PR)1 / (1+m) (11)
This fundamental equation also demonstrates instability in fault zones, until (-)m is reduced by pre- or post-treatment.
Example: Slate: QTBM ≈ 39 (from previous calculation, with 15 tnf cutter force). From Equation 7, PR ≈ 2.4m/h. Since: Q = 2, m1 ≈ -0.21 from Table 1. If the TBM diameter is 8m and if CLI = 45, q = 5%, and n = 1%, then m ≈ -(0.21) x 1.1 x 0.89 x 0.87 x 0.97 = -0.17 from Equation 6. If 1km of slate with similar orientation and rock quality is encountered, it will take the following time to bore it, according to Equation 11:
T = (1000 / 2.4) 1 / 0.83 = 1433h ≈ 2 months
i.e. AR ≈ 0.7m/h, as also found by using Equation 8 and T = 1433h.
The advance rate would be affected by cutter shift delays (a less favourable gradient m) if the rock had been more abrasive and more porous. (The latter gives self-sharpening wear due to deeper cutter penetration.) With diameter = 8m and Q = 2, light but continuous permanent support would be needed.
Related Files
Tunnel Stability
Tunnelling Sequence Diagram
Relative Difficulty Of Ground For TBM Use
Tunnelling Conditions
Advance Rate
