In an extensive literature search two years ago on tunnel construction rates, Nick Barton found that a realistic construction period could not be inferred by looking purely at the optimal advance and utilisation rates often reported in public presentations. A variety of factors, predominantly connected to rock mass quality, produced a correlation with the actual construction period. Building on his rock masses classification work with the Norwegian Geotechnical Institute in the 1970s, which established the tunnelling quality index Q as a yardstick for judging rock quality and tunnel stand-up times¹, he expanded the factors used in defining Q to take account of other tunnelling variables. The index QTBM was born². This report presents an overview of Barton’s address to the BTS.
Factors on tunnel progress
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TBM penetration rate is often quoted as a benchmark of tunnel construction speed. This is translated into an hourly, daily, monthly or annual rate of progress by multiplying it by the utilisation. This is expressed very simply mathematically as:
AR = PR x U
Where
AR = advance rate
PR = penetration rate
U = utilisation
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By GlobalDataIt is the factors influencing the utilisation U of the TBM that determine the overall speed of construction. The following factors, though not an exhaustive list, all have an impact on U:
The ratio of horizontal to vertical stress is an important factor in the amount of overbreak created. In drill and blast operations, the overbreak can be seen clearly. In TBMs the overbreak is often hidden behind the shield and has to be dealt with as it appears in the lining build/shotcreting area. While TBM penetration rate is not affected, the job is slowed by having to stop and deal with it.
The quartz content of rock influences the penetration rate in different ways. Strong highly abrasive rock containing quartz blunts the cutters quickly, requiring frequent changes. However, quartz contained in a weaker rock can have a cleaning and sharpening effect on the cutters.
The relationship between rock jointing and penetration rate is variable. The numbers of joints and their orientation to the drive direction are very influential on TBM penetration rate. Vertically jointed rock, with the joints running perpendicular to the direction of drive, is the most unfavourable. There is little chance of the cutters getting much purchase in the rock.
The compressive strength of the rock dominates the dynamics of cutting. Cutters have to chip the rock to get sufficient purchase to excavate it. Two or more joint sets presenting at around 45° to 60° to the direction of drive allow the cutters to rip the rock at the face. This obviously leads to faster and easier mucking. TBMs progress faster in a well-jointed medium, but it only takes a short section of faulted ground with water or a section of squeezing rock to slow them down. In turning the discussion to joints in rock, weathering, water ingress, the question approaches of the influence of Q on TBM penetration rates.
Q and tunnel advance rates
The calculation of the index Q takes account of rock RQD, in situ stress/hard/weak rock, number of joint sets, water ingress, weathering/alteration and joint roughness. To encompass the variability of rock in the world, Q varies over several orders of magnitude from around 0.001 for very poor rock to 1000 for good quality hard rock. A general interpretation of the relationship between Q, advance rate (AR) and penetration.
The classic formula for calculating Q is:
Q = (RQD ÷ Jn) x (Jr ÷ Ja) x (Jw ÷ SRF)¹
‘QTBM‘ is an expanded formula ²:
QTBM = (RQDo ÷ Jn) x (Jr ÷ Ja) x (Jw ÷ F/SIGMA)
where
RQDo = RQD measured in the direction of tunnelling
Jn, Ja, Jr, Jw all remain unchanged except that Jr and Ja should refer to the joint set which most assists (or hinders) tunnel boring
F = average cutter load
SIGMA = rock mass strength estimate
Estimation of completion time
Barton continued his presentation with observations on estimating tunnel completion times. He plotted the recorded hourly penetration rate, daily, monthly and annual advance rates for 145 tunnels against time on a log-log plot. He found that there was always a negative gradient showing declining advance rates with time (and distance).
By transforming the equation from
AR = PR x U to AR = PR x T.m
where T = time, the term m could be considered in more detail. In principle the term m was usually negative, relating to the negative gradient observed in the plots. Various values for m were calculated empirically from the data collected. Typical values range from -0.9 in bad ground or where an unexpected event occurred, to -0.2 in good rock. If m falls below -0.9 the time T approaches infinity. This is not good news for tunnellers, and unless the ground is improved the job is forced to stop. In good ground rock abrasiveness was found to have a significant effect on m ³.
Predicting advance rate
Barton made the observation that vertical drilling rates (m/h) through rock were often almost the same as TBM penetration rates. In the laboratory, cutter wear could be estimated using crushed rock material and cutter steel. Important standard tests were to test for the uniaxial compressive strength of the rock, the tensile strength, porosity, quartz content, density, P-wave sonic velocity and cutter life indices.
Geological predictions could be more appropriate by preparing a longitudinal log of the ground conditions. This should pay attention to the physical features such as jointing and faulting. These are then related to the orientation of the tunnel and the direction of drive. Q-value could be estimated from sonic testing.
So are tunnels faster by TBM?
Drill and blast operations are equally strongly influenced by rock conditions. If Q is good, then so is drill and blast progress. This type of operation may prove very competitive if there are large cumulations of faulted rock and poor ground and also if there is extensive extremely good quality massive rock. In areas where rock quality lies in the range Q (=Qo) = 0.1-10 the TBM would appear to be two to three times faster than drill and blast.
There is a common error perpetrated by extrapolating weekly advance rates into monthly or annual rates of TBM progress. They do not take into account the annual decline in advance rate discussed in this presentation. In long tunnels where there is statistically likely to be more extremes, drill and blast might perform better when considering the annual advance rate of a TBM. QTBM can be used as an aid to estimating these annual advance rates, allowing predictions on the bases of time or tunnel length. This depends on the way the basic equations are manipluated³.
Related Files
Hypothetical comparison
Suggested relationship between PR, AR and QTBM
PR and AR
Collated penetration rates and advance rates from 145 tunnel case histories
