TECHNICAL | MECHANISED TUNNELLING
theoretical, or ML models to predict TBM performance,
one should pay attention to the application range of the model and geological conditions that the original model was based upon.
MODEL LIMITATIONS The CART and empirical models developed in this investigation have some limitation in their application, similar to any other empirical models. The additional limitations are with respect to machine parameters, i.e., disc cutter diameter used on the machines, where the data used in this study are primarily from 432mm (17”) cutters. Although the thrust force per cutter is a normalised value by cutter number in the developed model, the concentrated stress acting on the rock face at the contact point (which initiates the fracture propagation) is still greatly affected by cutter diameter and cutter tip width, even if the force per cutter is the same as noted by Gong and Zhao (2009). Although, these machines have different diameters,
they are similar in most of their specifications, particularly in cutterhead design and disc cutter arrangement i.e., average spacing (within 60mm– 90mm). Consequently, when the machine parameters are changed (especially cutter dimeter, cutter width and spacing), the model needs to be used with consideration of the effects of these parameters. Perhaps existing models such as CSM’s formula, which allows for variation of these parameters, can be used for developing adjustment factors to extend the use of the proposed FPI numbers to the cases where disc diameter, and tip width or spacing, are outside the range of the available database. Furthermore, the estimated FPI and machine
performance are not valid for the following conditions: mixed face or transitional working conditions; unstable blocky ground; and, squeezing ground conditions.
DISCUSSION AND CONCLUSION Data from TBM field performance, covering eight hard rock tunnelling projects in different geological conditions, enabled a database to be compiled. It was subjected to statistical analysis to derive empirical regression formulas for estimation of FPI. The data were subsequently analysed by ML methods and CART charts/ graphs are offered for improving performance prediction for hard rock TBM tunnelling, while incorporating rock type in the analysis.
The ability of regression tree analysis to perform
recursive partitioning, as an alternative method to the traditional multiple regressions, allowed for its use for the analysis. The main advantage of CART is that the end user does not need a computer code, nor have to be an expert in the field to use the model. In many applications, such as TBM performance
prediction, CART offers better clarity of information, which makes the data understandable using graphic representations. It also allows for selection of the most important variables, threshold values, and finally implements proper rating and weights to each parameter based on the internal regression with the observed values. Moreover, the impact of each variable on the target can be obviously identified by the addressed tree structure in CART model. The proposed models in this study, consisting of
equations and graphs, have been developed based on categorisation of rock type. The results show that this incorporation is very useful as input parameters for TBM performance analysis, complementing the most influential parameters (UCS, Jv or RQD). The results also indicate that CART model outperforms the regression models with typical R2
multivariable regression equations that offer R2
mid 70% range. The suggested formulas and graphs in this study,
allowing incorporation of rock type, offer more accurate results compared to the previous generalised models based on CART. The results of the study are only valid for the geological and geotechnical conditions covered, and not for others, such as mixed face, transitional, unstable blocky or squeezing ground conditions.
This paper was originally published online in Rock Mechanics and Rock Engineering journal, (2022) 55:4869–4891, from Springer, under a Creative Commons Attribution 4.0 International Licence (
http://creativecommons.org/licenses/by/4.0/). Open access funding for original publication of the paper was enabled and organised by Projekt DEAL. As permitted under the particular open access facility, this version of the original paper is slightly abridged and edited for space, and images have been adapted to housestyle. The original paper is available in full at
https://doi.org/10.1007/s00603-022-02868-x.
Table 8: Descriptive statistics of absolute errors (E %) estimated for the prediction models ‘Hassanpour and CART’ respecting to rock type categorisations Rock Type
Models G & GN MV SLK C
Hassanpour CART
Hassanpour CART
Hassanpour CART
Hassanpour CART
N
38 38 23 23 21 21 16 16
Range 131.49 92.26
136.42 40.13
131.25 57.31
115.83 49.86
Min 0.55 0.31 3.87 0.58 2.36 0.08 3.07 2.24
Max
122.47 69.03 96.46 40.68 77.53 57.39 89.03 42.35
Mean 68.90 20.05 36.12 12.96 31.612 18.01 54.64 23.14
close to 90%, as compared to the in the
Std. Deviation 32.37 18.87 39.41 10.36 33.27 15.32 29.65 17.04
26 | July 2024
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