MECHANISED TUNNELLING | TECHNICAL
analysis, and, in particular, tree-based modelling is an excellent alternative to regression analysis. In addition, it can handle data that are not normally distributed, which is a clear advantage in this field as most data do not follow normal distribution. Also, CART models are easier in visual representation, making a complex predictive model much easier to interpret. Additionally, decision trees are less likely to be influenced by outliers or missing values as there are no assumptions about space distributions and classifier structure (Salimi 2021).
Comparison of the Proposed and Existing Models Among the different models presented in the last decade, the model proposed by Hassanpour et al. (2011) was developed based on the FPI model and has similarities in input parameters and shows promising results compared to the common prediction models, such as QTBM
(Hassanpour et al. 2016). The formula and associated chart introduced by
Hassanpour et al. (2011) is presented in Eq. 10, is very applicable/constructive, and reflects the practical approach in an early stage of tunnel design and construction. The model has been developed based on two commonly available inputs, including UCS and RQD. It is also worth to note that, in this study, the developed model for estimation of FPI in rock type G and GN is based on UCS and Jv, and a relevant formula that can convert Jv into RQD can be used to offer equivalency between the results of this study and that of Hassanpour (2011).
10 FPI =exp 0.008 ⋅ UCS + 0.015⋅ RQD + 1.384 Figure 8 shows the relationship between measured
and predicted values obtained from the Hassanpour’s model for each rock type in testing stage. Since among the developed models in this investigation the CART model shows better results for each of the rock type categorisations, this model has been selected to be compared by the estimated FPI via Hassanpour’s model. For this purpose, variations of absolute error or E(%) for each model and each of the rock type categorisations are calculated as follows:
11
E % = 100⋅ Actual FPI− Estimated FPI Actual FPI
Table 7: Performance indices for developed models Train R2
Regression Model Class G & GN Class MV Class SLK Class C
CART Model Class G & GN Class MV Class SLK Class C
0.70 0.71 0.73 0.72
0.88 0.91 0.92 0.84
Table 8 presents a summary of the statistical analysis
performed on calculated rates and respective errors. As can be seen, the Hassanpour model provides better
results in rock type categorisations MV and SLK whereas it shows higher error in other rock types, including G and GN as well as C. The reason could be the consideration of RQD as joint frequency in hard massive rock masses where the RQD cannot represent the joint spacing adequately due to the limitation in maximum 100. Another cause could be related to the range of the complied data in Hassanpour’s model. Additionally, the differences between geological characteristics of the sites used in development of the models has an impact on the accuracy of the models. However, note that the Hassanpour model shows
promising/acceptable results when similar conditions – such as range of UCS or disc cutter diameter (17”) as well as geological characteristics – are applied in TBM excavations. When choosing between empirical,
Above, figure 8:
Comparison between the calculated and predicted FPI based on rock type categorisation via Hassanpour’s model in testing stage
RMSE
15.41 7.82
3.071 2.43
10.89 4.3 2.11 1.81
MSE
10.55 4.78 2.21 1.93
7.95 3.03 1.65 1.39
Test R2
0.66 0.63 0.69 0.66
0.84 0.87 0.86 0.78
RMSE
25.57 8.87 5.78 3.36
12.91 4.86 2.86 2.37
MSE
20.84 7.001 5.25 2.92
10.12 4.13 2.3
1.88
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