# Reliability and Efficiency of Metamodel for Numerical Back Analysis of Tunnel Excavation
## 6 Conclusions  
In this study, the reliability of an ANN-based metamodel used for tunnel back analysis was analysed according to the number of values of each ground parameter. The real values of the ground parameters are not constant owing to their inherent uncertainties. Considering this, it is recommended to use a minimum of six values per parameter showing  
Figure 5: MAPE of each metamodel for the new test dataset.  
Figure 6: Results of global sensitivity analysis for five input parameters.  
results in a MAPE of 5% since it takes only 8% of the numerical analyses time using 10 values per parameter. Furthermore, it is recommended to use eight values per parameter to obtain higher reliability of the metamodel, although this requires four times as much computational time as using six values. Even so, this time is only 33% of the time required for a metamodel developed by 10 values per parameter. From the results of the GSA, it was confirmed that the \(S_{T_{i}}\) of the \(\gamma\), UCS, and \(\mathrm{m_{i}}\) are lower than 0.05, otherwise the \(S_{T_{i}}\) of the GSI and K exceed 0.9. It implies that GSI and K must be included in a back analysis as dependent parameters. These results show the priorities of only the ground parameters around a small radius tunnel of 4 m, so additional sensitivity analyses, including support parameters, are required. Therefore, a sensitivity analysis study is being conducted by considering GSI, K, and variables of the supports as dependent variables for a tunnel with a radius of 7 m using six values per parameter based on the results of the present study. In addition, we will attempt to create a metamodel of a tunnel construction site using six values and verify the applicability of this result.  
This study was undertaken to find the required minimum number of values per dependent parameter that can secure the reliability of the metamodel. According to the results of this research, geotechnical engineers can efficiently develop a metamodel using six or eight values for each dependent parameter during the design phase. This could reduce time by 92% and 67%, respectively, from the time required when using ten values. Additionally, these metamodels will immediately derive reliable results with a range of 5% and 1% error rates from the numerical analysis results. Therefore, in the tunnel construction stage, the values of ground parameters in abnormal situations can be quickly and reliably evaluated through inverse analysis using the developed metamodel. In this regard, it is possible to quickly apply initial countermeasures, such as changing the support pattern to secure stability.  
Data curation, Y.-H.C.; Formal analysis, Y.-H.C.; Investigation, Y.-H.C.; Methodology, Y.-H.C.; Project administration, Y.-H.C.; Validation, Y.-H.C.; Writing--original draft preparation, Y.-H.C.; Conceptualization, S.S.L.; Funding acquisition, S.S.L.; Project administration, S.S.L.; Supervision, S.S.L.; Writing--review and editing, S.S.L. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Korea Agency for Infrastructure Technology Advancement (KAIA) grant, funded by the Ministry of Land, Infrastructure and Transport (22 UUIT-C157786-03) and by the National Research Foundation of Korea (NRF) grant, funded by the Korean government (MSIT) (NRF-2020R1A6A3A13077513).  
Not applicable.  
The authors declare no conflict of interest. The funders had no role in the design of the study; the collection, analyses, or interpretation of data; the writing of the manuscript; or the decision to publish the results.