# Estimation of Rock Load of Multi-Arch Tunnel with Cracks Using Stress Variable Method
## 5 Conclusions  
The following conclusions are obtained from this study:  
1. A multi-arch tunnel consists of multiple tunnels connected parallel to each other, and it has a structurally weak shape because the tunnel width is typically greater than the tunnel height. After the excavation and provision of concrete lining in the initial tunnel, the adjacent tunnels are excavated and connected to the pre-excavated tunnel. The displacement and stress distribution in the periphery of the pre-excavated tunnel are affected by the excavation of the adjacent tunnels until the complete cross-section of the multi-arch tunnel is excavated. Therefore, the rock load developed owing to the excavation of the adjacent tunnels must be considered in designing the concrete lining for the pre-existing tunnel.
2. Although many empirical methods have been developed to investigate the rock load for single tunnels, some limitations remain regarding complex construction steps and the consideration of additional rock load for multi-arch tunnels. Therefore, a numerical analysis approach based on the result contours can be more efficient than the empirical method owing to its capability of considering these limitations.
3. The excavation of the three-arch tunnel was numerically simulated in this study according to the overburden values of 10-70 m in rock mass classes III, IV, and V. Considering the stress variable as 10% for all the rock mass classes, the rock load was estimated to be equal to the overburden when the overburden value was less than 1.0 D. However, when the overburden value was greater than 1.0 D, the rock load was estimated to be approximately 0.7 D, owing to the development of the arching effect, which was less than the empirical result (rock load calculated to be 1.0 D) obtained in the same conditions without considering the rock classification. Based on the estimation of rock load via numerical simulation, it is possible to develop a relatively economical design of the concrete lining in deep tunnels.
4. In the case of poor rock mass conditions, the estimated rock load in multi-arch tunnels varies largely with the construction steps. In rock conditions below rock mass class IV, approximately 60% of the rock load is developed in multi-arch tunnels when the last adjacent tunnel is excavated. Therefore, the design and stability analysis must be performed according to the construction steps while considering the varying rock loads under different rock conditions.
5. Cracks can occur at the shoulders of the central tunnel when the excavation of the adjacent tunnels is completed, resulting in an increase in the rock load and stress concentration. Through the back analysis, the crack-induced rock load should be computed with the corresponding deformation moduli of the rock mass. Therefore, the relation between the rock load height and the deformation moduli of the rock mass can provide better insights into the behavior of a three-arch tunnel.  
[PERSON], [PERSON] and [PERSON] supervised the overall study and designed the scheme for rock load estimation and performed numerical analyses. [PERSON] and [PERSON] analyzed the results and prepared the manuscript. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (No.NRF-2018R1D1A3B07045700 and NRF-2017R1D1A1B03034236).  
The authors declare no conflict of interest.