Abstract
A method of calculating the failure probability of the tunnel system combining finite element numerical simulation with multiple response surface method (MRSM) and Monte-Carlo simulation (MCS) is presented. The applicability of the proposed methodology is verified through a subway interval soft rock tunnel in Qingdao, China. The sensitivity of Monte-Carlo sampling number and coefficients of variation for rock masses on the failure probability of tunnel system is conducted. The primary failure modes in tunnel system are identified by reanalyzing the failure samples. The simulation results demonstrate that the failure probability of a tunnel system within soft upper and hard lower surrounding rock mass is mainly attributed to the soft upper part of the surrounding rock. The coefficients of variation of the elastic modulus E1 and the internal friction angle ϕ1 of the pebble layer (soft upper part) have significant effect on the failure probability. The failure probability of tunnel system increases as the coefficients of variation of E1 and ϕ1; increase. Two primary failure modes are found to contribute to the tunnel system reliability. The effect of rock bolt length L and pipe-roof thickness H on tunnel system reliability and two primary failure modes as well are investigated. The simulation results indicate that both the enhancements in L and H tend to be more effective than the enhancement in either L or H if a small target failure probability of tunnel system is expected. The supporting structures design can be performed based on the potential sets of (L, H) satisfying target failure probability.
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Acknowledgments
The work described in the paper was supported by National Natural Science Foundation of China (Grant No. 52171264) and by Research&Development Program from China State Construction (Grant No. CSCEC-2020-Z-49), the financial supports are gratefully acknowledged. The authors also thank the anonymous reviewers and editor for their value comments which improved quality of the manuscript.
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Liu, Z., Li, L., Yu, G. et al. Identification of Primary Failure Modes of Tunnel System and Influence of Supporting Structures on Tunnel System Reliability using Multiple Response Surfaces. KSCE J Civ Eng 27, 843–856 (2023). https://doi.org/10.1007/s12205-022-1924-1
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DOI: https://doi.org/10.1007/s12205-022-1924-1