An analytical solution for internal forces of shallow circular low-to-vacuum tunnel linings in soft soils
Abstract This paper presents an analytical solution derived with force method for the internal forces in the ring lining of maglev train tunnels, which are typically in a circular section and shallowly buried with low vacuum air pressure in the lining. The model incorporates the vacuum pressure indu...
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Nature Portfolio
2024-12-01
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| Series: | Scientific Reports |
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| Online Access: | https://doi.org/10.1038/s41598-024-83062-7 |
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| author | Long Shi Dongyuan Wang Yunzhou Zhang Feng Han Qianqian Lyu |
| author_facet | Long Shi Dongyuan Wang Yunzhou Zhang Feng Han Qianqian Lyu |
| author_sort | Long Shi |
| collection | DOAJ |
| description | Abstract This paper presents an analytical solution derived with force method for the internal forces in the ring lining of maglev train tunnels, which are typically in a circular section and shallowly buried with low vacuum air pressure in the lining. The model incorporates the vacuum pressure induced by the differences in air pressures outside and inside the lining, and the vacuum pressure is assumed to be the active load exerting to the outside of the lining. The model assumes the vertical overburden acting on the lining is proportional to the soil depth at every particular point along the tunnel lining circumference. The lining-ground interaction, represented by tangential and normal resistance to the lining, is combined into the model and is comprehensively evaluated. The Mohr-Coulomb theory is used to estimate the interaction between tangential and normal resistance. The comparison with other models and case histories implies that the proposed model fits well for the field measurement data and results predicted with other models. Analyses based on the proposed model indicated that the vacuum pressure has a negligible effect on the bending moments acting on the lining, but its effect on the normal forces is significant. Parametric studies show that a higher cohesion and internal angle of friction of soils can induce a lower maximum bending moment and higher normal force, indicating that the better the soil conditions the thinner the lining. The cover-to-diameter ratio C/D impacts the maximum bending moment and the optimum C/D is approximately 0.20 in this study, a generally soft soil case. |
| format | Article |
| id | doaj-art-96668209108248e59f7285d3d6f067c7 |
| institution | DOAJ |
| issn | 2045-2322 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Nature Portfolio |
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| spelling | doaj-art-96668209108248e59f7285d3d6f067c72025-08-20T02:43:36ZengNature PortfolioScientific Reports2045-23222024-12-0114111710.1038/s41598-024-83062-7An analytical solution for internal forces of shallow circular low-to-vacuum tunnel linings in soft soilsLong Shi0Dongyuan Wang1Yunzhou Zhang2Feng Han3Qianqian Lyu4School of Civil Engineering, Laznhou Jiaotong UniversityTransportation Engineer, Texas Department of TransportationGansu Hengtong Road & Bridge Engineering Co., LtdSchool of Civil Engineering, Laznhou Jiaotong UniversityState Key Laboratory of Shield Machine and Boring TechnologyAbstract This paper presents an analytical solution derived with force method for the internal forces in the ring lining of maglev train tunnels, which are typically in a circular section and shallowly buried with low vacuum air pressure in the lining. The model incorporates the vacuum pressure induced by the differences in air pressures outside and inside the lining, and the vacuum pressure is assumed to be the active load exerting to the outside of the lining. The model assumes the vertical overburden acting on the lining is proportional to the soil depth at every particular point along the tunnel lining circumference. The lining-ground interaction, represented by tangential and normal resistance to the lining, is combined into the model and is comprehensively evaluated. The Mohr-Coulomb theory is used to estimate the interaction between tangential and normal resistance. The comparison with other models and case histories implies that the proposed model fits well for the field measurement data and results predicted with other models. Analyses based on the proposed model indicated that the vacuum pressure has a negligible effect on the bending moments acting on the lining, but its effect on the normal forces is significant. Parametric studies show that a higher cohesion and internal angle of friction of soils can induce a lower maximum bending moment and higher normal force, indicating that the better the soil conditions the thinner the lining. The cover-to-diameter ratio C/D impacts the maximum bending moment and the optimum C/D is approximately 0.20 in this study, a generally soft soil case.https://doi.org/10.1038/s41598-024-83062-7Low-to-vacuum tunnelAnalytical solutionRing liningSoft soilForce method |
| spellingShingle | Long Shi Dongyuan Wang Yunzhou Zhang Feng Han Qianqian Lyu An analytical solution for internal forces of shallow circular low-to-vacuum tunnel linings in soft soils Scientific Reports Low-to-vacuum tunnel Analytical solution Ring lining Soft soil Force method |
| title | An analytical solution for internal forces of shallow circular low-to-vacuum tunnel linings in soft soils |
| title_full | An analytical solution for internal forces of shallow circular low-to-vacuum tunnel linings in soft soils |
| title_fullStr | An analytical solution for internal forces of shallow circular low-to-vacuum tunnel linings in soft soils |
| title_full_unstemmed | An analytical solution for internal forces of shallow circular low-to-vacuum tunnel linings in soft soils |
| title_short | An analytical solution for internal forces of shallow circular low-to-vacuum tunnel linings in soft soils |
| title_sort | analytical solution for internal forces of shallow circular low to vacuum tunnel linings in soft soils |
| topic | Low-to-vacuum tunnel Analytical solution Ring lining Soft soil Force method |
| url | https://doi.org/10.1038/s41598-024-83062-7 |
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