Abstract
Due to the limitations of the terrain and other reasons, twin-tunnels with small clear spacing are becoming more and more common. The reasonable clear spacing of twin-tunnels in weak surrounding rock is an urgent problem. In this paper, based on pressure-arch theory (PAT), the method used to calculate the loosening pressure on the surrounding rock of twin-tunnels under three cases was derived by considering the additional disturbance of the excavation on the middle rock pillar through the amplification factors of the sliding angles, k1 and k2. Taking the weak surrounding rock as an example, we discussed the effect of the clear spacing variation on the loosening pressure of the surrounding rock, and obtained the dangerous clear spacing of twin-tunnels. The accuracy and applicability of this approach were verified by the in-site data that were measured. Considering the limitation of the pressure-arch theory on a deep-buried tunnel under high geo-stress, based on the Jiuzhai valley-Mianyang highway in China, the reasonable clear spacing of twin-tunnels in weak surrounding rock at different buried depths, i.e., 400 m–1,600 m, is discussed using the numerical simulation method. The analytical solution indicated that the loosening pressure of the inner side of the first tunnel was greater than the one of the second due to the amplification factors of the sliding angles, k1 and k2. The in-site data showed that in the weak surrounding rock mass, when k1 and k2 are taken as 1.15 and 1.3, respectively, the loosening pressure distribution law is closest to the actual situation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Abbreviations
- B 0 :
-
Clear spacing of twin-tunnels
- B 12 :
-
Critical clear spacing of case I and case II
- B 23 :
-
Critical clear spacing of case II and case III
- D :
-
Span of twin-tunnels
- D p :
-
Length of the horizontal projection of the unilateral fracture surface
- DCS:
-
Dangerous clear spacing
- e i :
-
Horizontal loosening pressure
- e ′ i :
-
Horizontal loosening pressure of the left tunnel in case II
- e ″ i :
-
Horizontal loosening pressure of the right tunnel in case II
- f :
-
Consolidation coefficient of the surrounding rock
- G ′ m :
-
Gravitational force of the extra pressure arch
- H :
-
Height of the pressure arch
- H 1 :
-
Height of the pressure arch of the left tunnel in case II
- H 2 :
-
Height of the pressure arch of the right tunnel in case II
- H m :
-
Height of the entire large pressure arch
- H ′ m :
-
Height of the extra pressure arch
- \({H_{q_i^\prime}}\) :
-
Equivalent load height of the vertical loosening pressure of the left tunnel
- \({H_{q_i^{\prime \prime}}}\) :
-
Equivalent load height of the vertical loosening pressure of the right tunnel
- \(H_{q_i^\prime}^ * \) :
-
Equivalent load height of the vertical loosening pressure of the left tunnel at the limit state
- \(H_{q_i^{\prime \prime}}^ * \) :
-
Equivalent load height of the vertical loosening pressure of the right tunnel at the limit state
- k 0 :
-
Enhancing factor of the middle rock mass
- k i :
-
Amplification factors of sliding angle
- P 0 :
-
Supporting force on the extra pressure arch
- PA:
-
Pressure arch
- PAT:
-
Pressure-arch theory
- q :
-
Vertical loosening pressure
- q ′0 :
-
Inner edge load of the triangular-distribution load of the left tunnel
- q ″0 :
-
Inner edge load of the triangular-distribution load of the right tunnel
- q ″1 :
-
Extra loosening pressure of the external side of the left tunnel
- q ″2 :
-
Extra loosening pressure of the internal side of the left tunnel
- q ′1 :
-
Extra loosening pressure of the external side of the right tunnel
- q ′2 :
-
Extra loosening pressure of the internal side of the right tunnel
- R c :
-
Uniaxial compressive strength of surrounding rock
- R p :
-
The strength of the middle rock mass
- S i :
-
Area of the separated pressure arch
- S ″m :
-
m Area of the extra pressure arch
- T :
-
Height of twin-tunnels
- W :
-
Span of the pressure arch
- W 0 :
-
Effective load-bearing width of the middle rock pillar
- W 1 :
-
Span of the pressure arch of the left tunnel in case II
- W 2 :
-
Span of the pressure arch of the right tunnel in case II
- W m :
-
Span of the entire large pressure arch
- W ″ m :
-
m Span of the extra pressure arch
- γ :
-
Bulk density of the rock mass
- θ :
-
Sliding angle between the shear plane and the vertical plane
- θ 2 :
-
Inner sliding angle of the right tunnel (after the excavation of the left tunnel)
- θ 3 :
-
Inner sliding angle of the left tunnel (after the excavation of the right tunnel)
- φ g :
-
Calculated friction angle of the surrounding rock
References
Chapman DN, Rogers CDF, Hunt DVL (2004) Predicting the settlements above twin tunnels constructed in soft ground. Tunnelling and Underground Space Technology 19(4):378, DOI: https://doi.org/10.1016/j.tust.2004.02.008
Chen ZQ, He C, Xu GW, Ma GY, Yang WB (2019) Supporting mechanism and mechanical behavior of a double primary support method for tunnels in broken phyllite under high geo-stress: A case study. Bulletin of Engineering Geology and the Environment 78(7):5253–5267, DOI: https://doi.org/10.1007/s10064-019-01479-1
Chen ZQ, He C, Yang WB, Guo WQ, Li Z, Xu GW (2020) Impacts of geological conditions on instability causes and mechanical behavior of large-scale tunnels: A case study from the Sichuan–Tibet highway, China. Bulletin of Engineering Geology and the Environment 79(7):3667–3688, DOI: https://doi.org/10.1007/s10064-020-01796-w
Chen KH, Peng FL (2018) An improved method to calculate the vertical earth pressure for deep shield tunnel in Shanghai soil layers. Tunnelling and Underground Space Technology 75:43–66, DOI: https://doi.org/10.1016/j.tust.2018.01.027
Chen RP, Zhu J, Liu W, Tang XW (2011) Ground movement induced by parallel EPB tunnels in silty soils. Tunnelling and Underground Space Technology 26(1):163–171, DOI: https://doi.org/10.1016/j.tust.2010.09.004
Choi J-I, Lee S-W (2010) Influence of existing tunnel on mechanical behavior of new tunnel. KSCE Journal of Civil Engineering 14(5):773–783, DOI: https://doi.org/10.1007/s12205-010-1013-8
Das R, Singh PK, Kainthola A, Panthee S, Singh TN (2017) Numerical analysis of surface subsidence in asymmetric parallel highway tunnels. Journal of Rock Mechanics and Geotechnical Engineering 9(1):170–179, DOI: https://doi.org/10.1016/j.jrmge.2016.11.009
Dhar BB, Ratan S, Sharma DK, Rao PM (1981) Model study of fracture around underground excavations in weak rocks. ISRM international symposium, September 21–24, Tokyo, Japan
Divall S, Goodey RJ (2015) Twin-tunnelling-induced ground movements in clay. Proceedings of the Institution of Civil Engineers - Geotechnical Engineering 168(3):247–256, DOI: https://doi.org/10.1680/geng.14.00054
Elwood DEY, Martin CD (2016) Ground response of closely spaced twin tunnels constructed in heavily overconsolidated soils. Tunnelling and Underground Space Technology 51:226–237, DOI: https://doi.org/10.1016/j.tust.2015.10.037
Gao SM, Chen JP, Zuo CQ, Wang W (2017) Monitoring of three-dimensional additional stress and strain in shield segments of former tunnels in the construction of closely-spaced twin tunnels. Geotechnical and Geological Engineering 35(1):69–81, DOI: https://doi.org/10.1007/s10706-016-0085-8
Jia YL, Ouyang AH, Wang SY, Liang X, Wang B, Liu C, Ye F (2021) Development and application of model test system for reconstruction and expansion of existing shallow single-hole tunnel into twin-arch tunnel. Advances in Civil Engineering 2021, DOI: https://doi.org/10.1155/2021/6656165
Jiang Q, Liu XP, Yan F, Yang Y, Xu DP, Feng GL (2021) Failure performance of 3DP physical twin-tunnel model and corresponding safety factor evaluation. Rock Mechanics and Rock Engineering 54(1):109–128, DOI: https://doi.org/10.1007/s00603-020-02244-7
Jin DL, Shen X, Yuan DJ (2020) Theoretical analysis of three-dimensional ground displacements induced by shield tunneling. Applied Mathematical Modelling 79:85–105, DOI: https://doi.org/10.1016/j.apm.2019.10.014
Lei MF, Peng LM, Shi CH (2014) Calculation of the surrounding rock pressure on a shallow buried tunnel using linear and nonlinear failure criteria. Automation in Construction 37:191–195, DOI: https://doi.org/10.1016/j.autcon.2013.08.001
Li SJ, Feng XT, Li ZH, Chen BR, Zhang CQ, Zhou H (2012) In situ monitoring of rockburst nucleation and evolution in the deeply buried tunnels of Jinping II hydropower station. Engineering Geology 137–138:85–96, DOI: https://doi.org/10.1016/j.enggeo.2012.03.010
Li PF, Wang F, Fan LF, Wang HD, Ma GW (2019) Analytical scrutiny of loosening pressure on deep twin-tunnels in rock formations. Tunnelling and Underground Space Technology 83:373–380, DOI: https://doi.org/10.1016/j.tust.2018.10.007
Lin LB, Chen FQ, Lu YP, Li DY (2021a) Complex variable solutions for shallow twin tunnelling in visco-elastic geomaterial considering buoyancy effect and equivalent three-dimensional effects of tunnel faces. Applied Mathematical Modelling 91:149–185, DOI: https://doi.org/10.1016/j.apm.2020.09.038
Lin LB, Lu YP, Chen FQ, Li DY (2021b) Complex variable solutions for twin tunnelling at great depth in viscoelastic geomaterial considering the three-dimensional effects of tunnel faces. Applied Mathematical Modelling 89:919–951, DOI: https://doi.org/10.1016/j.apm.2020.07.040
Lyu HM, Shen SL, Zhou AN, Chen KL (2020) Calculation of pressure on the shallow-buried twin-tunnel in layered strata. Tunnelling and Underground Space Technology 103:103465, DOI: https://doi.org/10.1016/j.tust.2020.103465
Ma YC, Lu AZ, Zeng XT, Cai H (2020) Analytical solution for determining the plastic zones around twin circular tunnels excavated at great depth. International Journal of Rock Mechanics and Mining Sciences 136:104475, DOI: https://doi.org/10.1016/j.ijrmms.2020.104475
Ministry of Transport of PRC (2004) Code for design of road tunnels. China Communication Publisher Ltd., Beijing, China
Ministry of Transport of PRC (2018) Code for design of road tunnels. China Communication Publisher Ltd., Beijing, China
Osman AS (2010) Stability of unlined twin tunnels in undrained clay. Tunnelling and Underground Space Technology 25(3):290–296, DOI: https://doi.org/10.1016/j.tust.2010.01.004
Shivaei S, Hataf N, Pirastehfar K (2020) 3D numerical investigation of the coupled interaction behavior between mechanized twin tunnels and groundwater–A case study: Shiraz metro line 2. Tunnelling and Underground Space Technology 103:103458, DOI: https://doi.org/10.1016/j.tust.2020.103458
Soliman E, Duddeck H, Ahrens H (1993) Two and three-dimensional analysis of closely spaced double-tube tunnels. Tunnelling and Underground Space Technology 8:13–18, DOI: https://doi.org/10.1016/0886-7798(93)90130-N
Terzaghi K (1943) Theoretical soil mechanics. John Wiley & Sons, New York, NY, USA
Wang MN, Wang ZL, Zhang X, Zhao SG, Liu DG, Tong JJ (2020) Method for calculating deformation pressure of surrounding rock of deep-buried tunnels. Chinese Journal of Geotechnical Engineering 42(1):81–90 (in Chinese)
Wang Z, Yao WJ, Cai YQ, Xu B, Fu Y, Wei G (2019) Analysis of ground surface settlement induced by the construction of a large-diameter shallow-buried twin-tunnel in soft ground. Tunnelling and Underground Space Technology 83:520–532, DOI: https://doi.org/10.1016/j.tust.2018.09.021
Wu L, Zhang X, Zhang Z, Sun W (2020) 3D discrete element method modelling of tunnel construction impact on an adjacent tunnel. KSCE Journal of Civil Engineering 24(2):657–669, DOI: https://doi.org/10.1007/s12205-020-2054-2
Xia X, Li HB, Li JC, Liu B, Yu C (2013) A case study on rock damage prediction and control method for underground tunnels subjected to adjacent excavation blasting. Tunnelling and Underground Space Technology 35:1–7, DOI: https://doi.org/10.1016/j.tust.2012.11.010
Xu GW, He C, Wang J, Zhang JB (2020) Study on the damage evolution of secondary tunnel lining in layered rock stratum. Bulletin of Engineering Geology and the Environment 79, DOI: https://doi.org/10.1007/s10064-020-01775-1
Zheng HB, Li PF, Ma GW (2021) Stability analysis of the middle soil pillar for asymmetric parallel tunnels by using model testing and numerical simulations. Tunnelling and Underground Space Technology 108:103686, DOI: https://doi.org/10.1016/j.tust.2020.103686
Acknowledgments
This research was funded by the High Speed Railway and Natural Science United Foundation of China (U2034205), the Transportation Science and Technology Project of Sichuan Province, China (2019ZL09).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wu, F., He, C., Kou, H. et al. Discussion on Reasonable Clear Spacing of Twin-Tunnels in Weak Surrounding Rock: Analytical Solution and Numerical Analysis. KSCE J Civ Eng 26, 2428–2442 (2022). https://doi.org/10.1007/s12205-022-0898-3
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12205-022-0898-3