Ghaboussi & Ranken (1977)Ghaboussi, J., & Ranken, R.E. (1977). Interaction between two parallel tunnels. International Journal for Numerical and Analytical Methods in Geomechanics, 1(1), 75-103.
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Linear elastic K0 = 0.5 |
D = (?) m H / D = 1.5; 5.5 L / D = 0.25 to 1.0 |
Numerical 2D Excavation in full section |
Increase of forces in the lining in the zone around the pillar springline in both tunnels; Interaction more relevant for deep tunnels; Suggest no interaction for L / D > 2.0 |
Soliman et al. (1993)Soliman, E., Duddeck, H., & Ahrens, H. (1993). Two- and three-dimensional analysis of closely spaced double-tube tunnels. Tunnelling and Underground Space Technology, 8(1), 13-18. http://dx.doi.org/10.1016/0886-7798(93)90130-N. http://dx.doi.org/10.1016/0886-7798(93)9...
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Linear elastic Stiffness of the ground varied K0 = 0.5 |
D = 10 m H / D = 3.5 L / D = 0.25; 0.5 |
Numerical 2D / 3D Excavation in full section |
Increase of forces in the lining of both tunnels; Bending moments are more affected by the 2T excavation but no trend was observed with the increase of stiffness of the ground |
Adachi et al. (1993)Adachi, T., Kimura, M., & Osada, H. (1993). Interaction between multi-tunnels under construction. In Proceedings of the 11th Southeast Asian Geotechnical Conference (pp. 51-60). Singapore.
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Sand c’ = 0 kPa; ϕ’ = 30° K0 ≈ 0.7 |
D = 130 mm H / D = 1.0 to 4.5 L / D = 0.5 to 2.0 |
Small scale 1g model Excavation in full section by reducing the diameter |
Interaction between tunnels increases with the increase of the overburden. Interaction still occurs for L / D = 2.0 |
Kim et al. (1998)Kim, S.H., Burd, H.J., & Milligan, G.W.E. (1998). Model testing of closely spaced tunnels in clay. Geotechnique, 48(3), 375-388. http://dx.doi.org/10.1680/geot.1998.48.3.375. http://dx.doi.org/10.1680/geot.1998.48.3...
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Speswhite kaolin clay Su ≈ 20 kPa K0 ≈ 0.5 |
D = 70 mm H / D = 3.2 L / D = 0.4; 1.0 |
Small scale 1g model Simulation of an EPB-TBM |
Interaction between tunnels was observed with an increase of the bending moments on the 1T at the pillar springline |
Ng et al. (2004)Ng, C.W.W., Lee, K.M., & Tang, D.K.W. (2004). Three-dimensional numerical investigations of new Austrian tunnelling method (NATM) twin tunnel interactions. Canadian Geotechnical Journal, 41(3), 523-539. http://dx.doi.org/10.1139/T04-008. http://dx.doi.org/10.1139/T04-008...
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Drucker-Prager (equivalent Mohr-Coulomb: c’ = 5 kPa; ϕ’ = 22°) K0 = 1.5 |
D ≈ 8.6 m (Oval) H / D = 2.3 L / D = 1.0 |
Numerical 3D NATM modelling with 2 side-drifts and variable lagged distance |
Increase of the lining forces (bending and hoop) of the 1T with the increase of the lagged distance; The lining forces on both tunnels are minimum for a zero lagged distance |
Hage Chehade & Shahrour (2008)Hage Chehade, F., & Shahrour, I. (2008). Numerical analysis of the interaction between twin-tunnels: influence of the relative position and construction procedure. Tunnelling and Underground Space Technology, 23(2), 210-214. http://dx.doi.org/10.1016/j.tust.2007.03.004. http://dx.doi.org/10.1016/j.tust.2007.03...
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Mohr–Coulomb (c’ = 3 kPa; ϕ’ = 33°) K0 = 0.5 |
D = (?) m H / D = 2.5 L / D =1.0 to 4.0 |
Numerical 2D (β = 0.5) Excavation in full section |
No interaction was detected on the hoop forces while a residual increase was observed on the bending moments for L / D < 2.0 |
Liu et al. (2008)Liu, H.Y., Small, J.C., & Carter, J.P. (2008). Full 3D modelling for effects of tunnelling on existing support systems in the Sydney region. Tunnelling and Underground Space Technology, 23(4), 399-420. http://dx.doi.org/10.1016/j.tust.2007.06.009. http://dx.doi.org/10.1016/j.tust.2007.06...
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Mohr–Coulomb (c’ = 500 kPa; ϕ’ = 38°) K0 varies with depth and direction |
D ≈ 10 m (Oval) H / D = 1.5; 3.0 L / D = 1.0; 2.0 |
Numerical 3D NATM modelling with excavation in full section |
Stresses in the 1T lining increase after the 2T excavation; Interaction increases with the decrease of the pillar width |
Hossaini et al. (2012)Hossaini, S.M., Shaban, M., & Talebinejad, A. (2012). Relationship between twin tunnels distance and surface subsidence in soft ground of Tabriz Metro, Iran. In N. Aziz & B. Kininmonth (Eds.), 12th Coal Operators' Conference (pp. 163-168). University of Wollongong. (Section 1) |
Mohr–Coulomb (c’ = 0 kPa; ϕ’ = 35°) K0 = 0.43 |
D = 6.9 m H / D = 1.9 L / D = 0.5 to 1.5 |
Numerical 3D Simulation of an EPB-TBM |
Increase of forces (bending and hoop) in the lining of 1T after the 2T excavation; Minimum interaction for L / D > 1.5 |
Do et al. (2014a)Do, N., Dias, D., Oreste, P., & Djeran-Maigre, I. (2014a). 2D numerical investigations of twin tunnel interaction. Geomechanics and Engineering, 6(3), 263-275. http://dx.doi.org/10.12989/gae.2014.6.3.263. http://dx.doi.org/10.12989/gae.2014.6.3....
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Mohr–Coulomb (c’ = 0 kPa; ϕ’ = 37°) K0 = 0.5 |
D = 94 m H / D = 2.1 L / D = 0.25 to 3 |
Numerical 2D (β = 0.3) Excavation in full section |
Relevant increase of the hoop forces on both tunnels (mainly on 1T) while only a slight variation observed on the bending moments; Interaction is relevant for L / D < 1.0 and more relevant if in a jointed lining; Negligible interaction for L / D > 2.0 |
Do et al. (2015)Do, N., Dias, D., & Oreste, P. (2015). 3D numerical investigation on the interaction between mechanized twin tunnels in soft ground. Environmental Earth Sciences, 73(5), 2101-2113. http://dx.doi.org/10.1007/s12665-014-3561-6. http://dx.doi.org/10.1007/s12665-014-356...
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CY soil model (c’ = 0 kPa; ϕ’ = 37°) K0 = 0.5 |
D = 9.4 m H / D = 2.1 L / D = 0.25 to 2 |
Numerical 3D Simulation of an EPB-TBM considering a lagged distance of 10D
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Relevant increase of the lining forces (bending and hoop) on the 1T; Slight decrease of the lining forces (bending and hoop) on the 2T; Negligible interaction for L / D > 1.0 |
Do et al. (2016)Do, N., Dias, D., & Oreste, P. (2016). 3D numerical investigation of mechanized twin tunnels in soft ground–Influence of lagging distance between two tunnel faces. Engineering Structures, 109, 117-125. http://dx.doi.org/10.1016/j.engstruct.2015.11.053. http://dx.doi.org/10.1016/j.engstruct.20...
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CY soil model (c’ = 0 kPa; ϕ’ = 37°) K0 = 0.5 |
D = 9.4 m H / D = 2.1 L / D = 0.25 |
Numerical 3D Simulation of an EPB-TBM considering variable lagged distance |
Increase of the hoop forces of both tunnels with the lagged distance, while the opposite occurs for the bending moments; The lining forces on both tunnels are minimum for a zero lagged distance |
Shivaei et al. (2020)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. https://doi.org/https://doi.org/10.1016/j.tust.2020.103458
https://doi.org/https://doi.org/10.1016/...
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Modified Cam-Clay (M = 1.14; κ = 0.011; λ = 0.048) K0 = 0.55 |
D = 6.9 m H / D = 2.75 L / D = 1.2 |
Numerical 3D (coupled-consolidation) Simulation of an EPB-TBM Consolidation of the soil after the complete excavation of each tunnel |
Increase of the lining permeability from impermeable to fully permeable originates an increase of the lining forces (bending and hoop) on both tunnels, which is more relevant on the 1T on the pillar side; |
Cheng et al. (2020)Cheng, W., Li, G., Ong, D.E.L., Chen, S., & Ni, J.C. (2020). Modelling liner forces response to very close-proximity tunnelling in soft alluvial deposits. Tunnelling and Underground Space Technology, 103, 103455. https://doi.org/https://doi.org/10.1016/j.tust.2020.103455
https://doi.org/https://doi.org/10.1016/...
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Mohr–Coulomb (c’ = 5 kPa; ϕ’ = 33.3°) K0 = 0.7 |
D = 6.1 m H / D = 3.5 (1T) L / D = 0.4 (2T above 1T) |
Numerical 2D (β = 0.1) Excavation in full section Piggyback configuration |
Good agreement of the hoop forces between the numerical predictions and the field measurement |