A matrix-form complex variable method for multiple non-circular tunnels in layered media
•An exact matrix-form solution is proposed for analyzing multiple non-circular tunnels in layered media.•Generalized complex variable theory, conformal mapping and fast Fourier transform are used in derivation.•The proposed solution avoids complicated coefficient determinations and iterative algorit...
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| Published in: | Applied mathematical modelling Vol. 131; pp. 570 - 595 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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01.07.2024
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| ISSN: | 0307-904X |
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| Abstract | •An exact matrix-form solution is proposed for analyzing multiple non-circular tunnels in layered media.•Generalized complex variable theory, conformal mapping and fast Fourier transform are used in derivation.•The proposed solution avoids complicated coefficient determinations and iterative algorithm.•Effects of elastic properties, tunnels' position, equivalent layer and the layer thickness surrounding tunnels are discussed.
This paper presents a matrix-form complex variable method that can predict the stress and displacement field around multiple tunnels in layered media. The proposed matrix-form method avoids complicated coefficient determinations and iterative algorithm, which effectively improves the computation efficiency. Firstly, the expressions for the stress and displacement field are given under the generalized complex variable theory. The conformal mapping technique and fast Fourier transform algorithm are used to formulate the matrix-form expressions of boundary conditions. Considering the boundary conditions of the tunnels and soil interfaces, the global matrix solution for multiple tunnels in layered media are obtained by assembling the matrix solutions of all single layers. The present theory is verified by comparison with the existing literature, finite element analysis and field data in engineering practices, and several numerical examples are given to reveal the effects of elastic properties, tunnels' position, equivalent layer and the layer thickness surrounding tunnels. |
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| AbstractList | •An exact matrix-form solution is proposed for analyzing multiple non-circular tunnels in layered media.•Generalized complex variable theory, conformal mapping and fast Fourier transform are used in derivation.•The proposed solution avoids complicated coefficient determinations and iterative algorithm.•Effects of elastic properties, tunnels' position, equivalent layer and the layer thickness surrounding tunnels are discussed.
This paper presents a matrix-form complex variable method that can predict the stress and displacement field around multiple tunnels in layered media. The proposed matrix-form method avoids complicated coefficient determinations and iterative algorithm, which effectively improves the computation efficiency. Firstly, the expressions for the stress and displacement field are given under the generalized complex variable theory. The conformal mapping technique and fast Fourier transform algorithm are used to formulate the matrix-form expressions of boundary conditions. Considering the boundary conditions of the tunnels and soil interfaces, the global matrix solution for multiple tunnels in layered media are obtained by assembling the matrix solutions of all single layers. The present theory is verified by comparison with the existing literature, finite element analysis and field data in engineering practices, and several numerical examples are given to reveal the effects of elastic properties, tunnels' position, equivalent layer and the layer thickness surrounding tunnels. |
| Author | Ai, Zhi Yong Ye, Zi Kun |
| Author_xml | – sequence: 1 givenname: Zi Kun orcidid: 0000-0001-9691-7726 surname: Ye fullname: Ye, Zi Kun – sequence: 2 givenname: Zhi Yong orcidid: 0000-0001-5552-3683 surname: Ai fullname: Ai, Zhi Yong email: zhiyongai@tongji.edu.cn |
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| CitedBy_id | crossref_primary_10_1016_j_compgeo_2025_107538 crossref_primary_10_3390_buildings15173027 crossref_primary_10_1002_nag_4008 crossref_primary_10_3390_buildings14061760 |
| Cites_doi | 10.1680/geot.2008.58.6.513 10.1016/j.apm.2022.12.011 10.1142/S0219876210002428 10.3208/sandf.39.3_37 10.2140/jomms.2012.7.963 10.1139/t05-025 10.1016/j.compgeo.2023.105797 10.1002/nag.3244 10.1016/j.compgeo.2020.103891 10.1016/S1365-1609(02)00079-5 10.1016/j.apm.2020.12.012 10.1016/j.enganabound.2005.12.005 10.1016/j.apm.2020.09.038 10.1016/j.tust.2016.07.009 10.1002/nag.636 10.1680/geot.12.P.126 10.1016/S0894-9166(16)30004-0 10.1002/(SICI)1096-9853(199702)21:2<77::AID-NAG857>3.0.CO;2-M 10.1016/j.tust.2020.103446 10.1002/nag.246 10.1002/nag.2764 10.1002/nag.2375 10.1016/j.compgeo.2023.105520 10.1680/geot.1993.43.2.315 10.1063/1.1697875 10.1016/j.ijrmms.2016.08.004 10.1680/geot.1987.37.3.301 10.2307/1213774 10.1016/S0886-7798(01)00068-2 10.1061/(ASCE)1090-0241(1998)124:9(846) 10.1007/s00603-019-01844-2 10.1061/(ASCE)EM.1943-7889.0002093 10.1139/T08-026 10.1016/j.compgeo.2019.103385 10.1680/geot.1998.48.5.709 10.1016/S0020-7683(97)00194-7 10.1002/nag.2322 |
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| Keywords | Matrix-form solution Generalized complex variable theory Stress and displacement fields Multiple non-circular tunnels Fourier series fitting |
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| References | Ling (bib0009) 1948; 19 Verruijt (bib0017) 1997; 21 Exadaktylos, Stavropoulou (bib0042) 2002; 39 Frigo, Johnson (bib0043) 1998; 3 Bobet, Fernandez, Huo, Ramirez (bib0044) 2008; 45 Chou, Bobet (bib0023) 2002; 17 Wang, Wu, Jiang, Song (bib0036) 2018; 25 Peck (bib0001) 1969 K. Komiya, K. Soga, H. Akagi, T. Hagiwara, M.D. Bolton, 1999. Finite element modelling of excavation and advancement processes of a shield tunnelling machine, 39 (3) (1999) 37–52. Jeffery (bib0007) 1921; 221 Verruijt (bib0018) 1998; 35 Strack, Verruijt (bib0019) 2002; 26 Fang, Zhang, Fang, Wen (bib0029) 2021; 129 Lu, Zeng, Xu (bib0025) 2016; 89 Cao, Zhang, Fang (bib0027) 2020; 102 Fu, Yang, Yan, Abbas (bib0035) 2015; 39 Fang, Zhang, Huang, Fang, Zhou, Cao (bib0030) 2023; 116 Zhou, Chen, Liu, Miao (bib0003) 2020; 43 Wang, Gao, Wu, Jiang (bib0037) 2020; 120 Fang, Guo, Grasmick, Mooney (bib0045) 2016; 60 Ng, Lee (bib0005) 2005; 42 Mair, Taylor, Bracegirdle (bib0002) 1993; 43 Wongsaroj, Soga, Mair (bib0006) 2013; 63 Pinto, Whittle (bib0020) 2014; 140 Mindlin (bib0008) 1948; 5 Chen (bib0015) 2013; 7 Loganathan, Poulos (bib0012) 1998; 124 Ye, Ai (bib0031) 2023; 164 Pinto, Zymnis, Whittle (bib0021) 2014; 140 Qu, Chen (bib0016) 2015; 28 Verruijt, Strack (bib0022) 2008; 58 . Zeng, Wang, Jiang (bib0040) 2023; 160 Verruijt, Booker (bib0011) 1998; 48 Dejoie, Mogilevskaya, Crouch (bib0013) 2006; 30 Lin, Chen, Lu, Li (bib0038) 2021; 91 Muskhelishvili (bib0028) 1963 Lu, Zeng, Zhang (bib0033) 2021; 45 Lin, Lu, Chen, Li (bib0039) 2021; 93 Hirai (bib0026) 2008; 32 Tong, Zhou, Shen, Liu (bib0034) 2022; 148 Zeng, Cai, Lu (bib0032) 2019; 52 Lekhnitskii (bib0041) 1968 Sagaseta (bib0010) 1987; 37 Chen, Wang (bib0014) 2010; 7 Fang, Song, Zhang (bib0024) 2015; 39 Lin (10.1016/j.apm.2024.04.033_bib0039) 2021; 93 Ling (10.1016/j.apm.2024.04.033_bib0009) 1948; 19 Lu (10.1016/j.apm.2024.04.033_bib0033) 2021; 45 Qu (10.1016/j.apm.2024.04.033_bib0016) 2015; 28 Pinto (10.1016/j.apm.2024.04.033_bib0020) 2014; 140 Mair (10.1016/j.apm.2024.04.033_bib0002) 1993; 43 Peck (10.1016/j.apm.2024.04.033_bib0001) 1969 Lekhnitskii (10.1016/j.apm.2024.04.033_bib0041) 1968 Exadaktylos (10.1016/j.apm.2024.04.033_bib0042) 2002; 39 Fang (10.1016/j.apm.2024.04.033_bib0045) 2016; 60 Tong (10.1016/j.apm.2024.04.033_bib0034) 2022; 148 Chou (10.1016/j.apm.2024.04.033_bib0023) 2002; 17 Ye (10.1016/j.apm.2024.04.033_bib0031) 2023; 164 Pinto (10.1016/j.apm.2024.04.033_bib0021) 2014; 140 Wang (10.1016/j.apm.2024.04.033_bib0037) 2020; 120 Verruijt (10.1016/j.apm.2024.04.033_bib0018) 1998; 35 Wang (10.1016/j.apm.2024.04.033_bib0036) 2018; 25 Verruijt (10.1016/j.apm.2024.04.033_bib0022) 2008; 58 cr-split#-10.1016/j.apm.2024.04.033_bib0004.1 Lu (10.1016/j.apm.2024.04.033_bib0025) 2016; 89 Lin (10.1016/j.apm.2024.04.033_bib0038) 2021; 91 cr-split#-10.1016/j.apm.2024.04.033_bib0004.2 Hirai (10.1016/j.apm.2024.04.033_bib0026) 2008; 32 Sagaseta (10.1016/j.apm.2024.04.033_bib0010) 1987; 37 Cao (10.1016/j.apm.2024.04.033_bib0027) 2020; 102 Frigo (10.1016/j.apm.2024.04.033_bib0043) 1998; 3 Jeffery (10.1016/j.apm.2024.04.033_bib0007) 1921; 221 Muskhelishvili (10.1016/j.apm.2024.04.033_bib0028) 1963 Verruijt (10.1016/j.apm.2024.04.033_bib0017) 1997; 21 Fang (10.1016/j.apm.2024.04.033_bib0029) 2021; 129 Wongsaroj (10.1016/j.apm.2024.04.033_bib0006) 2013; 63 Dejoie (10.1016/j.apm.2024.04.033_bib0013) 2006; 30 Mindlin (10.1016/j.apm.2024.04.033_bib0008) 1948; 5 Zeng (10.1016/j.apm.2024.04.033_bib0032) 2019; 52 Zhou (10.1016/j.apm.2024.04.033_bib0003) 2020; 43 Fang (10.1016/j.apm.2024.04.033_bib0024) 2015; 39 Fang (10.1016/j.apm.2024.04.033_bib0030) 2023; 116 Zeng (10.1016/j.apm.2024.04.033_bib0040) 2023; 160 Strack (10.1016/j.apm.2024.04.033_bib0019) 2002; 26 Fu (10.1016/j.apm.2024.04.033_bib0035) 2015; 39 Chen (10.1016/j.apm.2024.04.033_bib0014) 2010; 7 Ng (10.1016/j.apm.2024.04.033_bib0005) 2005; 42 Loganathan (10.1016/j.apm.2024.04.033_bib0012) 1998; 124 Verruijt (10.1016/j.apm.2024.04.033_bib0011) 1998; 48 Chen (10.1016/j.apm.2024.04.033_bib0015) 2013; 7 Bobet (10.1016/j.apm.2024.04.033_bib0044) 2008; 45 |
| References_xml | – volume: 7 start-page: 963 year: 2013 end-page: 981 ident: bib0015 article-title: Boundary integral equation for notch problems in an elastic half-plane based on Green's function method publication-title: J. Mech. Mater. Struct. – volume: 42 start-page: 1015 year: 2005 end-page: 1029 ident: bib0005 article-title: Three-dimensional ground settlements and stress-transfer mechanisms due to open-face tunnelling publication-title: Can. Geotech. J. – volume: 3 start-page: 1381 year: 1998 end-page: 1384 ident: bib0043 article-title: FFTW: an adaptive software architecture for the FFT publication-title: Proc. IEEE Int. Conf. Acoust. Speech Signal Process. – volume: 43 start-page: 315 year: 1993 end-page: 320 ident: bib0002 article-title: Subsurface settlement profiles above tunnels in clays publication-title: Géotechnique – volume: 124 start-page: 846 year: 1998 end-page: 856 ident: bib0012 article-title: Analytical prediction for tunneling-induced ground movements in clays publication-title: J. Geotech. Geoenviron. Eng. – volume: 37 start-page: 301 year: 1987 end-page: 320 ident: bib0010 article-title: Analysis of undrained soil deformation due to ground loss publication-title: Géotechnique – volume: 39 start-page: 1821 year: 2015 end-page: 1835 ident: bib0024 article-title: Complex variable analysis for stress distribution of an underwater tunnel in an elastic half plane publication-title: Int. J. Numer. Anal. Methods Geomech. – volume: 58 start-page: 513 year: 2008 end-page: 515 ident: bib0022 article-title: Buoyancy of tunnels in soft soils publication-title: Géotechnique – volume: 45 start-page: 1833 year: 2021 end-page: 1853 ident: bib0033 article-title: A complex variable solution for a non-circular tunnel in an elastic half-plane publication-title: Int. J. Numer. Anal. Methods Geomech. – volume: 129 year: 2021 ident: bib0029 article-title: A generalized complex variable method for multiple tunnels at great depth considering the interaction between linings and surrounding rock publication-title: Comput. Geotech. – volume: 148 year: 2022 ident: bib0034 article-title: A complex variable solution for shallow rectangular tunnel in semi-infinite plane publication-title: J. Eng. Mech. – start-page: 225 year: 1969 end-page: 290 ident: bib0001 article-title: Deep excavations and tunneling in soft ground publication-title: Proceedings of the 7th International Conference on Soil Mechanics and Foundation Engineering – volume: 5 start-page: 56 year: 1948 end-page: 67 ident: bib0008 article-title: Stress distribution around a hole near the edge of a plate under tension publication-title: Proc. Soc. Exp. Stress Anal. – volume: 26 start-page: 1235 year: 2002 end-page: 1252 ident: bib0019 article-title: A complex variable solution for a deforming buoyant tunnel in a heavy elastic half-plane publication-title: Int. J. Numer. Anal. Methods Geomech. – volume: 19 start-page: 77 year: 1948 end-page: 82 ident: bib0009 article-title: On the stresses in a plate containing two circular holes publication-title: J. Appl. Phys. – volume: 48 start-page: 709 year: 1998 end-page: 713 ident: bib0011 article-title: Surface settlements due to deformation of a tunnel in an elastic half plane publication-title: Géotechnique – volume: 89 start-page: 34 year: 2016 end-page: 42 ident: bib0025 article-title: Solution for a circular cavity in an elastic half plane under gravity and arbitrary lateral stress publication-title: Int. J. Rock Mech. Min. Sci. – volume: 140 year: 2014 ident: bib0020 article-title: Ground movements due to shallow tunnels in soft ground. I: analytical solutions publication-title: J. Geotech. Geoenviron. Eng. – volume: 32 start-page: 523 year: 2008 end-page: 557 ident: bib0026 article-title: Settlements and stresses of multi-layered grounds and improved grounds by equivalent elastic method publication-title: Int. J. Numer. Anal. Methods Geomech. – volume: 39 start-page: 524 year: 2015 end-page: 538 ident: bib0035 article-title: An analytical solution for deforming twin-parallel tunnels in an elastic half plane publication-title: Int. J. Numer. Anal. Methods Geomech. – volume: 28 start-page: 626 year: 2015 end-page: 638 ident: bib0016 article-title: Fast multipole singular boundary method for large-scale plane elasticity problems publication-title: Acta Mech. Solida Sin. – volume: 91 start-page: 149 year: 2021 end-page: 185 ident: bib0038 article-title: Complex variable solutions for shallow twin tunnelling in visco-elastic geomaterial considering buoyancy effect and equivalent three-dimensional effects of tunnel faces publication-title: Appl. Math. Model. – volume: 17 start-page: 3 year: 2002 end-page: 19 ident: bib0023 article-title: Predictions of ground deformations in shallow tunnels in clay publication-title: Tunn. Undergr. Space Technol. – volume: 116 start-page: 749 year: 2023 end-page: 762 ident: bib0030 article-title: Analytical method for mechanical analysis of multiple shallow tunnels with concrete linings publication-title: Appl. Math. Model. – volume: 120 year: 2020 ident: bib0037 article-title: Analytical study on interaction between existing and new tunnels parallel excavated in semi-infinite viscoelastic ground publication-title: Comput. Geotech. – volume: 30 start-page: 450 year: 2006 end-page: 464 ident: bib0013 article-title: A boundary integral method for multiple circular holes in an elastic half-plane publication-title: Eng. Anal. Bound. Elem. – volume: 35 start-page: 2795 year: 1998 end-page: 2804 ident: bib0018 article-title: Deformations of an elastic half plane with a circular cavity publication-title: Int. J. Solids Struct. – year: 1963 ident: bib0028 article-title: Some Basic Problems of the Mathematical Theory of Elasticity – volume: 160 year: 2023 ident: bib0040 article-title: Analytical stress and displacement of twin noncircular tunnels in elastic semi-infinite ground publication-title: Comput. Geotech. – reference: . – volume: 39 start-page: 905 year: 2002 end-page: 916 ident: bib0042 article-title: A closed form elastic solution for stresses and displacements around tunnels publication-title: Int. J. Rock Mech. Min. Sci. – volume: 43 start-page: 315 year: 2020 end-page: 320 ident: bib0003 article-title: Theoretical prediction model for deformations caused by construction of new tunnels undercrossing existing tunnels based on the equivalent layered method publication-title: Comput. Geotech. – volume: 60 start-page: 80 year: 2016 end-page: 95 ident: bib0045 article-title: The effect of external water pressure on the liner behavior of large cross-section tunnels publication-title: Tunn. Undergr. Space Technol. – year: 1968 ident: bib0041 article-title: Anisotropic Plates – volume: 7 start-page: 539 year: 2010 end-page: 557 ident: bib0014 article-title: Multiple and periodic notch problems of elastic half-plane by using BIE based on Green's function method publication-title: Int. J. Comput. Methods – volume: 52 start-page: 4509 year: 2019 end-page: 4526 ident: bib0032 article-title: An analytical solution for an arbitrary cavity in an elastic half-plane publication-title: Rock Mech. Rock Eng. – volume: 21 start-page: 77 year: 1997 end-page: 89 ident: bib0017 article-title: A complex variable solution for a deforming circular tunnel in an elastic half-plane publication-title: Int. J. Numer. Anal. Methods Geomech. – reference: K. Komiya, K. Soga, H. Akagi, T. Hagiwara, M.D. Bolton, 1999. Finite element modelling of excavation and advancement processes of a shield tunnelling machine, 39 (3) (1999) 37–52. – volume: 45 start-page: 923 year: 2008 end-page: 938 ident: bib0044 article-title: A practical iterative procedure to estimate seismic-induced deformations of shallow rectangular structures publication-title: Can. Geotech. J. – volume: 102 year: 2020 ident: bib0027 article-title: Semi-analytical prediction for tunnelling-induced ground movements in multi-layered clayey soils publication-title: Tunn. Undergr. Space Technol. – volume: 164 year: 2023 ident: bib0031 article-title: A novel complex variable solution for the stress and displacement fields around a shallow non-circular tunnel publication-title: Comput. Geotech. – volume: 93 start-page: 485 year: 2021 end-page: 508 ident: bib0039 article-title: Analytic study of stress and displacement for shallow twin tunnels subjected to surcharge loads publication-title: Appl. Math. Model. – volume: 221 start-page: 265 year: 1921 end-page: 293 ident: bib0007 article-title: Plane stress and plane strain in bipolar coordinates publication-title: Philos. Trans. R. Soc. London, Ser. A – volume: 63 start-page: 1103 year: 2013 end-page: 1115 ident: bib0006 article-title: Tunnelling-induced consolidation settlements in London Clay publication-title: Géotechnique – volume: 140 year: 2014 ident: bib0021 article-title: Ground movements due to shallow tunnels in soft ground. II: analytical interpretation and prediction publication-title: J. Geotech. Geoenviron. Eng. – volume: 25 start-page: 809 year: 2018 end-page: 828 ident: bib0036 article-title: Analytical stress and displacement due to twin tunneling in an elastic semi-infinite ground subjected to surcharge loads publication-title: Int. J. Numer. Anal. Methods Geomech. – volume: 58 start-page: 513 issue: 6 year: 2008 ident: 10.1016/j.apm.2024.04.033_bib0022 article-title: Buoyancy of tunnels in soft soils publication-title: Géotechnique doi: 10.1680/geot.2008.58.6.513 – volume: 116 start-page: 749 year: 2023 ident: 10.1016/j.apm.2024.04.033_bib0030 article-title: Analytical method for mechanical analysis of multiple shallow tunnels with concrete linings publication-title: Appl. Math. Model. doi: 10.1016/j.apm.2022.12.011 – volume: 3 start-page: 1381 year: 1998 ident: 10.1016/j.apm.2024.04.033_bib0043 article-title: FFTW: an adaptive software architecture for the FFT publication-title: Proc. IEEE Int. Conf. Acoust. Speech Signal Process. – volume: 7 start-page: 539 issue: 4 year: 2010 ident: 10.1016/j.apm.2024.04.033_bib0014 article-title: Multiple and periodic notch problems of elastic half-plane by using BIE based on Green's function method publication-title: Int. J. Comput. Methods doi: 10.1142/S0219876210002428 – ident: #cr-split#-10.1016/j.apm.2024.04.033_bib0004.1 doi: 10.3208/sandf.39.3_37 – volume: 7 start-page: 963 issue: 10 year: 2013 ident: 10.1016/j.apm.2024.04.033_bib0015 article-title: Boundary integral equation for notch problems in an elastic half-plane based on Green's function method publication-title: J. Mech. Mater. Struct. doi: 10.2140/jomms.2012.7.963 – volume: 42 start-page: 1015 issue: 4 year: 2005 ident: 10.1016/j.apm.2024.04.033_bib0005 article-title: Three-dimensional ground settlements and stress-transfer mechanisms due to open-face tunnelling publication-title: Can. Geotech. J. doi: 10.1139/t05-025 – volume: 164 year: 2023 ident: 10.1016/j.apm.2024.04.033_bib0031 article-title: A novel complex variable solution for the stress and displacement fields around a shallow non-circular tunnel publication-title: Comput. Geotech. doi: 10.1016/j.compgeo.2023.105797 – volume: 5 start-page: 56 issue: 2 year: 1948 ident: 10.1016/j.apm.2024.04.033_bib0008 article-title: Stress distribution around a hole near the edge of a plate under tension publication-title: Proc. Soc. Exp. Stress Anal. – volume: 45 start-page: 1833 issue: 12 year: 2021 ident: 10.1016/j.apm.2024.04.033_bib0033 article-title: A complex variable solution for a non-circular tunnel in an elastic half-plane publication-title: Int. J. Numer. Anal. Methods Geomech. doi: 10.1002/nag.3244 – volume: 129 year: 2021 ident: 10.1016/j.apm.2024.04.033_bib0029 article-title: A generalized complex variable method for multiple tunnels at great depth considering the interaction between linings and surrounding rock publication-title: Comput. Geotech. doi: 10.1016/j.compgeo.2020.103891 – volume: 39 start-page: 905 issue: 7 year: 2002 ident: 10.1016/j.apm.2024.04.033_bib0042 article-title: A closed form elastic solution for stresses and displacements around tunnels publication-title: Int. J. Rock Mech. Min. Sci. doi: 10.1016/S1365-1609(02)00079-5 – volume: 140 issue: 4 year: 2014 ident: 10.1016/j.apm.2024.04.033_bib0020 article-title: Ground movements due to shallow tunnels in soft ground. I: analytical solutions publication-title: J. Geotech. Geoenviron. Eng. – volume: 93 start-page: 485 issue: 2 year: 2021 ident: 10.1016/j.apm.2024.04.033_bib0039 article-title: Analytic study of stress and displacement for shallow twin tunnels subjected to surcharge loads publication-title: Appl. Math. Model. doi: 10.1016/j.apm.2020.12.012 – volume: 30 start-page: 450 issue: 6 year: 2006 ident: 10.1016/j.apm.2024.04.033_bib0013 article-title: A boundary integral method for multiple circular holes in an elastic half-plane publication-title: Eng. Anal. Bound. Elem. doi: 10.1016/j.enganabound.2005.12.005 – volume: 91 start-page: 149 year: 2021 ident: 10.1016/j.apm.2024.04.033_bib0038 article-title: Complex variable solutions for shallow twin tunnelling in visco-elastic geomaterial considering buoyancy effect and equivalent three-dimensional effects of tunnel faces publication-title: Appl. Math. Model. doi: 10.1016/j.apm.2020.09.038 – year: 1968 ident: 10.1016/j.apm.2024.04.033_bib0041 – volume: 60 start-page: 80 year: 2016 ident: 10.1016/j.apm.2024.04.033_bib0045 article-title: The effect of external water pressure on the liner behavior of large cross-section tunnels publication-title: Tunn. Undergr. Space Technol. doi: 10.1016/j.tust.2016.07.009 – volume: 32 start-page: 523 year: 2008 ident: 10.1016/j.apm.2024.04.033_bib0026 article-title: Settlements and stresses of multi-layered grounds and improved grounds by equivalent elastic method publication-title: Int. J. Numer. Anal. Methods Geomech. doi: 10.1002/nag.636 – volume: 63 start-page: 1103 issue: 13 year: 2013 ident: 10.1016/j.apm.2024.04.033_bib0006 article-title: Tunnelling-induced consolidation settlements in London Clay publication-title: Géotechnique doi: 10.1680/geot.12.P.126 – volume: 28 start-page: 626 issue: 6 year: 2015 ident: 10.1016/j.apm.2024.04.033_bib0016 article-title: Fast multipole singular boundary method for large-scale plane elasticity problems publication-title: Acta Mech. Solida Sin. doi: 10.1016/S0894-9166(16)30004-0 – volume: 221 start-page: 265 issue: 582–593 year: 1921 ident: 10.1016/j.apm.2024.04.033_bib0007 article-title: Plane stress and plane strain in bipolar coordinates publication-title: Philos. Trans. R. Soc. London, Ser. A – volume: 21 start-page: 77 issue: 1 year: 1997 ident: 10.1016/j.apm.2024.04.033_bib0017 article-title: A complex variable solution for a deforming circular tunnel in an elastic half-plane publication-title: Int. J. Numer. Anal. Methods Geomech. doi: 10.1002/(SICI)1096-9853(199702)21:2<77::AID-NAG857>3.0.CO;2-M – start-page: 225 year: 1969 ident: 10.1016/j.apm.2024.04.033_bib0001 article-title: Deep excavations and tunneling in soft ground – volume: 102 year: 2020 ident: 10.1016/j.apm.2024.04.033_bib0027 article-title: Semi-analytical prediction for tunnelling-induced ground movements in multi-layered clayey soils publication-title: Tunn. Undergr. Space Technol. doi: 10.1016/j.tust.2020.103446 – volume: 26 start-page: 1235 issue: 12 year: 2002 ident: 10.1016/j.apm.2024.04.033_bib0019 article-title: A complex variable solution for a deforming buoyant tunnel in a heavy elastic half-plane publication-title: Int. J. Numer. Anal. Methods Geomech. doi: 10.1002/nag.246 – volume: 25 start-page: 809 year: 2018 ident: 10.1016/j.apm.2024.04.033_bib0036 article-title: Analytical stress and displacement due to twin tunneling in an elastic semi-infinite ground subjected to surcharge loads publication-title: Int. J. Numer. Anal. Methods Geomech. doi: 10.1002/nag.2764 – volume: 39 start-page: 1821 issue: 16 year: 2015 ident: 10.1016/j.apm.2024.04.033_bib0024 article-title: Complex variable analysis for stress distribution of an underwater tunnel in an elastic half plane publication-title: Int. J. Numer. Anal. Methods Geomech. doi: 10.1002/nag.2375 – volume: 160 year: 2023 ident: 10.1016/j.apm.2024.04.033_bib0040 article-title: Analytical stress and displacement of twin noncircular tunnels in elastic semi-infinite ground publication-title: Comput. Geotech. doi: 10.1016/j.compgeo.2023.105520 – volume: 43 start-page: 315 issue: 2 year: 1993 ident: 10.1016/j.apm.2024.04.033_bib0002 article-title: Subsurface settlement profiles above tunnels in clays publication-title: Géotechnique doi: 10.1680/geot.1993.43.2.315 – volume: 19 start-page: 77 issue: 4 year: 1948 ident: 10.1016/j.apm.2024.04.033_bib0009 article-title: On the stresses in a plate containing two circular holes publication-title: J. Appl. Phys. doi: 10.1063/1.1697875 – volume: 43 start-page: 315 issue: 2 year: 2020 ident: 10.1016/j.apm.2024.04.033_bib0003 article-title: Theoretical prediction model for deformations caused by construction of new tunnels undercrossing existing tunnels based on the equivalent layered method publication-title: Comput. Geotech. – volume: 89 start-page: 34 year: 2016 ident: 10.1016/j.apm.2024.04.033_bib0025 article-title: Solution for a circular cavity in an elastic half plane under gravity and arbitrary lateral stress publication-title: Int. J. Rock Mech. Min. Sci. doi: 10.1016/j.ijrmms.2016.08.004 – volume: 37 start-page: 301 issue: 3 year: 1987 ident: 10.1016/j.apm.2024.04.033_bib0010 article-title: Analysis of undrained soil deformation due to ground loss publication-title: Géotechnique doi: 10.1680/geot.1987.37.3.301 – volume: 140 issue: 4 year: 2014 ident: 10.1016/j.apm.2024.04.033_bib0021 article-title: Ground movements due to shallow tunnels in soft ground. II: analytical interpretation and prediction publication-title: J. Geotech. Geoenviron. Eng. – ident: #cr-split#-10.1016/j.apm.2024.04.033_bib0004.2 doi: 10.2307/1213774 – volume: 17 start-page: 3 issue: 1 year: 2002 ident: 10.1016/j.apm.2024.04.033_bib0023 article-title: Predictions of ground deformations in shallow tunnels in clay publication-title: Tunn. Undergr. Space Technol. doi: 10.1016/S0886-7798(01)00068-2 – volume: 124 start-page: 846 issue: 9 year: 1998 ident: 10.1016/j.apm.2024.04.033_bib0012 article-title: Analytical prediction for tunneling-induced ground movements in clays publication-title: J. Geotech. Geoenviron. Eng. doi: 10.1061/(ASCE)1090-0241(1998)124:9(846) – volume: 52 start-page: 4509 year: 2019 ident: 10.1016/j.apm.2024.04.033_bib0032 article-title: An analytical solution for an arbitrary cavity in an elastic half-plane publication-title: Rock Mech. Rock Eng. doi: 10.1007/s00603-019-01844-2 – volume: 148 issue: 4 year: 2022 ident: 10.1016/j.apm.2024.04.033_bib0034 article-title: A complex variable solution for shallow rectangular tunnel in semi-infinite plane publication-title: J. Eng. Mech. doi: 10.1061/(ASCE)EM.1943-7889.0002093 – volume: 45 start-page: 923 year: 2008 ident: 10.1016/j.apm.2024.04.033_bib0044 article-title: A practical iterative procedure to estimate seismic-induced deformations of shallow rectangular structures publication-title: Can. Geotech. J. doi: 10.1139/T08-026 – volume: 120 year: 2020 ident: 10.1016/j.apm.2024.04.033_bib0037 article-title: Analytical study on interaction between existing and new tunnels parallel excavated in semi-infinite viscoelastic ground publication-title: Comput. Geotech. doi: 10.1016/j.compgeo.2019.103385 – volume: 48 start-page: 709 issue: 5 year: 1998 ident: 10.1016/j.apm.2024.04.033_bib0011 article-title: Surface settlements due to deformation of a tunnel in an elastic half plane publication-title: Géotechnique doi: 10.1680/geot.1998.48.5.709 – volume: 35 start-page: 2795 issue: 19 year: 1998 ident: 10.1016/j.apm.2024.04.033_bib0018 article-title: Deformations of an elastic half plane with a circular cavity publication-title: Int. J. Solids Struct. doi: 10.1016/S0020-7683(97)00194-7 – volume: 39 start-page: 524 issue: 5 year: 2015 ident: 10.1016/j.apm.2024.04.033_bib0035 article-title: An analytical solution for deforming twin-parallel tunnels in an elastic half plane publication-title: Int. J. Numer. Anal. Methods Geomech. doi: 10.1002/nag.2322 – year: 1963 ident: 10.1016/j.apm.2024.04.033_bib0028 |
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| SubjectTerms | Fourier series fitting Generalized complex variable theory Matrix-form solution Multiple non-circular tunnels Stress and displacement fields |
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