Elastoplastic solutions for deep-buried twin tunnels with arbitrary shapes and various arrangements under biaxial in-situ stress field based on Mohr-Coulomb and generalized Hoek-Brown criteria

Caquot, 1966 Chang, 2023, Back analysis of rock mass parameters in tunnel engineering using machine learning techniques, Comput. Geotech., 163, 10.1016/j.compgeo.2023.105738 Chen, 2011, Bipolar coordinates, image method and the method of fundamental solutions for Green’s functions of Laplace problems containing circular boundaries, Eng. Anal. Bound. Elem., 35, 236, 10.1016/j.enganabound.2010.08.008 Chen, 2019, An improved collapse analysis mechanism for the face stability of shield tunnel in layered soils, Comput. Geotech., 17, 97 Fahimifar, 2005, A theoretical approach for analysis of the interaction between grouted rockbolts and rock masses, Tunn. Undergr. Space Technol., 20, 333, 10.1016/j.tust.2004.12.005 Hoek, 2002, Hoek-Brown failure criterion-2002 edition, Proc. NARMS-Tac., 1, 267 Jeffery, G.B., 1921. Plane stress and plane strain in bipolar co-ordinates. Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character. 221 (582-593), 265-293. Kumari, 2017, Stress analysis for an infinite plate with circular holes, Materials Today: Proceedings., 4, 2323 Li, 2020, New approach for face stability assessment of tunnels driven in nonuniform soils, Comput. Geotech., 121 Lu, 2015, Analytic method of stress analysis for an orthotropic rock mass with an arbitrary-shaped tunnel, Int. J. Geomech., 15, 04014068, 10.1061/(ASCE)GM.1943-5622.0000408 Lu, 2017, Analytical solution for a lined tunnel with arbitrary cross sections excavated in orthogonal anisotropic rock mass, Int. J. Geomech., 17, 04017044, 10.1061/(ASCE)GM.1943-5622.0000912 Lv, 2007 Ma, 2021, An analytical method for determining the plastic regions around two circular holes in an infinite medium, Appl. Math. Model., 89, 636, 10.1016/j.apm.2020.07.033 Ma, 2022, A semi-analytical method for elastic-plastic analysis of a deep-buried elliptical tunnel, Comput. Geotech., 142, 10.1016/j.compgeo.2021.104589 Ma, 2022, Analytical solution for determining the plastic zones around two unequal circular tunnels, Tunn. Undergr. Space Technol., 120, 10.1016/j.tust.2021.104267 Mahdevari, 2021, A hybrid PSO-ANFIS model for predicting unstable zones in underground roadways, Tunn. Undergr. Space Technol., 117, 10.1016/j.tust.2021.104167 Pan, 1996, Influence of axial stress and dilatancy on rock tunnel stability, J. Geotech. Eng., 122, 139, 10.1061/(ASCE)0733-9410(1996)122:2(139) Pan, 2016, Face stability analysis for a shield-driven tunnel in anisotropic and nonhomogeneous soils by the kinematical approach, Int. J. Geomech., 16, 04015076, 10.1061/(ASCE)GM.1943-5622.0000569 Pan, 2017, Upper-bound analysis on the face stability of a non-circular tunnel, Tunn. Undergr. Space Technol., 62, 96, 10.1016/j.tust.2016.11.010 Pan, 2018, Three-dimensional static and seismic stability analysis of a tunnel face driven in weak rock masses, Int. J. Geomech., 18, 04018055, 10.1061/(ASCE)GM.1943-5622.0001174 Park, 2006, Analytical solution for a circular opening in an elastic-brittle-plastic rock, Int. J. Rock Mech. Min. Sci., 43, 616, 10.1016/j.ijrmms.2005.11.004 Qin, 2015, 74 Qin, 2022, Closed-form solutions for collapse mechanisms of tunnel crown in saturated non-uniform rock surrounds, Tunn. Undergr. Space Technol., 126, 10.1016/j.tust.2022.104529 Roateşi, 2014, Analytical and numerical approach for tunnel face advance in a viscoplastic rock mass, Int. J. Rock Mech. Min. Sci., 70, 123, 10.1016/j.ijrmms.2014.04.007 Sharan, 2003, Elastic-brittle-plastic analysis of circular openings in Hoek-Brown media, Int. J. Rock Mech. Min. Sci., 40, 817, 10.1016/S1365-1609(03)00040-6 Sharan, 2008, Analytical solutions for stresses and displacements around a circular opening in a generalized Hoek-Brown rock, Int. J. Rock Mech. Min. Sci., 45, 78, 10.1016/j.ijrmms.2007.03.002 Sheng, 2022, Novel perturbation solutions for deep-buried non-circular tunnels under biaxial in situ stress field based on Mohr-Coulomb criterion, Appl. Math. Model., 110, 408, 10.1016/j.apm.2022.06.006 Sheng, 2023, Semi-analytical solutions for elastic-brittle-plastic surrounding rock under biaxial in situ stress field based on unified strength criterion, Int. J. Geomech., 10.1061/IJGNAI.GMENG-8092 Tan, 2021, Analytical stress solution for rock mass containing two holes based on an improved Schwarz alternating method, Theor. Appl. Fract. Mech., 116, 10.1016/j.tafmec.2021.103092 Wang, 2017, Analytical solutions of stresses and displacements for deeply buried twin tunnels in viscoelastic rock, Int. J. Rock Mech. Min. Sci., 93, 13, 10.1016/j.ijrmms.2017.01.002 Xue, 2020, A novel swarm intelligence optimization approach: sparrow search algorithm, Systems science & control engineering., 8, 22, 10.1080/21642583.2019.1708830 Yu, 2002, A unified strength criterion for rock material, Int. J. Rock Mech. Min. Sci., 39, 975, 10.1016/S1365-1609(02)00097-7 Yue, 2023, Review and empirical analysis of sparrow search algorithm, Artif. Intell. Rev., 1 Zeng, 2010, Slip line field of plane strain problem obeying the generalized Hoek-Brown failure criterion, J. Civ. Architect. Environ. Eng., 32, 4 Zeng, 2019, Stress solution for an infinite elastic plate containing two arbitrarily shaped holes, AIAA Journal., 57, 1691, 10.2514/1.J057578 Zhang, 2008, A generalized three-dimensional Hoek-Brown strength criterion, Int. J. Rock Mech. Min. Sci., 41, 893 Zhang, 2022, A bioinspired path planning approach for mobile robots based on improved sparrow search algorithm, Adv. Manuf., 10, 114, 10.1007/s40436-021-00366-x Zhou, 2014, Analytical solution of undrained cylindrical cavity expansion in saturated soil under anisotropic initial stress, Comput. Geotech., 55, 232, 10.1016/j.compgeo.2013.09.011 Zhou, 2016, A semi-analytical solution for cylindrical cavity expansion in elastic-perfectly plastic soil under biaxial in situ stress field, Geotechnique., 66, 584, 10.1680/jgeot.15.P.115 Zhou, 2017, A general semi-analytical solution for consolidation around an expanded cylindrical and spherical cavity in modified Cam Clay, Comput. Geotech., 91, 71, 10.1016/j.compgeo.2017.07.005 Zhou, 2022, Non-circular cavity expansion in undrained soil: Semi-analytical solution, J. Eng. Mech., 148, 04022032, 10.1061/(ASCE)EM.1943-7889.0002118 Zhuang, 2019, A unified analytical solution for elastic-plastic stress analysis of a cylindrical cavity in Mohr-Coulomb materials under biaxial in situ stresses, Geotechnique., 69, 369, 10.1680/jgeot.17.P.281 Zou, 2017, A new procedure for ground response curve (GRC) in strain-softening surrounding rock, Comput. Geotech., 89, 81, 10.1016/j.compgeo.2017.04.009 Zou, 2020, A novel numerical-iterative-approach for strain-softening surrounding rock incorporating rockbolts effectiveness and hydraulic-mechanical coupling based on Three-Dimensional Hoek-Brown strength criterion, Tunn. Undergr. Space Technol., 101, 10.1016/j.tust.2020.103358