Abstract
A three-dimensional collapse mechanism that can consider a combined collapse of the tunnel roof and the side walls is proposed in this work. The three-dimensional upper bound support pressure is formulated with the power balance principal in the upper bound theorem. The nonlinear Mohr-Coulomb failure criterion is used to replace the commonly used linear MohrCoulomb failure criterion. The method has been validated by a series of examples, in which the three-dimensional collapse mechanism and support pressures are in a good agreement with the numerical results and solutions found in the literatures. Furthermore, sensitivity analyses of the geotechnical and geometrical parameters on the support pressure are conducted and the collapsing range is measured. The results show that a higher value of nonlinear failure coefficient, tensile strength, initial cohesion and tangential internal friction angle can increase tunnel stability, while tunnel stability is threatened by a higher value of burial depth, unit weight, tunnel width and height. The predicted collapse range increases noticeably with the increase of the nonlinear coefficient. This study is of great significance for predicting the three-dimensional safety support pressure and collapse mechanism of tunnel.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Assadi A, Sloan SW (1991) Undrained stability of shallow square tunnel. Journal of Geotechnical Engineering 117(8):1152–1173, DOI: https://doi.org/10.1061/(ASCE)0733-9410(1991)117:8(1152)
Augarde CE, Lyamin AV, Sloan SW (2003) Prediction of undrained sinkhole collapse. Journal of Geotechnical and Geoenvironmental Engineering 129(3):197–205, DOI: https://doi.org/10.1061/(ASCE)1090-0241(2003)129:3(197)
Davis EH, Gunn MJ, Mair RJ, Seneviratne HN (1980) The stability of shallow tunnels and underground openings in cohesive material. Geotechnique 30(4):397–416, DOI: https://doi.org/10.1680/geot.1980.30.4.397
Fraldi M, Guarracino F (2010) Analytical solutions for collapse mechanisms in tunnels with arbitrary cross sections. International Journal of Solids and Structures 47(2):216–223, DOI: https://doi.org/10.1016/j.ijsolstr.2009.09.028
Guan K, Zhu WC, Niu LL, Wang QY (2017) Three-dimensional upper bound limit analysis of supported cavity roof with arbitrary profile in Hoek-Brown rock mass. Tunnelling and Underground Space Technology 69:147–154, DOI: https://doi.org/10.1016/j.tust.2017.06.016
Huang F, Yang XL, Ling TH (2013) Prediction of collapsing region above deep spherical cavity roof under axis-symmetrical conditions. Rock Mechanics and Rock Engineering 47(4):1511–1516, DOI: https://doi.org/10.1007/s00603-013-0455-y
Li T, Gong, W, Tang H (2021) Three-dimensional stochastic geological modeling for probabilistic stability analysis of a circular tunnel face. Tunnelling and Underground Space Technology 118:104190, DOI: https://doi.org/10.1016/j.tust.2021.104190
Liu ZZ, Cao P, Lin H, Meng JJ, Wang YX (2020) Three-dimensional upper bound limit analysis of underground cavities using nonlinear Baker failure criterion. Transactions of Nonferrous Metals Society of China 30(7):1916–1927, DOI: https://doi.org/10.1016/s1003-6326(20)65350-x
Luo WJ, Yang XL (2018) 3D stability of shallow cavity roof with arbitrary profile under influence of pore water pressure. Geomechanics and Engineering 16(6):569–575, DOI: https://doi.org/10.12989/GAE.2018.16.6.569
Lyamin AV, Jack DL, Sloan SW (2001) Collapse analysis of square tunnels in cohesive-frictional soils. Computational Mechanics—New Frontiers for the New Millennium 405–414, DOI: https://doi.org/10.1016/B978-0-08-043981-5.50063-8
Lyu C, Yu L, Wang M, Xia P, Sun Y (2020) Upper bound analysis of collapse failure of deep tunnel under karst cave considering seismic force. Soil Dynamics and Earthquake Engineering 132:106003, DOI: https://doi.org/10.1016/j.soildyn.2019.106003
Osman AS, Mair RJ, Bolton MD (2006) On the kinematics of 2D tunnel collapse in undrained clay. Géotechnique 56(9):585–595, DOI: https://doi.org/10.1680/geot.2006.56.9.585
Park D, Michalowski RL (2020) Three-dimensional roof collapse analysis in circular tunnels in rock. International Journal of Rock Mechanics and Mining Sciences 128:104275, DOI: https://doi.org/10.1016/j.ijrmms.2020.104275
Qin C, Chian SC (2018) Revisiting crown stability of tunnels deeply buried in non-uniform rock surrounds. Tunnelling and Underground Space Technology 73:154–161, DOI: https://doi.org/10.1016/j.tust.2017.12.006
Senent S, Yi C, Jimenez R (2020) An upper bound solution for tunnel face stability analysis considering the free span. Tunnelling and Underground Space Technology 103:103515, DOI: https://doi.org/10.1016/j.tust.2020.103515
Vo-Minh T, Nguyen-Son L, Nguyen-Van G, Thai-Phuong T (2021) Upper bound limit analysis of circular tunnel in cohesive-frictional soils using isogeometric analysis based on Bézier extraction. Tunnelling and Underground Space Technology 114:103995, DOI: https://doi.org/10.1016/j.tust.2021.103995
Wang HT, Liu P, Liu C, Zhang X, Yang Y, Liu LY (2019) Three-dimensional upper bound limit analysis on the collapse of shallow soil tunnels considering roof stratification and pore water pressure. Mathematical Problems in Engineering 2019:2019, DOI: https://doi.org/10.1155/2019/8164702
Wang Z, Qiao C, Song C, Xu J (2014) Upper bound limit analysis of support pressures of shallow tunnels in layered jointed rock strata. Tunnelling and Underground Space Technology 43:171–183, DOI: https://doi.org/10.1016/j.tust.2014.05.010
Wilson DW, Abbo AJ, Sloan SW, Yamamoto K (2017) Undrained stability of rectangular tunnels where shear strength increases linearly with depth. Canadian Geotechnical Journal 54(4):469–480, DOI: https://doi.org/10.1139/cgj-2016-0072
Wu Y, Zhou X, Gao Y, Zhang L, Yang J (2019). Effect of soil variability on bearing capacity accounting for non-stationary characteristics of undrained shear strength. Computers and Geotechnics 110:199–210, DOI: https://doi.org/10.1016/j.compgeo.2019.02.003
Yang XL, Yin JH (2004) Slope stability analysis with nonlinear failure criterion[J]. Journal of Engineering Mechanics 130(3):267–273, DOI: https://doi.org/10.1061/(ASCE)0733-9399(2004)130:3(267)
Yu L, Lyu C, Wang M, Xu T (2019) Three-dimensional upper bound limit analysis of a deep soil-tunnel subjected to pore pressure based on the nonlinear Mohr-Coulomb criterion. Computers and Geotechnics 112:293–301, DOI: https://doi.org/10.1016/j.compgeo.2019.04.025
Zhang C, Han K, Zhang D (2015) Face stability analysis of shallow circular tunnels in cohesive—frictional soils. Tunnelling and Underground Space Technology 50:345–357, DOI: https://doi.org/10.1016/j.tust.2015.08.007
Zhang D, Zhang B (2020) Stability analysis of the pressurized 3D tunnel face in anisotropic and nonhomogeneous soils. International Journal of Geomechanics 20(4):04020018, DOI: https://doi.org/10.1061/(ASCE)GM.1943-5622.0001635
Zou J, Chen G, Qian Z (2019) Tunnel face stability in cohesion-frictional soils considering the soil arching effect by improved failure models. Computers and Geotechnics 106:1–17, DOI: https://doi.org/10.1016/j.compgeo.2018.10.014
Acknowledgments
This study was financially supported by the National Natural Science Foundation of China (5210041777), the Water Conservancy Science and Technology Major Project of Hunan Province (XSKJ2019081-10), the Hunan Province Natural Science Foundation of China (2018JJ0540), the Fundamental Research Funds for the Central Universities of Central South University (2021zzts0281), the CRSRI Open Research Program (SN: CKWV2017512/KY).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Liu, Z., Cao, P., Wang, F. et al. Three-Dimensional Upper Bound Limit Analysis of Tunnel Stability with an Extended Collapse Mechanism. KSCE J Civ Eng 26, 5318–5327 (2022). https://doi.org/10.1007/s12205-022-2065-2
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12205-022-2065-2