Abstract
Loosening of earth pressure by tunnels is an important parameter for the structural design of subway stations, this study analyzes the difference between the loosening pressures of each span of a shallow multi-span tunnel station using the pile-beam-arch (PBA) method. By conducting a similarity model test of the PBA method, we simulate the complete excavation process. We study the sliding failure mode of the overlying soil of the shallow-buried station and the law of change of the loosening pressure of each span. A simplified calculation model for the loosening pressure of shallow buried multi-span tunnels by the cavity pile method was developed, and the applicability of the formulae and sensitivity analysis of the parameters were carried out. The results reveal that the loosening pressure of the mid-span is transferred to the stress of the side-span during tunnel excavation. This finding contradicts Terzaghi’s and Bierbaumer’s methods, which do not consider the influence of tunnel structure on the loosening pressure of the overlying soil. The side span relaxation pressure is only related to the soil capacity and the depth of burial of the tunnel This research can provide an important theoretical reference for the design of the overburden load and lateral confining pressure of the PBA structure design.
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References
Bierbaumer A (1913) Die dimensionerung des tunnel mauerwerks. Engelmann, Leipzig, Germany
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
Cheng XH (2012) Theoretical solution for the dividing depth of deep tunnel and shallow tunnel in earth. Chinese Journal of Underground Space and Engineering 8(1):37–42+128 (in Chinese)
Costa YD, Zornberg JG, Bueno BS, Costa CL (2009) Failure mechanisms in sand over a deep active trapdoor. Journal of Geotechnical & Geoenvironmental Engineering 135(11):1741–1753, DOI: https://doi.org/10.1061/(ASCE)GT.1943-5606.0000134
Fang X, Kikumoto M, Cui Y (2020) A theory of loosening earth pressure above a shallow tunnel in unsaturated ground. International Journal for Numerical and Analytical Methods in Geomechanics 44(10):1495–1508, DOI: https://doi.org/10.1002/nag.3072
Fang Y, Xu C, Cui G, Kenneally B (2016) Scale model test of highway tunnel construction underlying mined-out thin coal seam. Tunnelling and Underground Space Technology 56:105–116, DOI: https://doi.org/10.1016/j.tust.2016.03.007
Fraldi M, Guarracino F (2009) Limit analysis of collapse mechanisms in cavities and tunnels according to the Hoek-Brown failure criterion. International Journal of Rock Mechanics and Mining Sciences 46(4):665–673, DOI: https://doi.org/10.1016/j.ijrmms.2008.09.014
Guan YP, Zhao W, Li SG, Zhang GB (2014) Key techniques and risk management for the application of the pile-beam-arch (PBA) excavation method: A case study of the Zhongjie subway station. The Scientific World Journal 2014:275362, DOI: https://doi.org/10.1155/2014/275362
Hobbs DW (1968) Scale model study of strata movement around mine roadways. The dependence of roadway closure upon rock strength. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 5:219–235, DOI: https://doi.org/10.1016/0148-9062(68)90010-7
Hobbs DW (1969) Scale model study of strata movement around mine roadways. Roadway shape and size. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 6:305–340, DOI: https://doi.org/10.1016/0148-9062(69)90040-0
Huang F, Wu CZ, Jang BA, Hong Y, Guo N, Guo W (2020) Instability mechanism of shallow tunnel in soft rock subjected to surcharge loads. Tunnelling and Underground Space Technology 99:103350, DOI: https://doi.org/10.1016/j.tust.2020.103350
Huang JZ, Zhang Y, Ouyang XW, Xu GY (2019) Lagged settlement in sandy cobble strata and earth pressure on shield tunnel. Mathematical Biosciences and Engineering 16(6):6209–6230, DOI: https://doi.org/10.3934/mbe.2019309
Jeon S, Kim J, Seo Y, Hong C (2004) Effect of a fault and weak plane on the stability of a tunnel in rock-a scaled model test and numerical analysis. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts 41(s1):658–663, DOI: https://doi.org/10.1016/j.ijrmms.2004.03.115
Jia J, Zhou SH, Yao XP, Shen C (2012) Deformation and stability study of PBA extension method based on air defense tunnel. Applied Mechanics and Materials 204–208:1347–1355
Jiang Y, Yoneda H, Tanabashi Y (2001) Theoretical estimation of loosening pressure on tunnels in soft rocks. Tunnelling and Underground Space Technology 16(2):99–105, DOI: https://doi.org/10.1016/S0886-7798(01)00034-7
Lee CJ, Chiang KH, Kuo CM (2004) Ground movement and tunnel stability when tunneling in sandy ground. Journal of the Chinese Institute of Engineers 27(7):1021–1032
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
Lei MF, Peng LM, Shi CH (2015) Model test to investigate the failure mechanisms and lining stress characteristics of shallow buried tunnels under unsymmetrical loading. Tunnelling and Underground Space Technology 46:64–75, DOI: https://doi.org/10.1016/j.tust.2014.11.003
Li PF, Wang F, Fan L, Wang H, Ma G (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
Liang LJ, Xu CJ (2019) Numerical and theoretical research on stress distribution in the loosening zone of the trapdoor problem. International Journal for Numerical and Analytical Methods in Geomechanics 43:1426–1447, DOI: https://doi.org/10.1002/nag.2906
Liang LJ, Xu CJ, Chen QZ, Chen QS (2020) Experimental and theoretical investigations on evolution of soil-arching effect in 2D trapdoor problem. International Journal of Geomechanics 20(6):06020007, DOI: https://doi.org/10.1061/(ASCE)GM.1943-5622.0001643
Liu J, Wang F, He S, Wang E, Zhou H (2015) Enlarging a large-diameter shield tunnel using the pile-beam-arch method to create a metro station. Tunnelling and Underground Space Technology 49:130–143, DOI: https://doi.org/10.1016/j.tust.2015.04.006
Meguid MA, Saada O, Nunes MA, Matter J (2008) Physical modeling of tunnels in soft ground: A review. Tunneling and Underground Space Technology 23(1):187–192, DOI: https://doi.org/10.1016/j.tust.2007.02.003
Shukla S, Gaurav, Sivakugan N (2009) A simplified extension of the conventional theory of arching in soils. International Journal of Geotechnical Engineering 3(3):353–359, DOI: https://doi.org/10.3328/IJGE.2009.03.03.353-359
Sitharam TG, Madhavi Latha G (2002) Simulation of excavations in jointed rock masses using a practical equivalent continuum approach. International Journal of Rock Mechanics & Mining Sciences 39:517–525, DOI: https://doi.org/10.1016/S1365-1609(02)00024-2
Sterpi D (1999) An analysis of geotechnical problems involving strain softening effects. International Journal for Numerical and Analytical Methods in Geomechanics 23(13):1427–1454, DOI: https://doi.org/10.1002/(SICI)1096-9853(199911)23:13<1427::AID-NAG6>3.0.CO;2-B
Sterpi D (2002) Application of the FEM to the stability of shallow tunnels. New frontiers in computational geotechnics — Proceedings of the 1st international workshop on new frontiers in computational geotechnics-banef, September, Gifu, Japan
Sterpi D, Cividini A (2004) A physical and numerical investigation on the stability of shallow tunnels in strain softening media. Rock Mechanics and Rock Engineering 37(4):277–298, DOI: https://doi.org/10.1007/s00603-003-0021-0
Terzaghi K (1948) Theoretical soil mechanics. John Wiley & Sons, Inc., New York, NY, USA
Wang ZW, Qiao CS, Song CY (2014) Calculation method of relaxation pressure of shallow large span tunnel in up-soft/low-hard rock stratum. Rock and Soil Mechanics 35(8):2342–2352 (in Chinese)
Wu J, Liao SM, Liu MB (2019) An analytical solution for the arching effect induced by ground loss of tunneling in sand. Tunnelling and Underground Space Technology 83:175–186, DOI: https://doi.org/10.1016/j.tust.2018.09.025
Xie JJ (1964) Formation pressure of shallow buried tunnel. China Civil Engineering Journal (6):58–70 (in Chinese)
Acknowledgments
This study was supported by the National Natural Science Foundation of China (Project No. 51508556), the Key Special Project of National Key R&D Program (Project No. 2016YFC080250504), the Fundamental Research Fund for the Central Universities (Project No. 2020YJSLJ14), and the Yue Qi Young Scholars of China University of Mining and Technology-Beijing (Project No. 00800015Z1166).
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Li, T., Zhang, Z., Luo, M. et al. Analytical Solution of Loosening Pressure Model for Shallow Tunnel Based on Pile-Beam-Arch Method. KSCE J Civ Eng 26, 3648–3662 (2022). https://doi.org/10.1007/s12205-022-2190-y
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DOI: https://doi.org/10.1007/s12205-022-2190-y