Abstract
The traditional simplified model for ground pressure calculation is widely used in the anti-seismic design of shallow tunnels. However, it presents two obvious deficiencies, which are related to the block equilibrium and the additional seismic load respectively. A modified calculation model is proposed in this article by introducing the concept of slip angle, so that the deflection of potential slip planes and the distribution of ground pressure can be considered and further discussed. By combining the horizontal slice method and graphical method, a series of explicit formulas for calculating ground pressure are presented so that the vertical ground pressure, the rupture angle, and the lateral thrust can be calculated more accurately. The proposed modified model is compared with the existing model to validate the correctness of calculation results. The results show that the explicit formula of modified model could be reduced to Liu’s formula when the potential slip planes are assumed to be vertical. Additionally, the sensitivity analyses on the vertical ground pressure, block volume, and distribution pattern of the lateral thrust are carefully investigated. The lateral thrusts acting on the left and right wedges distribute logarithmically and exponentially respectively, which implies that the distribution pattern is mainly affected by the direction of earthquake inertia force, while the cohesion and the friction angle merely influence the magnitude of lateral thrust to some extent.
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References
Chakraborty D, Kumar J (2013) Stability of a long unsupported circular tunnel in soils with seismic forces. Natural Hazards 68(2):419–431, DOI: https://doi.org/10.1007/s11069-013-0633-y
Dey A, Dey A, Sukladas S (2017) 3N Formulation of the horizontal slice method in evaluating pseudostatic method for analysis of seismic active earth pressure. International Journal of Geomechanics 17(1):1–11, DOI: https://doi.org/10.1061/(Asce)Gm.1943-5622.0000662
Fang XQ, Jin HX, Liu JX, Huang MJ (2016) Imperfect bonding effect on dynamic response of a non-circular lined tunnel subjected to shear waves. Tunnelling and Underground Space Technology 56: 226–231, DOI: https://doi.org/10.1016/j.tust.2016.03.008
Ghanbari A, Taheri M (2012) An analytical method for calculating active earth pressure in reinforced retaining walls subject to a line surcharge. Geotextiles and Geomembranes 34:1–10, DOI: https://doi.org/10.1016/j.geotexmem.2012.02.009
Iida H, Hiroto T, Yoshida N, Iwafuji M (1996) Damage to daikai subway station. Soils and Foundations 36 (Special):283–300, DOI: https://doi.org/10.3208/sandf.36.Special_283
JTG 3370.1–2018 (2018) Specifications for design of highway tunnels. Specifications for Design of Highway Tunnels China Communications Press, Beijing, China
Kontoe S, Zdravkovic L, Potts D, Menkiti C (2008) Case study on seismic tunnel response. Canadian Geotechnical Journal 45(12):1743–1764, DOI: https://doi.org/10.1139/t08-087
Liu QJ, Zhang C, Todorovska M (2016) Scattering of SH waves by a shallow rectangular cavity in an elastic half space. Soil Dynamics and Earthquake Engineering 90:147–157, DOI: https://doi.org/10.1016/j.soildyn.2016.08.027
Liu XR, Li DL, Wang JB, Wang Z (2015) Surrounding rock pressure of shallow-buried bilateral bias tunnels under earthquake. Geomechanics and Engineering 9(4):427–445, DOI: https://doi.org/10.12989/gae.2015.9.4.427
Mei WQ, Xia YY, Han GS, Pan PZ (2021) Theoretical responses of shallow-buried circular cavity subjected to transient P wave. Computers and Geotechnics 139:1–14, DOI: https://doi.org/10.1016/j.compgeo.2021.104411
Pain A, Choudhury D, Bhattacharyya S (2017) Effect of dynamic soil properties and frequency content of harmonic excitation on the internal stability of reinforced soil retaining structure. Geotextiles and Geomembranes 45(5):471–486, DOI: https://doi.org/10.1016/j.geotexmem.2017.07.003
Pan QJ, Dias D (2018) Three-dimensional static and seismic stability analysis of a tunnel face driven in weak rock masses. International Journal of Geomechanics 18(6):1–10, DOI: https://doi.org/10.1061/(ASCE)GM.1943-5622.0001174
Pelli E, Sofianos A (2018) Analytical calculation of the half space stress field around tunnels under seismic loading of SV waves. Tunnelling and Underground Space Technology 79:150–174, DOI: https://doi.org/10.1016/j.tust.2018.01.019
Roy N, Sarkar R (2017) A review of seismic damage of mountain tunnels and probable failure mechanisms. Geotechnical and Geological Engineering 35(1):1–28, DOI: https://doi.org/10.1007/s10706-016-0091-x
Saada Z, Maghous S, Garnier D (2013) Pseudo-static analysis of tunnel face stability using the generalized Hoek-Brown strength criterion. International Journal for Numerical and Analytical Methods in Geomechanics 37(18):3194–3212, DOI: https://doi.org/10.1002/nag.2185
Song WJ, Xiang YY (2020) An analytical method of continuous upper bound limit analysis for the stability of shallow shield tunnels in cohesive-frictional soils. Journal of Engineering Mathematics 122(1): 101–116, DOI: https://doi.org/10.1007/s10665-020-10050-x
Wang TT, Kwok O, Jeng F (2021) Seismic response of tunnels revealed in two decades following the 1999 Chi-Chi earthquake (Mw 7.6) in Taiwan: A review. Engineering Geology 287, DOI: https://doi.org/10.1016/j.enggeo.2021.106090
Wu J, Li SC, Xu ZH, Zhao J (2019) Determination of required rock thickness to resist water and mud inrush from karst caves under earthquake action. Tunnelling and Underground Space Technology 85:43–55, DOI: https://doi.org/10.1016/j.tust.2018.11.048
Yang XL, Wang HY (2018) Catastrophe analysis of active-passive mechanisms for shallow tunnels with settlement. Geomechanics and Engineering 15(1):621–630, DOI: https://doi.org/10.12989/gae.2018.15.1.621
Yu HT, Chen JT, Bobet A, Yuan Y (2016) Damage observation and assessment of the Longxi tunnel during the Wenchuan earthquake. Tunnelling and Underground Space Technology 54:102–116, DOI: https://doi.org/10.1016/j.tust.2016.02.008
Yu HT, Yuan Y, Bobet A (2017) Seismic analysis of long tunnels: A review of simplified and unified methods. Underground Space 2(2):73–87, DOI: https://doi.org/10.1016/j.undsp.2017.05.003
Zhang N, Chen X, Gao YF, Dai DH (2020a) Analytical solution to scattering of SH waves by a circular lined tunnel embedded in a semi-circular alluvial valley in an elastic half-space. Tunnelling and Underground Space Technology 106:1–18, DOI: https://doi.org/10.1016/j.tust.2020.103615
Zhang XP, Jiang YJ, Maegawa K (2020b) Mountain tunnel under earthquake force: A review of possible causes of damages and restoration methods. Journal of Rock Mechanics and Geotechnical Engineering 12(2): 414–426, DOI: https://doi.org/10.1016/j.jrmge.2019.11.002
Zhang XP, Jiang YJ, Sugimoto S (2018) Seismic damage assessment of mountain tunnel: A case study on the Tawarayama tunnel due to the 2016 Kumamoto Earthquake. Tunnelling and Underground Space Technology 71:138–148, DOI: https://doi.org/10.1016/j.tust.2017.07.019
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This work was supported by the National Natural Science Foundation of China (No. 51678155, No. 41977233) and the Natural Science Foundation in Fujian Province of China (2021J01599).
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Lu, Q., Guan, Z. & Zheng, L. The Modification and the Application of Ground Pressure Calculation Model for the Shallow Tunnels under Seismic Scenario. KSCE J Civ Eng 26, 4146–4156 (2022). https://doi.org/10.1007/s12205-022-2142-6
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DOI: https://doi.org/10.1007/s12205-022-2142-6