Abstract
Earthquakes can have a very adverse effect on tunnel excavation. The Mohr-Coulomb failure criterion is modified by introducing tensile strength cut-off, which allows nonlinear strength reduction of soil under tensile conditions, and kinematic analysis of tunnel face subjected to the earthquake is carried out. The pseudo-dynamic method is adopted to simulate the earthquake with the acceleration varying with time and space, improving the accuracy of the simulation. The external power and internal energy dissipation rate are equal to obtain the expression of tunnel face support pressure under the limit analysis framework. And the most unfavorable tunnel face support pressure is optimized by using the method of exhaustion. Compared with other research results, the validity of this method is proved. The influence of soil parameters and pseudo-dynamic parameters on the critical support pressure is revealed by further parameter analysis. Finally, this study provides an effective reference for seismic design of tunnel engineering construction.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Abbreviations
- a h :
-
Horizontal seismic accelerations
- a v :
-
Vertical seismic accelerations
- c :
-
Cohesion
- d :
-
Tunnel diameter
- f :
-
Factor of amplitude enhancement
- G :
-
Shear modulus
- g :
-
Acceleration of gravity
- k h :
-
Horizontal seismic acceleration coefficient
- k v :
-
Vertical seismic acceleration coefficient
- R :
-
Radius of the cross section circle
- r A :
-
Length of radial line OA
- r B :
-
Length of radial line OB
- r E :
-
Length of radial line OE
- r F :
-
Length of radial line OF
- r G :
-
Length of radial line OG
- r m :
-
The distance between the origin O and the center of the cross section circle
- T s :
-
Seismic vibration period
- u v :
-
Ratio of vertical to horizontal seismic coefficients
- V s :
-
Shear wave velocity
- V p :
-
Primary wave velocity
- γ :
-
Unit weight of soil
- δ :
-
Dilatancy angle
- δ n :
-
Maximum dilatancy angle
- θ A :
-
Angle between vertical direction and radial line OA
- θ B :
-
Angle between vertical direction and radial line OB
- θ F :
-
Angle between vertical direction and radial line OF
- θ G :
-
Angle between vertical direction and radial line OG
- θ O :
-
Angle between vertical direction and radial line OE
- λ s :
-
Wavelengths of shear wave
- λ p :
-
Wavelengths of primary wave
- μ :
-
Poisson’s ratio of soil
- ξ :
-
The coefficient of tension cut-off
- ρ :
-
Density of soil
- ϕ :
-
Friction angle
- ω :
-
Angular velocity
References
Anagnostou G, Kovári K (1996) Face stability conditions with earth pressure balanced shields. Tunnelling and Underground Space Technology 11(2):165–173, DOI: https://doi.org/10.1016/0886-7798(96)00017-X
Ausilio E, Conte E, Dente G (2000) Seismic stability analysis of reinforced slopes. Soil Dynamics and Earthquake Engineering 19(3):159–172, DOI: https://doi.org/10.1016/S0267-7261(00)00005-1
Gui YL, Bui HH, Kodikara J, Zhang QB, Zhao J, Rabczuk T (2016) Modelling the dynamic failure of brittle rocks using a hybrid continuum-discrete element method with a mixed-mode cohesive fracture model. International Journal of Impact Engineering 87:146–155, DOI: https://doi.org/10.1016/j.ijimpeng.2015.04.010
Karray M, Hussien MN, Delisle MC, Ledoux C (2018) Framework to assess pseudostatic approach for seismic stability of clayey slopes. Canadian Geotechnical Journal 55(12):1860–1876, DOI: https://doi.org/10.1139/cgj-2017-0383
Leca E, Dormieux L (1990) Upper and lower bound solutions for the face stability of shallow circular tunnels in frictional material. Geotechnique 40(4):581–606, DOI: https://doi.org/10.1680/geot.1990.40.4.581
Li TZ, Li YX, Yang XL (2017) Rock burst prediction based on genetic algorithms and extreme learning machine. Journal of Central South University 24(9):2105–2113, DOI: https://doi.org/10.1007/s11771-017-3619-1
Li TZ, Yang XL (2018a) Probabilistic stability analysis of subway tunnels combining multiple failure mechanisms and response surface method. International Journal of Geomechanics 18(12):04018167, DOI: https://doi.org/10.1061/(ASCE)GM.1943-5622.0001315
Li TZ, Yang XL (2018b) Risk assessment model for water and mud inrush in deep and long tunnels based on normal grey cloud clustering method. KSCE Journal of Civil Engineering 22(5):1991–2001, DOI: https://doi.org/10.1007/s12205-017-0553-6
Li TZ, Yang XL (2019) An efficient uniform design for Kriging-based response surface method and its application. Computers and Geotechnics 109:12–22, DOI: https://doi.org/10.1016/j.compgeo.2019.01.009
Liu B, Vu-Bac N, Rabczuk T (2021) A stochastic multiscale method for the prediction of the thermal conductivity of Polymer nanocomposites through hybrid machine learning algorithms. Composite Structures 273:114269, DOI: https://doi.org/10.1016/j.compstruct.2021.114269
Liu B, Vu-Bac N, Zhuang XY, Rabczuk T (2020) Stochastic multiscale modeling of heat conductivity of Polymeric clay nanocomposites. Mechanics of Materials 142:103280, DOI: https://doi.org/10.1016/j.mechmat.2019.103280
Michalowski RL, Drescher A (2009) Three-dimensional stability of slopes and excavations. Géotechnique 59(10):839–850, DOI: https://doi.org/10.1680/geot.8.P.136
Mollon G, Dias D, Soubra AH (2009) Probabilistic analysis and design of circular tunnels against face stability. International Journal of Geomechanics 9(6):237–249
Mollon G, Dias D, Soubra AH (2011) Rotational failure mechanisms for the face stability analysis of tunnels driven by a pressurized shield. International Journal for Numerical Analytical Methods in Geomechanics 35(12):1363–1388, DOI: https://doi.org/10.1002/nag.962
Nimbalkar SS, Choudhury D, Mandal JN (2006) Seismic stability of reinforced soil-wall by pseudo-dynamic method. Geosynthetics International 13(3):111–119, DOI: https://doi.org/10.1680/gein.2006.13.3.111
Nouri H, Fakher A, Jones C (2008) Evaluating the effects of the magnitude and amplification of pseudo-static acceleration on reinforced soil slopes and walls using the limit equilibrium horizontal slices method. Geotextiles and Geomembranes 26(3):263–278, DOI: https://doi.org/10.1016/j.geotexmem.2007.09.002
Perazzelli P, Anagnostou G (2013) Stress analysis of reinforced tunnel faces and comparison with the limit equilibrium method. Tunnelling and Underground Space Technology 38:87–98, DOI: https://doi.org/10.1016/j.tust.2013.05.008
Qin CB, Chian SC (2018) Kinematic analysis of seismic slope stability with a discretisation technique and pseudo-dynamic approach: A new perspective. Géotechnique 68(6):492–503, DOI: https://doi.org/10.1680/jgeot.16.P.200
Rabczuk T, Areias PMA (2006) A new approach for modelling slip lines in geological materials with cohesive models. International Journal for Numerical Analytical Methods in Geomechanics 30(11): 1159–1172, DOI: https://doi.org/10.1002/nag.522
Rabczuk T, Belytschko T (2004) Cracking particles: A simplified meshfree method for arbitrary evolving cracks. International Journal for Numerical Methods in Engineering 61(13):2316–2343, DOI: https://doi.org/10.1002/nme.1151
Rabczuk T, Belytschko T (2007) A three-dimensional large deformation meshfree method for arbitrary evolving cracks. Computer Methods in Applied Mechanics and Engineering 196(29–30):2777–2799, DOI: https://doi.org/10.1016/j.cma.2006.06.020
Rabczuk T, Ren H (2017) A peridynamics formulation for quasi-static fracture and contact in rock. Engineering Geology 225:42–48, DOI: https://doi.org/10.1016/j.enggeo.2017.05.001
Rabczuk T, Zi G, Bordas S, Nguyen-Xuan H (2010) A simple and robust three-dimensional cracking-particle method without enrichment. Computer Methods in Applied Mechanics and Engineering 199(37–40):2437–2455, DOI: https://doi.org/10.1016/j.cma.2010.03.031
Ren H, Zhuang X, Cai Y, Rabczuk T (2016) Dual-horizon peridynamics. International Journal for Numerical Methods in Engineering 108(12): 1451–1476, DOI: https://doi.org/10.1002/nme.5257
Ren H, Zhuang X, Rabczuk T (2017) Dual-horizon peridynamics: A stable solution to varying horizons. Computer Methods in Applied Mechanics and Engineering 318:762–782, DOI: https://doi.org/10.1016/j.cma.2016.12.031
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 Analytical Methods in Geomechanics 37(18):3194–3212, DOI: https://doi.org/10.1002/nag.2185
Sahoo JP, Kumar J (2014) Stability of a circular tunnel in presence of pseudostatic seismic body forces. Tunnelling and Underground Space Technology 42:264–276, DOI: https://doi.org/10.1016/j.tust.2014.03.003
Soubra AH, Dias D Emeriault F, Kastner R (2008) Three-dimensional face stability analysis of circular tunnels by a kinematical approach. GeoCongress 2008, March 9–12, New Orleans, LA, USA, 894–901, DOI: https://doi.org/10.1061/40972(311)112
Subrin D, Wong H (2002) Stability of the front of a tunnel in a rubbing environment: A new 3D break mechanism. Rendus Mécanique 330(7):513–9, DOI: https://doi.org/10.1016/S1631-0721(02)01491-2
Vu-Bac N, Lahmer T, Zhuang X, Nguyen-Thoi T, Rabczuk T (2016) A software framework for probabilistic sensitivity analysis for computationally expensive models. Advances in Engineering Software 100:19–31, DOI: https://doi.org/10.1016/j.advengsoft.2016.06.005
Yang XL, Huang F (2011) Collapse mechanism of shallow tunnel based on nonlinear Hoek-Brown failure criterion. Tunnelling and Underground Space Technology 26(6):686–691, DOI: https://doi.org/10.1016/j.tust.2011.05.008
Yang XL, Wang JM (2011) Ground movement prediction for tunnels using simplified procedure. Tunnelling and Underground Space Technology 26(3):462–471, DOI: https://doi.org/10.1016/j.tust.2011.01.002
Yang XL, Yin JH (2004) Slope stability analysis with nonlinear failure criterion. Journal of Engineering Mechanics 130(3):267–273, DOI: https://doi.org/10.1061/(ASCE)0733-9399(2004)130:3(267)
Yang XL, Yin JH (2005) Upper bound solution for ultimate bearing capacity with a modified Hoek-Brown failure criterion. International Journal of Rock Mechanics and Mining Sciences 42(4):550–560, DOI: https://doi.org/10.1016/j.ijrmms.2005.03.002
Zhong JH, Yang XL (2022) Pseudo-dynamic stability of rock slope considering Hoek-Brown strength criterion. Acta Geotechnica, DOI: https://doi.org/10.1007/s11440-021-01425-0
Acknowledgments
This manuscript was supported by the Fundamental Research Funds entitled “Pseudo-dynamic Stability of Tunnel Face Based on 3D Discretization Technique” for the Central Universities of Central South University.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Liu, J., Luo, WJ. & Liu, LL. Seismic Stability of 3D Tunnel Face considering Tensile Strength Cut-Off. KSCE J Civ Eng 26, 3620–3632 (2022). https://doi.org/10.1007/s12205-022-1967-3
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12205-022-1967-3