Seismic stability analysis of tunnel face in inclined layered soils with unsaturated flow

Abstract

The tunnel face stability is investigated in inclined layered soils under steady unsaturated seepage and seismic loading. The rigorous estimate of the maximum face pressure is provided during tunnel excavation. The modified pseudo-dynamic method is applied to capture the spatial and temporal characteristics of seismic forces. A spatial distribution formula for suction stress under steady seepage conditions is derived for inclined layered soils. The study examines how inclined stratification influences the shape of failure mechanisms, the suction head profile, and variations in seismic acceleration. The spatial and temporal changes in suction stress and seismic loading are integrated into the energy equilibrium formulation based on a three-dimensional discretized failure model, and the critical face support pressure can be calculated via an integrated optimization strategy. The distributions of seismic acceleration ratios are obtained under various dynamic parameter conditions and the spatial variation of suction stress in the soil ahead of the tunnel face under different hydraulic hysteresis scenarios. The proposed analytical approach is compared with previous research, and the differences in results under different representations of seismic waves are also discussed. The research results can provide a valid framework to evaluate the influence of seismic excitation, steady-unsaturated infiltration, hydraulic hysteresis, and inclined stratification on tunnel face stability.

Keywords

stability of tunnel face / inclined layered soils / pseudo-dynamic approach / steady unsaturated seepage / hydraulic hysteresis

References

[1] Chambon P, Corté J F. Shallow tunnels in cohesionless soil: Stability of tunnel face [J]. Journal of Geotechnical Engineering. 1994, 120(7): 1148-1165

[2] Sterpi D, Cividini A, Sakurai A, et al. . Laboratory model tests and numerical analysis of shallow tunnels [C]. ISRM EUROCK. 1996ISRM-EUROCK-1996-086

[3] Kamata H, Mashimo H. Centrifuge model test of tunnel face reinforcement by bolting [J]. Tunnelling and Underground Space Technology. 2003, 18(23): 205-212

[4] Jin D-l, Zhang Z-y, Yuan D-J. Effect of dynamic cutterhead on face stability in EPB shield tunneling [J]. Tunnelling and Underground Space Technology. 2021, 110: 103827

[5] Paternesi A, Schweiger H F, Scarpelli G. Numerical analyses of stability and deformation behavior of reinforced and unreinforced tunnel faces [J]. Computers and Geotechnics. 2017, 88: 256-266

[6] Cheng C, Jia P-j, Ni P-p, et al. . Upper bound analysis of longitudinally inclined EPB shield tunnel face stability in dense sand strata [J]. Transportation Geotechnics. 2023, 41: 101031

[7] Yang X L, Wang J M. Ground movement prediction for tunnels using simplified procedure [J]. Tunnelling and Underground Space Technology. 2011, 26(3): 462-471

[8] HORN N. Horizontaler erddruck auf senkrechte abschlussflächen von tunnelröhren [J]. Landeskonferenz Der Ung-Arischen Tiefbauindustrie, 1961: 7–16.

[9] Anagnostou G, Kovári K. The face stability of slurry-shield-driven tunnels [J]. Tunnelling and Underground Space Technology. 1994, 9(2): 165-174

[10] Oreste P P, Dias D. Stabilisation of the excavation face in shallow tunnels using fibreglass dowels [J]. Rock Mechanics and Rock Engineering. 2012, 45(4): 499-517

[11] Leca E, Dormieux L. Upper and lower bound solutions for the face stability of shallow circular tunnels in frictional material [J]. Géotechnique. 1990, 40(4): 581-606

[12] Soubra A H. Three-dimensional face stability analysis of shallow circular tunnels [C]. ISRM International Symposium. 2000ISRM-IS-2000-594

[13] CHAMBON, P. CORTE, J F. Stability of the tunnel face in a frictional medium: a kinematic approach in limit analysis [J]. Revue Française de Géotechnique, 1990(51): 51–59. DOI: https://doi.org/10.1051/geotech/1990051051. (in French)

[14] Mollon G, Dias D, Soubra A H. Rotational failure mechanisms for the face stability analysis of tunnels driven by a pressurized shield [J]. International Journal for Numerical and Analytical Methods in Geomechanics. 2011, 35(12): 1363-1388

[15] Li T Z, Yang X L. Three-dimensional face stability of shallow-buried tunnels with tensile strength cut-off [J]. Computers and Geotechnics. 2019, 110: 82-93

[16] Hou C-t, Yang X-li. Seismic stability of 3D tunnel face considering tensile strength cut-off [J]. KSCE Journal of Civil Engineering. 2020, 24(7): 2232-2243

[17] Yang X L, Huang F. Collapse mechanism of shallow tunnel based on nonlinear Hoek–Brown failure criterion [J]. Tunnelling and Underground Space Technology. 2011, 26(6): 686-691

[18] Li T Z, Yang X L. Face failure potential of a circular tunnel driven in anisotropic and nonhomogeneous soils [J]. International Journal of Geomechanics. 2020, 20(8): 04020112

[19] Hou C-t, Yang X-li. Three-dimensional face stability of tunnels in unsaturated soils with nonlinear soil strength [J]. International Journal of Geomechanics. 2021, 21(4): 06021006

[20] Li T Z, Yang X L. An efficient uniform design for Kriging-based response surface method and its application [J]. Computers and Geotechnics. 2019, 109: 12-22

[21] Yang X-l, Yin J-H. Slope stability analysis with nonlinear failure criterion [J]. Journal of Engineering Mechanics. 2004, 130(3): 267-273

[22] Yang X-l, Yin J-H. Upper bound solution for ultimate bearing capacity with a modified Hoek-Brown failure criterion [J]. International Journal of Rock Mechanics and Mining Sciences. 2005, 42(4): 550-560

[23] Yang X L, Li L, Yin J H. Seismic and static stability analysis for rock slopes by a kinematical approach [J]. Géotechnique. 2004, 54(8): 543-549

[24] Shan J-t, Wu Y-m, Yang X-li. Three-dimensional stability of two-step slope with crack considering temperature effect on unsaturated soil [J]. Journal of Central South University. 2025, 32(3): 1060-1079

[25] Khalili N, Khabbaz M H. A unique relationship for χ for the determination of the shear strength of unsaturated soils [J]. Géotechnique. 2002, 52(1): 76-77

[26] Fredlund D G, Morgenstern N R, Widger R A. The shear strength of unsaturated soils [J]. Canadian Geotechnical Journal. 1978, 15(3): 313-321

[27] Likos W J, Lu N. Hysteresis of capillary stress in unsaturated granular soil [J]. Journal of Engineering Mechanics. 2004, 130(6): 646-655

[28] Likos W J, Wayllace A, Godt J, et al. . Modified direct shear apparatus for unsaturated sands at low suction and stress [J]. Geotechnical Testing Journal. 2010, 33(4): 286-298

[29] Li T Z, Yang X L. Stability of plane strain tunnel headings in soils with tensile strength cut-off [J]. Tunnelling and Underground Space Technology. 2020, 95: 103138

[30] Hou C T, Yang X L. 3D stability analysis of tunnel face with influence of unsaturated transient flow [J]. Tunnelling and Underground Space Technology. 2022, 123: 104414

[31] Hou C-t, Yang X-l, Liu M-f, et al. . Stability assessment of a non-circular tunnel face with tensile strength cut-off subject to seepage flows: A comparison analysis [J]. Computers and Geotechnics. 2023, 163: 105764

[32] Karray M, Hussien M N, Delisle M C, et al. . Framework to assess pseudo-static approach for seismic stability of clayey slopes [J]. Canadian Geotechnical Journal. 2018, 55(12): 1860-1876

[33] Qiu W-g, Li B-t, Gong L, et al. . Seismic capacity assessment of cracked lining tunnel based on the pseudo-static method [J]. Tunnelling and Underground Space Technology. 2020, 97: 103281

[34] Steedman R S, Zeng X. The influence of phase on the calculation of pseudo-static earth pressure on a retaining wall [J]. Géotechnique. 1990, 40(1): 103-112

[35] Qin C-b, Chian S C, Gazetas G. Kinematic analysis of seismic slope stability with discretisation technique and pseudo-dynamic approach: A new perspective [J]. Géotechnique. 2019, 69(11): 1031-1033

[36] Zhong J-h, Yang X-li. Kinematic analysis of the three-dimensional stability for tunnel faces by pseudodynamic approach [J]. Computers and Geotechnics. 2020, 128: 103802

[37] Xu S, Liu J, Yang X-li. Pseudo-dynamic analysis of a 3D tunnel face in inclined weak strata [J]. Underground Space. 2023, 12: 156-166

[38] Tang X-w, Liu W, Albers B, et al. . Upper bound analysis of tunnel face stability in layered soils [J]. Acta Geotechnica. 2014, 9(4): 661-671

[39] Li T Z, Yang X L. New approach for face stability assessment of tunnels driven in nonuniform soils [J]. Computers and Geotechnics. 2020, 121: 103412

[40] Shahmoradi J, Salari Rad H, Roghanchi P. Face stability analysis for the Earth pressure balance method in nonhomogeneous inclined soil layers: Case study [J]. International Journal of Geomechanics. 2020, 20(10): 05020005

[41] Man J-h, Huang H-w, Ai Z-y, et al. . Analytical model for tunnel face stability in longitudinally inclined layered rock masses with weak interlayer [J]. Computers and Geotechnics. 2022, 143: 104608

[42] Tu S-q, Li W, Zhang C-p, et al. . Seepage effect on progressive failure of shield tunnel face in granular soils by coupled continuum-discrete method [J]. Computers and Geotechnics. 2024, 166: 106009

[43] Wu H-j, Liao H, Wu C-G. Stability of 3D tunnel face under steady unsaturated seepage coupled multi-layer soil suction head distributions [J]. Alexandria Engineering Journal. 2025, 117: 609-623

[44] Choudhury D, Nimbalkar S. Seismic passive resistance by pseudo-dynamic method [J]. Géotechnique. 2005, 55(9): 699-702

[45] Ghosh P. Seismic active earth pressure behind a nonvertical retaining wall using pseudo-dynamic analysis [J]. Canadian Geotechnical Journal. 2008, 45(1): 117-123

[46] Basha B M, Babu G L S. Seismic reliability assessment of internal stability of reinforced soil walls using the pseudo-dynamic method [J]. Geosynthetics International. 2011, 18(5): 221-241

[47] Ghosh S, Saha A. Active earth pressure on retaining wall supporting c-Φ backfill considering Rayleigh wave [J]. Indian Geotechnical Journal. 2015, 45(1): 121-134

[48] Bellezza I. A new pseudo-dynamic approach for seismic active soil thrust [J]. Geotechnical and Geological Engineering. 2014, 32(2): 561-576

[49] Li Z W, Yang X L, Li T Z. Face stability analysis of tunnels under steady unsaturated seepage conditions [J]. Tunnelling and Underground Space Technology. 2019, 93: 103095

[50] Subrin D, Wong H. Tunnel face stability in frictional material: a new 3D failure mechanism [J]. Comptes Rendus Mécanique. 2002, 330(7): 513-519 in French)

[51] Kramer S L, Stewart J P. Geotechnical earthquake engineering [M]. 2024, Boca Raton, CRC Press

[52] Schnellmann R. Uncertainties in the estimation of unsaturated shear strength from soil-water characteristic curve [D]. 2015, Singapore, Nanyang Technological University

[53] Kool J B, Parker J C. Development and evaluation of closed-form expressions for hysteretic soil hydraulic properties [J]. Water Resources Research. 1987, 23(1): 105-114

[54] Chen P, Mirus B, Lu N, et al. . Effect of hydraulic hysteresis on stability of infinite slopes under steady infiltration [J]. Journal of Geotechnical and Geoenvironmental Engineering. 2017, 143(9): 04017041

[55] Faybishenko B A. Hydraulic behavior of quasi-saturated soils in the presence of entrapped air: Laboratory experiments [J]. Water Resources Research. 1995, 31(10): 2421-2435

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