Abstract
Face bolting has been widely utilized to enhance the stability of tunnel face, particularly in soft soil tunnels. However, the influence of bolt reinforcement and its layout on tunnel face stability has not been systematically studied. Based on the theory of linear elastic mechanics, this study delved into the specific mechanisms of bolt reinforcement on the tunnel face in both horizontal and vertical dimensions. It also identified the primary failure types of bolts. Additionally, a design approach for tunnel face bolts that incorporates spatial layout was established using the limit equilibrium method to enhance the conventional wedge-prism model. The proposed model was subsequently validated through various means, and the specific influence of relevant bolt design parameters on tunnel face stability was analyzed. Furthermore, design principles for tunnel face bolts under different geological conditions were presented. The findings indicate that bolt failure can be categorized into three stages: tensile failure, pullout failure, and comprehensive failure. Increasing cohesion, internal friction angle, bolt density, and overlap length can effectively enhance tunnel face stability. Due to significant variations in stratum conditions, tailored design approaches based on specific failure stages are necessary for bolt design.
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Abbreviations
- A :
-
Cross-section area of the borehole
- A dowel :
-
Cross-section area of the bolt
- A t :
-
Cross-section area of the tunnel
- B :
-
Width of the tunnel
- C :
-
Buried depth of the tunnel
- c :
-
Cohesion force of soil
- c collapse :
-
Limit cohesion at the occur of face collapse
- dA :
-
Lateral area of the soil slice
- dF :
-
Incremental axis force of the bolt
- dG :
-
Gravity of the soil slice
- dN :
-
Normal stress on the sliding surface
- dS :
-
Horizontal resistance
- dT :
-
Tangential stress along the sliding surface
- dT fb :
-
Vertical resistance
- dT s :
-
Shear stress between the soil slice of the reinforced wedge and its adjacent soil mass on both sides of the excavated surface
- d s :
-
Displacement of the sliding wedge on the sliding surface
- d h :
-
Horizontal displacement
- d v :
-
Vertical displacement
- d hole :
-
Diameter of the borehole
- d bolt+grout :
-
Diameter of the bolt and grout
- E :
-
Equivalent Young’s module of the integral of the bolts and grouting
- E bolt :
-
Equivalent Young’s module of the bolts
- E grout :
-
Elastic module of the grout
- E soil :
-
Elastic module of the soil
- E s :
-
Soil reaction modulus
- F :
-
Axis force of the bolt
- F w and F ow :
-
Axial force of bolts embedded within the wedge and outside of the wedge
- F test :
-
Pullout load
- H :
-
Height of the tunnel
- I :
-
Moment of inertia of the bolts
- J :
-
Inertial moment of the bolt section
- k :
-
Foundation coefficient of the soil
- L test :
-
Length of the bolt
- l us :
-
Unsupported span of the tunnel
- l w and l ow :
-
Length of the glass fiber bolt inside the sliding wedge and outside of the wedge
- l ol :
-
Overlap length of the glass fiber bolt
- M bolt :
-
Moment at any point of the bolt
- n :
-
Density of face bolt
- n r :
-
Minimum required face bolt density
- P hole :
-
Area of perimeter of the borehole
- P max :
-
Limit yield pressure of the rock pertaining to localized compression
- S dowel :
-
Static moment of half cross-section of the bolt
- T bolt :
-
Shear force at any point of the bolt
- u :
-
Relative movement between the grouting and soil in the analyzed differential element
- u w and u ow :
-
Movement of bolts embedded within the wedge and outside of the wedge
- u test :
-
Movement of the bolt
- V :
-
Counter-stress exerted by the lower part of the soil slice
- w :
-
Inclination angle of the wedge
- z :
-
Distance from the soil slice to the bottom of the wedge
- z 1 :
-
At which the shear resistance from parts within the wedge and outside the wedge would be the same
- z 2 :
-
When a specific bolt is deployed above this elevation, it would be embedded in the wedge totally and not contribute to the face stability
- β :
-
The inverse of the characteristic length of the bolt
- β c :
-
Shear stiffness at the interface between the grouting and soil
- γ :
-
Unit weight of the soil slice
- φ :
-
Internal friction angle of soil
- φ collapse :
-
Limit frictional angle at the occur of face collapse
- λ :
-
Lateral pressure coefficient
- λ w :
-
Lateral stress ratio for the wedge
- τ :
-
Shear stress at the interface between grouting and soil
- τ max :
-
Maximum value of shear stress at the interface between grouting and soil
- τ w and τ ow :
-
Shear stress of bolts embedded within the wedge and outside of the wedge
- ε x :
-
Strain at the interface between the grouting and soil
- σ prism :
-
Vertical soil pressure
- σ x :
-
Axis stress of the bolt
- σ y :
-
Tensile strength of the bolt
- σ z :
-
Vertical soil stress
- ϕ dowel :
-
Diameter of the bolt
References
Ahmed M, Iskander M (2012) Evaluation of tunnel face stability by transparent soil models. Tunn Undergr Sp Tech 27(1): 101–110. https://doi.org/10.1016/j.tust.2011.08.001
Alagha A, Chapman SN, David N (2019) Numerical modelling of tunnel face stability in homogeneous and layered soft ground. Tunn Undergr Sp Tech 94, 103096. https://doi.org/10.1016/j.tust.2019.103096
Anagnostou G, Kovári K (1996) Face stability conditions with earth-pressure-balanced shields. Tunn Undergr Sp Tech 11(2): 165–173. https://doi.org/10.1016/0886-7798(96)00017-X
Anagnostou G, Perazzelli P (2015) Analysis method and design charts for bolt reinforcement of the tunnel face in cohesive-frictional soils. Tunn Undergr Sp Tech 47(3): 162–181. https://doi.org/10.1016/j.tust.2014.10.007
Anagnostou G, Serafeimidis K (2007) The dimensioning of tunnel face reinforcemen. Underground Space–the 4th Dimension of Metropolises. ITA World Tunnel Congress, Prague, 2007, pp 291–296.
Anagnostou G (2012) The contribution of horizontal arching to tunnel face stability. Geotechnik 35(1): 34–44. https://doi.org/10.1002/gete.201100024
Anagnostou G, Perazzelli P (2013) The stability of a tunnel face with a free span and a non - uniform support. Geotechnik 36(1): 40–50. https://doi.org/10.1002/gete.201200014
Cao LQ, Zhang, DL, Fang Q, et al. (2020) Movements of ground and existing structures induced by slurry pressure-balance tunnel boring machine (SPB TBM) tunnelling in clay. Tunn Undergr Sp Tech 97. https://doi.org/10.1016/j.tust.2019.103278
Chambon P, Corte JF (1994) Shallow tunnels in cohesionless soil: stability of tunnel face. J Geotech Eng 120(7): 1148–1165. https://doi.org/10.1061/(ASCE)0733-9410(1994)120:7(1148)
Chen GH, Zou JF, **ang XY, et al. (2021) Stability assessments of reinforced tunnel face using improved homogenization approach. Int J Geomech 21(10): 04021183. https://doi.org/10.1061/(ASCE)GM.1943-5622.000215
Chen RP, Tang LJ, Yin XS, et al. (2015) An improved 3D wedge-prism model for the face stability analysis of the shield tunnel in cohesionless soils. Acta Geotech 10(5): 683–692. https://doi.org/10.1007/s11440-014-0304-5
Chen RP, Li J, Kong LG, et al. (2013) Experimental study on face instability of shield tunnel in sand. Tunn Undergr Sp Tech 33: 12–21. https://doi.org/10.1016/j.tust.2012.08.001
Chen RP, Lin XT, Wu HN (2019) An analytical model to predict the limit support pressure on a deep shield tunnel face. Comput Geotech 115(11): 103174. https://doi.org/10.1016/j.compgeo.2019.103174
Chen RP, Yin XS, Tang LJ, et al. (2018) Centrifugal model tests on face failure of earth pressure balance shield induced by steady state seepage in saturated sandy silt ground. Tunn Undergr Sp Tech 81: 315–325. https://doi.org/10.1016/j.tust.2018.06.031
Di PC, Flessati L, Frigerio G, et al. (2018) Experimental investigation of the time-dependent response of unreinforced and reinforced tunnel faces in cohesive soils. Acta Geotech 13(3): 651–670. https://doi.org/10.1007/s11440-017-0573-x
Guan BS, Zhao Y (2011) Construction Technology of Tunnel in Weak Surrounding Rock: China Communications Press.
Horn M (1961) Horizontal earth pressure on perpendicular tunnel face. Hungarian National Conference of the Foundation Engineer Industry, Budapest.(In Hungarian), 1961.
Ibrahim E, Soubra AH, Mollon G, et al. (2015) Three-dimensional face stability analysis of pressurized tunnels driven in a multilayered purely frictional medium. Tunn Undergr Sp Tech 49: 18–34. https://doi.org/10.1016/j.tust.2015.04.001
Idinger G, Aklik P, Wu W, et al. (2011) Centrifuge model test on the face stability of shallow tunnel. Acta Geotech 6(2): 105–117. https://doi.org/10.1007/s11440-011-0139-2
Jiang M, Bo Y, Wang H, et al. (2023) Study on the reinforcement mechanism of grouted bolts with or without prestress via the hybrid DEM-FDM method. Transp Geotech 40: 100967. https://doi.org/10.1016/j.trgeo.2023.100967
Kamata H, Mashimo H (2003) Centrifuge model test of tunnel face reinforcement by bolting. Tunn Undergr Sp Tech 18(2–3): 205–212. https://doi.org/10.1016/S0886-7798(03)00029-4
Kavvadas M, Prountzopoulos G (2009) 3D Analyses of tunnel face reinforcement using fibreglass nails. Eur: Tun 2009 Conference. Bochum, 2009.
Kirsch A (2010) Experimental investigation of the face stability of shallow tunnels in sand. Acta Geotech 5(1): 43–62. https://doi.org/10.1007/s11440-010-0110-7
Leca E, Dormieux L (1990) Upper and lower bound solutions for the face stability of shallow circular tunnels in frictional material. Géotechnique 40(4): 581–606. https://doi.org/10.1680/geot.1990.40.4.581
Li B, Hong Y, Gao B, et al. (2015) Numerical parametric study on stability and deformation of tunnel face reinforced with face bolts. Tunn Undergr Sp Tech 47: 73–80. https://doi.org/10.1016/j.tust.2014.11.008
Liang X, Ye F, Ouyang AH, et al. (2020) Theoretical analyses of the stability of excavation face of shield tunnel in Lanzhou Metro crossing beneath the Yellow River. Int J Geomech 20(11). https://doi.org/10.1061/(ASCE)GM.1943-5622.0001836
Lunardi P (2008) Design and construction of tunnels: Analysis of controlled deformations in rock and soils (ADECO-RS): Springer Science & Business Media.
Lunardi P, Bindi, Renzo (2004) The evolution of reinforcement of the advance core using fibre-glass elements. Gluckauf Forschungshefte 91–100.
Mollon G, Dias D, Soubra AH (2010) Face stability analysis of circular tunnels driven by a pressurized shield. J Geotech Geoenviron 136(1): 215–229. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000194
Mollon G, Dias D, Soubra AH (2011) Rotational failure mechanisms for the face stability analysis of tunnels driven by a pressurized shield. Int J Numer Anal Met 35(12): 1363–1388. https://doi.org/10.1002/nag.962
Murayama S, Endo M, Hashiba T, et al. (1966) Geotechnical aspects for the excavating performance of the shield machine. The 21st annual lecture in meeting of Japan Society of Civil Engineers, 1966, pp. 265.
Ng C, Lee G (2002) A three-dimensional parametric study of the use of soil nails for stabilising tunnel faces. Comput Geotech 29(8): 673–697. https://doi.org/10.1016/S0266-352X(02)00012-5
Oreste P, Spagnoli G (2020a) A simplified mathematical approach for the evaluation of the stabilizing forces applied by a passive cemented bolt to a sliding rock block. Tunn Undergr Sp Tech 103(11): 103459. https://doi.org/10.1016/j.tust.2020.103459
Oreste P, Spagnoli G (2020b) A simplified mathematical approach for the evaluation of the stabilizing forces applied by a passive cemented bolt to a sliding rock block. Tunn Undergr Sp Tech 103: 103459. https://doi.org/10.1016/j.tust.2020.103459
Oreste P, Spagnoli G (2021) A probabilistic approach for the evaluation of the stabilizing forces of fully grouted bolts. Transp Geotech 28: 100516. https://doi.org/10.1016/j.trgeo.2021.100516
Oreste P (2009a) The dimensioning of dowels for the stabilization of potentially unstable rock blocks on the walls of underground chambers. Geotech Geol Eng 27(1): 53–69. https://doi.org/10.1007/s10706-008-9211-6
Oreste P (2009b) Face stabilisation of shallow tunnels using fibreglass dowels. Proceedings of the Institution of Civil Engineers-Geotechnical Engineering 162(2): 95–109.
Oreste P, Cravero M (2008) An analysis of the action of dowels on the stabilization of rock blocks on underground excavation walls. Rock Mech Rock Eng 41(6): 835–868. https://doi.org/10.1007/s00603-008-0162-2
Oreste P, Dias D (2012) Stabilisation of the excavation face in shallow tunnels using fibreglass dowels. Rock Mech Rock Eng 45(4): 499–517. https://doi.org/10.1007/s00603-012-0234-1
Pan QJ, Dias D (2017a) Safety factor assessment of a tunnel face reinforced by horizontal dowels. Eng Struct 142: 56–66. https://doi.org/10.1016/j.engstruct.2017.03.056
Pan QJ, Dias D (2017b) Upper-bound analysis on the face stability of a non-circular tunnel. Tunn Undergr Sp Tech 62: 96–102. https://doi.org/10.1016/j.tust.2016.11.010
Pan QJ, Dias D (2016) Face stability analysis for a shield-driven tunnel in anisotropic and nonhomogeneous soils by the kinematical approach. Int J Geomech 16(3): 04015076. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000569
Paternesi A, Schweiger HF, Scarpelli G (2017) Numerical analyses of stability and deformation behavior of reinforced and unreinforced tunnel faces. Comput Geotech 88: 256–266. https://doi.org/10.1016/j.compgeo.2017.04.002
Peila D (1994) A theoretical study of reinforcement influence on the stability of a tunnel face. Geotech Geol Eng 12(3): 145–168. https://doi.org/10.1007/BF00426984
Perazzelli P, Anagnostou G (2013) Stress analysis of reinforced tunnel faces and comparison with the limit equilibrium method. Tunn Undergr Sp Tech 38: 87–98. https://doi.org/10.1016/j.tust.2013.05.008
Perazzelli P, Anagnostou G (2017) Analysis method and design charts for bolt reinforcement of the tunnel face in purely cohesive soils. J Geotech Geoenviron 143(9): 04017046. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001702
Perazzelli P, Cimbali G, Anagnostou G (2017) Stability under seepage flow conditions of a tunnel face reinforced by bolts. Pro Eng 191(5): 215–224. https://doi.org/10.1016/j.proeng.2017.05.174
Qian ZH, Zou JF, Pan QJ, et al. (2019) Safety factor calculations of a tunnel face reinforced with umbrella pipes: A comparison analysis. Eng Struct 199: 109639. https://doi.org/10.1016/j.engstruct.2019.109639
Shin JH, Choi YK, Kwon OY, et al. (2008) Model testing for pipe-reinforced tunnel heading in a granular soil. Tunn Undergr Sp Tech 23(3): 241–250. https://doi.org/10.1016/j.tust.2007.04.012
Takano D, Otani J, Nagatani H, et al. (2006) Application of x-ray CT on boundary value problems in geotechnical engineering: research on tunnel face failure. In GeoCongress 2006: Geotechnical Engineering in the Information Technology Age. pp 1–6.
Terazaghi K (1965) Theoretical soil mechanics. John Wiley and Sons.
Ukritchon B, Keawsawasvong S (2017) Design equations for undrained stability of opening in underground walls. Tunn Undergr Sp Tech 70(11): 214–220. https://doi.org/10.1016/j.tust.2017.08.004
Vermeer PA, Ruse N, Marcher T (2002) Tunnel heading stability in drained ground. Felsbau 20(6): 8–18
Wang HN, **ao G, Jiang MJ, et al. (2018) Investigation of rock bolting for deeply buried tunnels via a new efficient hybrid DEM-Analytical model. Tunn Undergr Sp Tech 82: 366–379. https://doi.org/10.1016/j.tust.2018.08.048
Weng XL, Sun YF, Yan BH, et al. (2020) Centrifuge testing and numerical modeling of tunnel face stability considering longitudinal slope angle and steady state seepage in soft clay. Tunn Undergr Sp Tech 101: 103406. https://doi.org/10.1016/j.tust.2020.103406
Yokota Y, Yamamoto T (2011) Verification of reinforcing effects of a tunnel face reinforcement method by centrifuge model tests and numerical analysis. 12th ISRM Congress, 2011. OnePetro.
Yoo C, Shin HK (2003) Deformation behaviour of tunnel face reinforced with longitudinal pipes—laboratory and numerical investigation. Tunn Undergr Sp Tech 18(4): 303–319. https://doi.org/10.1016/S0886-7798(02)00101-3
Yu L, Zhang DL, Fang Q, et al. (2019) Surface settlement of subway station construction using pile-beam-arch approach. Tunn Undergr Sp Tech 90: 340–356. https://doi.org/10.1016/j.tust.2019.05.016
Zhang X, Wang MN, Lyu C, et al. (2022) Experimental and numerical study on tunnel faces reinforced by horizontal bolts in sandy ground. Tunn Undergr Sp Tech 123: 104412. https://doi.org/10.1016/j.tust.2022.104412
Zhang X, Wang MN, Wang ZL, et al. (2020a) A limit equilibrium model for the reinforced face stability analysis of a shallow tunnel in cohesive-frictional soils. Tunn Undergr Sp Tech 105: 103562. https://doi.org/10.1016/j.tust.2020.103562
Zhang X, Wang MN, Wang ZL, et al. (2020b) Stability analysis model for a tunnel face reinforced with bolts and an umbrella arch in cohesive-frictional soils. Comput Geotech 124(8): 103635. https://doi.org/10.1016/j.compgeo.2020.103635
Zhang ZQ, Shi XQ, Wang B, et al. (2018) Stability of NATM tunnel faces in soft surrounding rocks. Comput Geotech 96: 90–102. https://doi.org/10.1016/j.compgeo.2017.10.009
Acknowledgments
This work is financially supported by the Fundamental Research Funds for the Central Universities, CHD (300102212706), the National Natural Science Foundation of China [Grant No. 52108360], the Science and Technology Project of Department of Transportation of Yunnan Province (No. YJKJ [2019]59).
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TIAN Chongming, JIANG Yin: methodology, data curation, writing - review and editing. YE Fei, OUYANG Aohui: conceptualization, writing - original draft, validation, investigation. HAN **ngbo: investigation, resources. SONG Guifeng: funding acquisition.
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Conflict of Interest: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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Tian, C., Jiang, Y., Ye, F. et al. Stability analysis of tunnel face reinforced with face bolts. J. Mt. Sci. 21, 2445–2461 (2024). https://doi.org/10.1007/s11629-023-8400-3
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DOI: https://doi.org/10.1007/s11629-023-8400-3