Abstract
The methods for calculating the elliptical cone’s geometric parameters of multiple elliptical cone sliders were improved by introducing expression of elliptical path in 3D space. This elliptical path is the intersecting line of a cone and inclined cutting plane. Based on upper-bound limit analysis method and an improved method, Sequential Quadratic Programming (SQP) method was employed to obtain optimal upper bound solutions of failure pressure. The effectiveness of this method was verified by a comparative analysis, and a detailed parametric study on the failure pressure and failure modes was presented. In this study, the stability and failure modes of tunnel face are significantly affected by internal friction angle φ and dimensionless parameter C/D for both active and passive failure; by contrast, dimensionless parameters γD/c and σs/c have small effects. It is also found that dimensionless parameters C/D and σs/c have no effect on the results if the failure region does not reach the ground surface.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Chambon, P. and Corté, J. (1994). “Shallow tunnels in cohesionless soil: Stability of tunnel face.” Journal of Geotechnical Engineering, Vol. 120, No. 7, pp. 1148–1165, DOI: 10.1061/(ASCE)0733-9410(1994) 120:7(1148).
Han, K. H., Zhang, C. P., and Zhang, D. L. (2016). “Upper-bound solutions for the face stability of a shield tunnel in multilayered cohesive–frictional soils.” Computers and Geotechnics, Vol. 79, pp. 1–9, DOI: 10.1016/j.compgeo.2016.05.018.
Leca, E. and Dormieux, L. (1990). “Upper and lower bound solutions for the face stability of shallow circular tunnels in frictional material.” Geotechnique, Vol. 40, No. 4, pp. 581–606, DOI: 10.1680/geot.1990.40.4.581.
Li, D. J., Zhao, L. H., Yang, F., and Cheng, X. (2016). “Three-dimensional stability analysis of passive failure on shallow tunnel face based on the nonlinear failure criterion.” Chinese Journal of Rock Mechanics and Engineering, Vol. 35, No. 4, pp. 743–752, DOI: 10.13722/j.cnki.jrme.2015.0376.
Mollon, G., Dias, D., and Soubra, A. H. (2009). “Probabilistic analysis and design of circular tunnels against face stability.” International Journal of Geomechanics, Vol. 9, No. 6, pp. 237–249, DOI: 10.1061/ASCE1532-364120099:6237.
Mollon, G., Dias, D., and Soubra, A. H. (2010). “Face stability analysis of circular tunnels driven by a pressurized shield.” Journal of Geotechnical and Geoenvironmental Engineering, Vol. 136, No. 1, pp. 215–229, DOI: 10.1061/(ASCE)GT.1943-5606.0000194.
Mollon, G., Dias, D., and Soubra, A. H. (2011). “Rotational failure mechanisms for the face stability analysis of tunnels driven by a pressurized shield.” International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 35, No. 12, pp. 1363–1388, DOI: 10.1002/nag.962.
Mollon, G., Dias, D., and Soubra, A. H. (2013). “Range of the safe retaining pressures of a pressurized tunnel face by a probabilistic approach.” Journal of Geotechnical and Geoenvironmental Engineering, Vol. 139, No. 11, pp. 1954–1967, DOI: 10.1061/(ASCE)GT.1943-5606.0000911.
Senent, S. and Jimenez, R. (2015). “A tunnel face failure mechanism for layered ground, considering the possibility of partial collapse.” Tunnelling and Underground Space Technology, Vol. 47, pp. 182–192, DOI: 10.1016/j.tust.2014.12.014.
Sloan, S. W. (2013). “Geotechnical stability analysis.” Géotechnique, Vol. 63, No. 7, pp. 531–572, DOI: 10.1680/geot.12.RL.001.
Soubra, A. H., Dias, D., and Kastner, R. (2008). “Three-dimensional face stability analysis of circular tunnels by a kinematical approach.” GeoCongress, Vol. 30, No. 5, pp. 894–901, DOI: 10.1061/40972 (311)112.
Tang, X. W., Liu, W., Albers, B., and Savidis, S. (2014). “Upper bound analysis of tunnel face stability in layered soils.” Acta Geotechnica, Vol. 9, No. 4, pp. 661–671, DOI: 10.1007/s11440-013-0256-1.
Yang, F., Zhang, J., Zhao, L. H., and Yang, J. S. (2016). “Upper-bound finite element analysis of stability of tunnel face subjected to surcharge loading in cohesive-frictional soil.” KSCE Journal of Civil Engineering, Vol. 20, No. 6, pp. 2270–2279, DOI: 10.1007/s12205-015-0067-z.
Zhang, C. P., Han, K. H., and Zhang, D. L. (2015). “Face stability analysis of shallow circular tunnels in cohesive–frictional soils.” Tunnelling and Underground Space Technology, Vol. 50, pp. 345–357, DOI: 10.1016/j.tust.2015.08.007.
Zhang, J., Yang, F., and Liu, Z. (2014). “Three-dimensional limit analysis of blow-out failure modes of shallow shield tunnels.” Chinese Journal of Geotechnical Engineering, Vol. 36, No. 7, pp. 1344–1349, DOI: 10.11779/CJGE201407019.
Zhao, L. H., Li, D. J., Li, L., Yang, F., Cheng, X., and Luo, W. (2017). “Three-dimensional stability analysis of a longitudinally inclined shallow tunnel face.” Computers and Geotechnics, Vol. 87, pp. 32–48, DOI: 10.1016/j.compgeo.2017.01.015.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhao, L., Li, D., Yang, F. et al. Dimensionless Parameter Diagrams for the Active and Passive Stability of a Shallow 3D Tunnel Face. KSCE J Civ Eng 23, 866–878 (2019). https://doi.org/10.1007/s12205-018-5835-0
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12205-018-5835-0