Interplay of Tunnel Geometry and Shallow Foundation Stability in Rock: Comparative Insights into Failure Modes
Publication: International Journal of Geomechanics
Volume 24, Issue 9
Abstract
This study delved into the intricate relationship between tunnel geometry and the stability of shallow foundations. It investigated the influence of various tunnel geometries on the behavior of a strip footing (width, B) subjected to uniform loading positioned above a single/dual-tunnel system. The analysis encompassed three different tunnel geometries, namely, circular, square, and horseshoe, for both single- and dual-tunnel configurations. The primary focus of the study was quantifying the stability number, Nv, as a measure of tunnel’s impact on footing stability using finite-element analysis. For the single-tunnel configuration, the study examined the vertical depth between the footing base and the tunnel crest (Z) and the horizontal distance between the central vertical axis of the footing and the center of the tunnel (X). Additionally, in the case of the dual-tunnel configuration, the influence of horizontal spacing between the two tunnels (S) on Nv and also the impact of asymmetrical shapes of tunnels with three different cases, i.e., Case I (circular and square-shaped tunnels), Case II (circular and horseshoe-shaped tunnels), and Case III (square- and horseshoe-shaped tunnels), were studied. The findings of this study emphasize that tunnel geometries have a substantial impact on Nv, especially when the Z/B ratio is less than 3 for both tunnel configurations. However, when Z/B exceeds 3, the influence of tunnel geometries on Nv becomes negligible. Furthermore, in the case of asymmetrical tunnel configurations, Case II consistently exhibits the highest stability number (Nv), followed by Case I and Case III, across all combinations of S/B and Z/B values. Additionally, the study identifies zones of plastic stress deformation associated with different tunnel geometries. It underscores the importance of implementing supplementary support systems in cases where these deformations are prominent, ensuring the overall stability of the footing–tunnel system.
Practical Applications
In the dynamic realm of underground space utilization, ensuring the safety of structures above and below ground is paramount. With the increasing construction of tunnels near existing buildings, it is crucial to prioritize their protection and assess their suitability for use. In response to contemporary challenges, this study investigated the impact of nearby tunnels on load-bearing capacity of structures. It delved into how the shape of tunnels influences the behavior of surrounding structures, taking into account the regions of the rock mass affected by such interactions. Additionally, the study provided insights into the practical implications of planning and constructing asymmetrical tunnels—a common scenario where new tunnels with varying shapes are built near pre-existing ones. The findings of this research offer practical applications in determining the load-carrying capacity of shallow foundations in the vicinity of tunnels with diverse configurations, shapes, and locations from the foundation. The special significance of this research lies in its ability to guide the design of surrounding structures and identify specific zones around tunnels that require attention, ultimately contributing valuable insights for establishing suitable support systems.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All data, models, and codes generated or used during the study appear in the published paper.
Notation
The following symbols are used in this paper:
- a,s
- generalized Hoek–Brown failure criterion constants for the rock mass;
- B
- footing width (m);
- D
- disturbance factor of the rock mass;
- d1 and d2
- diameters of tunnels (circular) (m);
- H
- height of the tunnel (square, horseshoe) (m);
- mb
- material constant for rock mass strength;
- mi
- material constant;
- Nv
- stability number;
- Qc
- imposed uniformly distributed load;
- qu
- ultimate bearing capacity of the footing with an underlying tunnel (kPa);
- ultimate bearing capacity of the footing without an underlying tunnel (kPa);
- R2
- coefficient of determination;
- Rf
- reduction factor;
- S/B
- normalized horizontal spacing between tunnels;
- S
- horizontal spacing between two tunnels (m);
- T1 and T2
- dual tunnels;
- W
- width of the tunnel (square, horseshoe) (m);
- X/B
- normalized horizontal distance of a single tunnel;
- X
- horizontal distance for the single tunnel configuration from the ground level (m);
- Z/B
- normalized vertical depth of the tunnel;
- Z
- vertical depth from the tunnel crest to the ground surface (roof) (m);
- Γ
- unit weight of the rock mass (kN/m3);
- σci
- uniaxial compressive strength (kPa);
- maximum effective principal stress (kPa); and
- minimum effective principal stress (kPa).
References
Abbo, A. J., D. W. Wilson, S. W. Sloan, and A. V. Lyamin. 2013. “Undrained stability of wide rectangular tunnels.” Comput. Geotech. 53: 46–59. https://doi.org/10.1016/j.compgeo.2013.04.005.
Athar, M. F., M. Zaid, and M. R. Sadique. 2019. “Stability of different shapes of tunnels in weathering stages of basalt.” In Proc., of National Conf. on Advances in Structural Technology, 320–327. Sichar, India: NIT Silchar.
Badie, A., and M. C. Wang. 1984. “Stability of spread footing above void in clay.” J. Geotech. Eng. 110 (11): 1591–1605. https://doi.org/10.1061/(ASCE)0733-9410(1984)110:11(1591).
Banerjee, S. K., and D. Chakraborty. 2018. “Stability analysis of a circular tunnel underneath a fully liquefied soil layer.” Tunnelling Underground Space Technol. 78: 84–94. https://doi.org/10.1016/j.tust.2018.04.024.
Baus, R. L., and M. C. Wang. 1983. “Bearing capacity of strip footing above void.” J. Geotech. Eng. 109: 1–14. https://doi.org/10.1061/(ASCE)0733-9410(1983)109:1(1).
Chauhan, V. B., P. Kumar, and S. Keawsawasvong. 2023. “Limit analysis solution for ultimate bearing capacity of footing resting on the rock mass with a circular void subjected to line loading.” Indian Geotech. J. 53: 334–347. https://doi.org/10.1007/s40098-022-00676-2.
Chen, H. L., Z. C. Xia, J. N. Zhou, H. L. Fan, and F. N. Jin. 2013. “Dynamic responses of underground arch structures subjected to conventional blast loads: Curvature effects.” Arch. Civ. Mech. Eng. 13: 322–333. https://doi.org/10.1016/j.acme.2013.04.004.
Ciria, H., J. Peraire, and J. Bonet. 2008. “Mesh adaptive computation of upper and lower bounds in limit analysis.” Int. J. Numer. Methods Eng. 75 (8): 899–944. https://doi.org/10.1002/nme.2275.
Craig, R. 2004. Craig's soil mechanics. 7th ed. London, UK: CRC Press.
Dancygier, A. N., Y. S. Karinski, and A. Chacha. 2016. “A model to assess the response of an arched roof of a lined tunnel.” Tunnelling Underground Space Technol. 56: 211–225. https://doi.org/10.1016/j.tust.2016.03.009.
Davis, T., D. Healy, A. Bubeck, and R. Walker. 2017. “Stress concentrations around voids in three dimensions: The roots of failure.” J. Struct. Geol. 102: 193–207. https://doi.org/10.1016/j.jsg.2017.07.013.
Fam, M. A., G. Cascante, and M. B. Dusseault. 2002. “Large and small strain properties of sands subjected to local void increase.” J. Geotech. Geoenviron. Eng. 128 (12): 1018–1025. https://doi.org/10.1061/(ASCE)1090-0241(2002)128:12(1018).
Hjiaj, M., A. V. Lyamin, and S. W. Sloan. 2005. “Numerical limit analysis solutions for the bearing capacity factor Nγ.” Int. J. Solids Struct. 42 (5–6): 1681–1704. https://doi.org/10.1016/j.ijsolstr.2004.08.002.
Hoek, E., C. Carranza-Torres, and B. Corkum. 2002. “Hoek–Brown failure criterion-2002 edition.” Proc. NARMS-Tac 1 (1): 267–273. https://doi.org/10.1061/(ASCE)0733-9410(1983)109:1(1).
Hoek, E., and P. Marinos. 2007. “A brief history of the development of the Hoek–Brown failure criterion.” Soils Rocks 2 (2): 2–13.
Jaiswal, S., and V. B. Chauhan. 2021, In press “Ultimate bearing capacity of strip footing resting on rock mass using adaptive finite element method.” J. King Saud Univ. Eng. Sci.. https://doi.org/10.1016/j.jksues.2021.09.004.
Jaiswal, S., A. Srivastava, and V. B. Chauhan. 2022. “Performance of strip footing on sand bed reinforced with multilayer geotextile with wraparound ends.” In Vol. 152 of Ground improvement and reinforced soil structures, edited by C. N. V. Satyanarayana Reddy, S. Saride, and A. M. Krishna, 721–732. Singapore: Springer. Lecture Notes in Civil Engineering.
Kumar, P., and V. B. Chauhan. 2022a. “On the eccentrically loaded strip footing resting over a circular cavity in the rock mass: Adaptive finite-element analysis, observations, and recommendations.” Int. J. Geomech. 23 (2): 04022287. https://doi.org/10.1061/IJGNAI.GMENG-7985.
Kumar, P., and V. B. Chauhan. 2022b. “Bearing capacity of strip footing resting above a circular void in the rock mass using adaptive finite element method.” Innovative Infrastruct. Solutions 7 (1): 72. https://doi.org/10.1007/s41062-021-00666-y.
Kumar, P., and V. B. Chauhan. 2022c. “Ultimate bearing capacity of a foundation on the rock media due to the presence of a circular void: Design tables, failure mechanism, and recommendations.” Arabian J. Geosci. 15 (15): 1–11. https://doi.org/10.1007/s12517-022-10620-6.
Kumar, P., and V. B. Chauhan. 2023a. “Observations and recommendations for shallow foundation stability over dual cavities in rock mass under eccentric loading utilizing limit analysis.” Arabian J. Sci. Eng. 49: 5875–5895. https://doi.org/10.1007/s13369-023-08524-y.
Kumar, A., and V. B. Chauhan. 2023b. “Advanced finite element limit analysis and machine learning for assessing the stability of square tunnels in rock slope.” Transp. Infrastruct. Geotechnol. 1–35. https://doi.org/10.1007/s40515-023-00338-7.
Kumar, P., and V. B. Chauhan. 2024. “Behavior of footing resting above dual circular cavities in a rock mass: Insights from an AFELA study.” Int. J. Geomech. 24 (1): 04023248. https://doi.org/10.1061/IJGNAI.GMENG-9036.
Kumar, A., V. B. Chauhan, and P. Kumar. 2024. “Integration of AFELA and machine learning for analysis of shallow foundation over horseshoe tunnel in rock mass.” Model. Earth Syst. Environ. 10: 651–670. https://doi.org/10.1007/s40808-023-01802-6.
Mase, L. Z., and V. Febriyanto. 2023. “Numerical analysis of jetty platform countermeasure effort at Muaro Kualo area in Bengkulu City, Indonesia.” Transp. Infrastruct. Geotechnol. 10 (6): 1145–1169. https://doi.org/10.1007/s40515-022-00258-y.
Mase, L. Z., J. Saputra, A. F. Edriani, S. Keawsawasvong, and V. Q. Lai. 2022. “Finite element analysis to estimate bearing capacity of strip footing in coastal sandy soils in Bengkulu City, Indonesia.” Eng. J. 26 (5): 59–75. https://doi.org/10.4186/ej.2022.26.5.59.
Mase, L. Z., M. A. Putri, A. F. Edriani, V. Q. Lai, and S. Keawsawasvong. 2023. “Prediction of the bearing capacity of strip footing at the homogenous sandy slope based on the finite element method and multivariate adaptive regression spline.” Transp. Infrastruct. Geotechnol. 1–27. https://doi.org/10.1007/s40515-023-00334-x.
Optum G2. 2020. “Finite element program for geotechnical analysis Optum computational engineering.” Accessed November 5, 2023. www.optum.com.
Panji, M., H. Koohsari, M. Adampira, H. Alielahi, and J. A. Marnani. 2016. “Stability analysis of shallow tunnels subjected to eccentric loads by a boundary element method.” J. Rock Mech. Geotech. Eng. 8 (4): 480–488. https://doi.org/10.1016/j.jrmge.2016.01.006.
Sahoo, J. P., and J. Kumar. 2013. “Stability of long unsupported twin circular tunnels in soils.” Tunnelling Underground Space Technol. 38: 326–335. https://doi.org/10.1016/j.tust.2013.07.005.
Shiau, J. S., A. V. Lyamin, and S. W. Sloan. 2003. “Bearing capacity of a sand layer on clay by finite element limit analysis.” Can. Geotech. J. 40 (5): 900–915. https://doi.org/10.1139/t03-042.
Sireesh, S., T. G. Sitharam, and S. K. Dash. 2009. “Bearing capacity of circular footing on geocell–sand mattress overlying clay bed with void.” Geotext. Geomembr. 27 (2): 89–98. https://doi.org/10.1016/j.geotexmem.2008.09.005.
Wilson, D. W., A. J. Abbo, S. W. Sloan, and A. V. Lyamin. 2013. “Undrained stability of a square tunnel where the shear strength increases linearly with depth.” Comput. Geotech. 49: 314–325. https://doi.org/10.1016/j.compgeo.2012.09.005.
Wu, G., M. Zhao, R. Zhang, and G. Liang. 2020. “Ultimate bearing capacity of eccentrically loaded strip footings above voids in rock masses.” Comput. Geotech. 128: 103819. https://doi.org/10.1016/j.compgeo.2020.103819.
Xiao, Y., M. Zhao, R. Zhang, H. Zhao, and G. Wu. 2019. “Stability of dual square tunnels in rock masses subjected to surcharge loading.” Tunnelling Underground Space Technol. 92: 103037. https://doi.org/10.1016/j.tust.2019.103037.
Xiao, Y., M. Zhao, H. Zhao, and R. Zhang. 2018. “Finite element limit analysis of the bearing capacity of strip footing on a rock mass with voids.” Int. J. Geomech. 18 (9): 04018108. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001262.
Yamamoto, K., A. V. Lyamin, D. M. Wilson, S. W. Sloan, and A. J. Abbo. 2013. “Stability of dual circular tunnels in cohesive-frictional soil subjected to surcharge loading.” Comput. Geotech. 50: 41–54. https://doi.org/10.1016/j.compgeo.2012.12.008.
Zhang, Z. X., C. Liu, X. Huang, C. Y. Kwok, and L. Teng. 2016. “Three-dimensional finite-element analysis on ground responses during twin-tunnel construction using the URUP method.” Tunnelling Underground Space Technol. 58: 133–146. https://doi.org/10.1016/j.tust.2016.05.001.
Zhang, R., H. Zhao, and G. Wu. 2023. “FELA investigation of eccentrically-loaded footing on parallel tunnels constructed in rock masses.” Comput. Geotech. 153: 105102. https://doi.org/10.1016/j.compgeo.2022.105102.
Zhao, L., S. Huang, Z. Zeng, R. Zhang, G. Tang, and S. Zuo. 2021. “Study on the ultimate bearing capacity of a strip footing influenced by an irregular underlying cavity in karst areas.” Soils Found. 61 (2): 259–270. https://doi.org/10.1016/j.sandf.2020.09.011.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 24 • Issue 9 • September 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Oct 18, 2023
Accepted: Feb 27, 2024
Published online: Jun 27, 2024
Published in print: Sep 1, 2024
Discussion open until: Nov 27, 2024
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.