Technical Notes
Jul 30, 2021

Support Characteristic of a Novel Type of Support in Loess Tunnels Using the Convergence–Confinement Method

Publication: International Journal of Geomechanics
Volume 21, Issue 10

Abstract

The convergence–confinement method (CCM), a widely used tunnel design method, is an analysis approach that can intuitively reflect the interaction between the surroundings and the support in tunnels. In this article, the CCM approach is used to determine the support performance of a steel–concrete composite support (SCCS) system, which is characterized by an improved stiffness of the initial support due to its unique arch type (π-type) and construction steps. In view of the tunneling process, the support characteristics of a conventional support system and the SCCS system are determined from the perspectives of single and combined support structures. A sensitivity analysis by considering the arch installation spacing, wall thickness, and concrete grade is performed. The results reveal that the stiffness and support pressure of the hollow π-type steel arch increase linearly with a decrease of the installation spacing and an increase of the wall thickness, while its support performance only slightly improves with an increase of the inner concrete grade after filling with concrete. Additionally, the support characteristic curves for different support systems are obtained, and the safety factor of the SCCS system is found to be greater than 3.48. The maximum support pressure of the SCCS system is found to increase by 1.25 MPa and its support performance increases by 4.57 times as compared to those of the conventional support system. Finally, the construction technology of the SCCS system is discussed, and some application suggestions are provided.

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Acknowledgments

This study was supported by the National Natural Science Foundation of China (Grant No. 52008028), the Fundamental Research Funds for the Central Universities, CHD (Grant Nos. 300102210112 and 300102210530), the Project Program of Key Laboratory of Urban Underground Engineering of Ministry of Education (TUL2020-01), and Project on Social Development of Shaanxi Provincial Science and Technology Department (Grant No. 2021SF-513).

References

AISC. 1994. Load and resistance factor design. Chicago: AISC.
Alejano, L. R., E. Alonso, A. Rguez-Dono, and G. Fdez-Manin. 2010. “Application of the convergence–confinement method for tunnels excavated in rock masses exhibiting Hoek–Brown strain-softening behaviour.” Int. J. Rock Mech. Min. Sci. 47 (1): 150–160. https://doi.org/10.1016/j.ijrmms.2009.07.008.
Alejano, L. R., A. Rodriguez-Dono, A. Alonso, and G. Fdez-Manín. 2009. “Ground reaction curves for tunnels excavated in different quality rock masses showing several types of post-failure behaviour.” Tunnelling Underground Space Technol. 24 (6): 689–705. https://doi.org/10.1016/j.tust.2009.07.004.
Alonso, E., L. R. Alejano, F. Varas, G. Fdez-Manin, and C. Carranza-Torres. 2003. “Ground response curves for rock masses exhibiting strain-softening behaviour.” Int. J. Numer. Anal. Methods Geomech. 27 (13): 1153–1185. https://doi.org/10.1002/nag.315.
Brown, E. T., J. W. Bray, B. Ladanyi, and E. Hoek. 1983. “Ground response curves for rock tunnels.” J. Geotech. Eng. 109 (1): 15–39. https://doi.org/10.1061/(ASCE)0733-9410(1983)109:1(15).
Cai, Y., Y. Jiang, I. Djamaluddin, T. Iura, and T. Esaki. 2015. “An analytical model considering interaction behavior of grouted rock bolts for convergence–confinement method in tunneling design.” Int. J. Rock Mech. Min. Sci. 76: 112–126. https://doi.org/10.1016/j.ijrmms.2015.03.006.
Carranza-Torres, C. 2004. “Elasto-plastic solution of tunnel problems using the generalized form of the Hoek–Brown failure criterion.” Int. J. Rock Mech. Min. Sci. 41: 629–639. https://doi.org/10.1016/j.ijrmms.2004.03.111.
Carranza-Torres, C., and M. Diederichs. 2009. “Mechanical analysis of circular liners with particular reference to composite supports. For example, liners consisting of shotcrete and steel sets.” Tunnelling Underground Space Technol. 24 (5): 506–532. https://doi.org/10.1016/j.tust.2009.02.001.
Carranza-Torres, C., and C. Fairhurst. 2000. “Application of the convergence–confinement method of tunnel design to rock masses that satisfy the Hoek–Brown failure criterion.” Tunnelling Underground Space Technol. 15 (2): 187–213. https://doi.org/10.1016/S0886-7798(00)00046-8.
Carranza-Torres, C., B. Rysdhal, and M. Kasim. 2013. “On the elastic analysis of a circular lined tunnel considering the delayed installation of the support.” Int. J. Rock Mech. Min. Sci. 61: 57–85. https://doi.org/10.1016/j.ijrmms.2013.01.010.
Chang, X., X. L. Luo, C. G. Zhu, and C. N. Tang. 2014. “Analysis of circular concrete-filled steel tube (CFT) support in high ground stress conditions.” Tunnelling Underground Space Technol. 43: 41–48. https://doi.org/10.1016/j.tust.2014.04.002.
De La Fuente, M., R. Taherzadeh, J. Sulem, X.-S. Nguyen, and D. Subrin. 2019. “Applicability of the convergence-confinement method to full-face excavation of circular tunnels with stiff support system.” Rock Mech. Rock Eng. 52 (7): 2361–2376. https://doi.org/10.1007/s00603-018-1694-8.
Dias, D. 2011. “Convergence–confinement approach for designing tunnel face reinforcement by horizontal bolting.” Tunnelling Underground Space Technol. 26 (4): 517–523. https://doi.org/10.1016/j.tust.2011.03.004.
Duncan Fama, M. E. 1993. “Numerical modeling of yield zones in weak rock.” In Vol. 2 of Comprehensive rock engineering, edited by J. A. Hudson, 49–75. Oxford, UK: Pergamon.
Fang, Q., J. M. Du, J. Y. Li, D. L. Zhang, and L. Q. Cao. 2021. “Settlement characteristics of large-diameter shield excavation below existing subway in close vicinity.” J. Central South Univ. 28 (3): 882–897. https://doi.org/10.1007/s11771-021-4628-7.
Fang, Q., D. L. Zhang, P. Zhou, and L. N. Y. Wong. 2013. “Ground reaction curves for deep circular tunnels considering the effect of ground reinforcement.” Int. J. Rock Mech. Min. Sci. 60: 401–412. https://doi.org/10.1016/j.ijrmms.2013.01.003.
Gao, Y. F., B. Wang, J. Wang, B. Li, F. Xing, Z. G. Wang, and T. L. Jin. 2010. “Test on structural property and application of concrete-filled steel tube support of deep mine and soft rock roadway.” [In Chinese.] Chin. J. Rock Mech. Eng. 29: 2604–2609.
Gesta, P., J. Kerisel, P. Londe, C. Louis, and M. Panet. 1979. “Stability of tunnels by the convergence–confinement method.” Construction (11): 17–24.
Guan, Z., Y. Jiang, and Y. Tanabasi. 2007. “Ground reaction analyses in conventional tunnelling excavation.” Tunnelling Underground Space Technol. 22 (2): 230–237. https://doi.org/10.1016/j.tust.2006.06.004.
Guo, Y. T., J. Chen, X. Nie, M. X. Tao, J. J. Wang, and J. S. Fan. 2020. “Investigation of the shear resistances of steel–concrete–steel composite structures with bidirectional webs.” J. Constr. Steel Res. 164: 105846. https://doi.org/10.1016/j.jcsr.2019.105846.
Guo, Y. T., M. X. Tao, X. Nie, S. Y. Qiu, L. Tang, and J. S. Fan. 2018. “Experimental and theoretical studies on the shear resistance of steel–concrete–steel composite structures with bidirectional steel webs.” J. Struct. Eng. 144 (10): 04018172. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002182.
He, S.Y., J. X. Lai, Y. J. Zhong, K. Wang, W. Xu, L. X. Wang, T. Liu, and C. P. Zhang. 2021. “Damage behaviors, prediction methods and prevention methods of rockburst in 13 deep traffic tunnels in China.” Eng. Fail. Anal. 121: 105178. https://doi.org/10.1016/j.engfailanal.2020.105178.
Hou, H., S. Ma, Q. Wang, Y. Jin, and L. Chen. 2017. “Experimental study on mechanical behavior of concrete-filled thin-walled steel tube supported in tunnel.” [In Chinese.] J. Central South Univ. 48 (5): 1316–1325.
Huang, W. P., Q. Yuan, Y. L. Tan, J. Wang, J. L. Liu, G. L. Qu, and C. Li. 2018. “An innovative support technology employing a concrete-filled steel tubular structure for a 1000-m-deep roadway in a high in situ stress field.” Tunnelling and Underground Space Technology 73: 26–36. https://doi.org/10.1016/j.tust.2017.11.007.
Kastner, H. 1971. Statik des Tunnel- und Stollenbaues auf der Grundlage geomechanischer Erkenntnisse. Chinese ed. Shanghai, China: Shanghai Science Press.
Kitagawa, T., T. Kumeta, T. Ichizyo, S. Soga, M. Sato, and M. Yasukawa. 1991. “Application of convergence confinement analysis to the study of preceding displacement of a squeezing rock tunnel.” Rock Mech. Rock Eng. 24 (1): 31–51. https://doi.org/10.1007/BF01042717.
Lai, J. X., J. L. Qiu, H. B. Fan, Q. Zhang, Z. N. Hu, J. B. Wang, and J. X. Chen. 2016. “Fiber Bragg grating sensors-based in situ monitoring and safety assessment of loess tunnel.” J. Sens. 2016: 1–10. https://doi.org/10.1155/2016/8658290.
Li, H., E. L. Ma, J. X. Lai, L. X. Wang, S. S. Xu, K. Wang, and T. Liu. 2020a. “Tunnelling-induced settlement and treament techniques for a loess metro in Xi’an.” Adv. Civ. Eng. 2020: 1854813. https://doi.org/10.1155/2020/1854813.
Li, J., and Z. Tan. 2013. “On the interaction mechanism of the primary support and rock mass in a loess tunnel with a large section.” [In Chinese.] Mod. Tunnelling Technol. 50 (3): 79–86.
Li, L., H. H. Chen, J. P. Li, and D. A. Sun. 2021. “An elastoplastic solution to undrained expansion of a cylindrical cavity in SANICLAY under plane stress condition.” Comput. Geotech. 132: 103990. https://doi.org/10.1016/j.compgeo.2020.103990.
Li, S. C., W. Lu, Q. Wang, H. B. Sun, B. Jiang, and Q. Qin. 2018. “Study on failure mechanism and mechanical properties of casing joints of square steel confined concrete arch.” Eng. Fail. Anal. 92: 539–552. https://doi.org/10.1016/j.engfailanal.2018.05.011.
Li, S. C., Q. Yan, C. Xie, and J. Wu. 2017. “The mechanical behavior of composite supports of steel-grid in loess tunnel.” [In Chinese.] Chin. J. Rock Mech. Eng. 36 (2): 446–256.
Li, W. T., N. Yang, Y. C. Mei, Y. H. Zhang, L. Wang, and H. Y. Ma. 2020b. “Experimental investigation of the compression-bending property of the casing joints in a concrete filled steel tubular supporting arch for tunnel engineering.” Tunnelling Underground Space Technol. 96: 103184. https://doi.org/10.1016/j.tust.2019.103184.
Liu, S. F., J. C. Feng, P. H. Zhu, and X. Li. 2018. “Stability analysis of two parallel closely spaced tunnels based on convergence-confinement principle.” J. Constr. Eng. Manage. 144 (6): 04018041. https://doi.org/10.1061/(ASCE)CO.1943-7862.0001496.
Lombardi, G. 1980. “Some comments on the convergence–confinement method.” Underground Space 4 (4): 249–258.
MOT (Ministry of Transport of the People’s Republic of China). 2018. Specifications for design of highway tunnels. JTG 3370.1-2018. Beijing: MOT.
Mousivand, M., and M. Maleki. 2018. “Constitutive models and determining methods effects on application of convergence-confinement method in underground excavation.” Geotech. Geol. Eng. 36 (3): 1707–1722. https://doi.org/10.1007/s10706-017-0426-2.
Oke, J., N. Vlachopoulos, and M. Diederichs. 2018. “Improvement to the convergence–confinement method: Inclusion of support installation proximity and stiffness.” Rock Mech. Rock Eng. 51 (5): 1495–1519. https://doi.org/10.1007/s00603-018-1418-0.
Oreste, P. P. 2003. “Analysis of structural interaction in tunnels using the convergence–confinement approach.” Tunnelling Underground Space Technol. 18 (4): 347–363. https://doi.org/10.1016/S0886-7798(03)00004-X.
Oreste, P. P., and D. Peila. 1997. “Modelling progressive hardening of shotcrete in convergence–confinement approach to tunnel design.” Tunnelling Underground Space Technol. 12 (3): 425–431. https://doi.org/10.1016/S0886-7798(97)00033-3.
Pan, Y. W., and J. J. Dong. 1991. “Time-dependent tunnel convergence—II. Advance rate and tunnel-support interaction.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 28 (6): 477–488. https://doi.org/10.1016/0148-9062(91)91123-9.
Panet, M. 1993. “Understanding deformations in tunnels.” In Vol. 1 of Comprehensive rock engineering, edited by J. A. Hudson, E. T. Brown, C. Fairhurst, and E. Hoek, 663–690. London: Pergamon Press.
Qiu, S. Y., Y. T. Guo, X. Nie, J. S. Fan, and M. X. Tao. 2020. “Experimental study on shaped steel shear connectors used in large-scale composite structures.” J. Constr. Steel Res. 172: 106201. https://doi.org/10.1016/j.jcsr.2020.106201.
Su, Y. H., X. Fu, and X. Wang. 2015. “The analysis for stability coefficient of underground structure with the shapes of ground response curves.” [In Chinese.] J. Hunan Univ. 42 (7): 87–92.
Su, Y. H., S. F. Liu, K. X. Wang, and B. Liang. 2014. “Stability analysis of underground structures based on convergence–confinement method.” [In Chinese.] Chin. J. Geotech. Eng. 36 (11): 2002–2009.
Sun, K. G., Y. Q. Hong, W. P. Xu, Z. H. Hou, X. Liu, M. Z. Yu, and Z. Y. Yuan. 2021. “Analysis and prediction of mechanical characteristics of corrugated plate as primary support in tunnels.” Tunnelling Underground Space Technol. 111: 103845. https://doi.org/10.1016/j.tust.2021.103845.
Tan, C. H. 2016. “Difference solution of passive bolts reinforcement around a circular opening in elastoplastic rock mass.” Int. J. Rock Mech. Min. Sci. 81: 28–38. https://doi.org/10.1016/j.ijrmms.2015.11.001.
Vlachopoulos, N., and M. S. Diederichs. 2009. “Improved longitudinal displacement profiles for convergence confinement analysis of deep tunnels.” Rock Mech. Rock Eng. 42 (2): 131–149. https://doi.org/10.1007/s00603-009-0176-4.
Wang, M. N., Y. C. Dong, and L. Yu. 2020a. “Analytical solution for a loess tunnel based on a bilinear strength criterion.” Soil Mech. Found. Eng. 57 (3): 296–304. https://doi.org/10.1007/s11204-020-09669-w.
Wang, Q., B. Jiang, S. C. Li, P. H. Wang, W. T. Li, and Z. Li. 2011. “Supporting effect and economic benefit analysis on new type concrete-filled steel tube supports.” In Advanced materials research, edited by G. Zhang and J. Xu, 608–613. Baech, Switzerland: Trans Tech.
Wang, Q., B. Jiang, Y. Li, X. Shao, F. Q. Wang, S. C. Li, S. G. Zhang, and G. Q. Ruan. 2015. “Mechanical behaviors analysis on a square-steel-confined-concrete arch centering and its engineering application in a mining project.” Eur. J. Environ. Civ. Eng. 21 (4): 389–411. https://doi.org/10.1080/19648189.2015.1124809.
Wang, Q., Y. C. Luan, B. Jiang, S. C. Li, M. C. He, H. B. Sun, Q. Qin, and W. Lu. 2019a. “Study on key technology of tunnel fabricated arch and its mechanical mechanism in the mechanized construction.” Tunnelling Underground Space Technol. 83: 187–194. https://doi.org/10.1016/j.tust.2018.10.002.
Wang, X. Y., Z. S. Tan, M. S. Wang, and M. Zhang. 2008. “Analysis of mechanical character of surrounding rock with controlled drainage in mountain tunnels.” [In Chinese.] Rock Soil Mech. 29 (1): 75–80.
Wang, Z. C., K. Du, Y. L. Xie, X. L. Su, Y. F. Shi, X. Li, and T. Liu. 2021a. “Buckling analysis of an innovative type of steel–concrete composite support in tunnels.” J. Constr. Steel Res. 179: 106503. https://doi.org/10.1016/j.jcsr.2020.106503.
Wang, Z. C., X. L. Su, H. P. Lai, Y. L. Xie, Y. W. Qin, and T. Liu. 2020b. “Conception and evaluation of a novel type of support in loess tunnels.” J. Perform. Constr. Facil. 35 (1): 04020144. https://doi.org/10.1061/(ASCE)CF.1943-5509.0001533.
Wang, Z. C., Y. Xie, J. X. Lai, Y. L. Xie, X. L. Su, Y. F. Shi, and C. X. Guo. 2021b. “Designing an innovative support system in loess tunnel.” Geomech. Eng. 24 (3): 253–266. https://doi.org/10.12989/gae.2021.24.3.253.
Wang, Z. C., Y. L. Xie, H. Q. Liu, and Z. H. Feng. 2019b. “Analysis on deformation and structural safety of a novel concrete-filled steel tube support system in loess tunnel.” Eur. J. Environ. Civ. Eng. 25 (1): 39–59. https://doi.org/10.1080/19648189.2018.1515665.
Weng, X. L., R. M. Zhou, W. Rao, and D. Wang. 2021. “Research on subway shield tunnel induced by local water immersion of collapsible loess.” Natural Hazards. https://doi.org/10.1007/s11069-021-04727-4.
Wu, K., Z. S. Shao, S. Qin, W. Wei, and Z. Chu. 2021. “A critical review on the performance of yielding supports in squeezing tunnels.” Tunnelling Underground Space Technol. 114 (1): 103815. https://doi.org/10.1016/j.tust.2021.103815.
Xu, S. S., H. Lei, C. Li, H. Q. Liu, J. X. Lai, and T. Liu. 2021. “Model test on mechanical characteristics of shallow tunnel excavation failure in gully topography.” Eng. Fail. Anal. 119: 104978. https://doi.org/10.1016/j.engfailanal.2020.104978.
Yan, Q., S. C. Li, C. Xie, and Y. Li. 2018. “Analytical solution for bolted tunnels in expansive loess using the convergence–confinement method.” Int. J. Geomech. 18 (1): 04017124. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000989.
Yan, Y. F., J. L. Qiu, Q. B. Huang, Z. C. Wang, Y. L. Xie, and T. Liu. 2021. “Ground fissures geology in Xi'an and failure mitigation measures for utility tunnel system due to geohazard.” Arabian J. Geosci. 14. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000989.
Yang, C. Y., J. P. Li, L. Li, and D. A. Sun. 2021. “Expansion responses of a cylindrical cavity in overconsolidated unsaturated soils: A semi-analytical elastoplastic solution.” Comput. Geotech. 130: 103922. https://doi.org/10.1016/j.compgeo.2020.103922.
Zhang, W. J., W. T. Li, N. Yang, Q. Wang, T. C. Li, and G. Wang. 2017. “Determination of the bearing capacity of a concrete-filled steel tubular arch support for tunnel engineering: Experimental and theoretical studies.” KSCE J. Civ. Eng. 21 (7): 2932–2945. https://doi.org/10.1007/s12205-017-1418-8.
Zhao, G. W., M. Z. Guo, J. F. Cui, J. P. Li, and L. F. Xu. 2021. “Partially-exposed cast-in-situ concrete degradation induced by internal-external sulfate and magnesium multiple coupled attack.” Constr. Build. Mater. 294: 123560. https://doi.org/10.1016/j.conbuildmat.2021.123560.
Zheng, H. B., P. F. Li, and G. W. Ma. 2021. “Stability analysis of the middle soil pillar for asymmetric parallel tunnels by using model testing and numerical simulations.” Tunnelling Underground Space Technol. 108: 103686. https://doi.org/10.1016/j.tust.2020.103686.

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Go to International Journal of Geomechanics
International Journal of Geomechanics
Volume 21Issue 10October 2021

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Received: Nov 17, 2020
Accepted: Mar 5, 2021
Published online: Jul 30, 2021
Published in print: Oct 1, 2021
Discussion open until: Dec 30, 2021

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Zhichao Wang, Ph.D. [email protected]
School of Highway, Chang’an Univ., Xi’an 710064, China (corresponding author). Email: [email protected]
Master’s Student, School of Highway, Chang’an Univ., Xi’an 710064, China. Email: [email protected]
Professor, School of Highway, Chang’an Univ., Xi’an 710064, China. Email: [email protected]
Mengze Zhang [email protected]
Ph.D. Student, School of Highway, Chang’an Univ., Xi’an 710064, China. Email: [email protected]
Professor, School of Science, Xi’an Univ. of Architecture and Technology, Xi’an 710055, China. Email: [email protected]
Master’s Student, School of Highway, Chang’an Univ., Xi’an 710064, China. Email: [email protected]
Chengping Zhang
Professor, Key Laboratory of Urban Underground Engineering of the Education Ministry, Beijing Jiaotong Univ., Beijing 100044, China.

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