Technical Papers
Jul 22, 2022

Influence of Wavelength-to-Excavation Span Ratio on Dynamic Failure Characteristics of a Deep-Buried Tunnel Subjected to Disturbance

Publication: International Journal of Geomechanics
Volume 22, Issue 10

Abstract

Deep-buried structures are frequently and inevitably subjected to aperiodic perturbation during their life circle, resulting in damage to the rock mass surrounding the structures under the coupled action of excavation-induced local stress and dynamic perturbation. The investigation presented in this paper concentrates on the analytical and numerical dynamic responses around an unsupported deep-buried tunnel subjected to blasting disturbance with different wavelength-to-excavation span ratios (λ/D). Based on the complex function theory, the integral transform and its inversion, the elastic responses around the tunnel are obtained theoretically. Then the corresponding elastoplastic counterparts are explored using a self-developed code: elastoplastic cellular automaton. The analytical results indicate that Poisson’s ratio, the ratio of total time for blasting load to rising time, and λ/D have a significant influence on the distributions of dynamic stress concentration and velocity vibrations. Moreover, the numerical results reveal that tensile failure and the compression–shear counterpart are major damage mechanisms for the rock mass when the wavelength is less than the excavation span, while the compression–shear failure is major damage mechanism when the wavelength exceeds the excavation span. The analytical and numerical results can provide guidance for the support of deep-buried rock tunnels.

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Acknowledgments

This work was supported by National Natural Science Foundation of China (Grant Nos. 42077228, 52125903).

References

Abate, J., G. L. Choudhury, and W. Whitt. 1996. “On the Laguerre method for numerically inverting Laplace transforms.” INFORMS J. Comput. 8: 413–427. https://doi.org/10.1287/ijoc.8.4.413.
Abate, J., and P. P. Valkó. 2004. “Multi-precision Laplace transform inversion.” Int. J. Numer. Methods Eng. 60 (5): 979–993. https://doi.org/10.1002/nme.995.
Banaugh, R. P., and W. Goldsmith. 1963. “Diffraction of steady elastic waves by surfaces of arbitrary shape.” J. Appl. Mech. 30 (4): 589–597. https://doi.org/10.1115/1.3636624.
Baron, M. L., and A. T. Matthews. 1961. “Diffraction of a pressure wave by a cylindrical cavity in an elastic medium.” J. Appl. Mech. 28 (3): 347–354. https://doi.org/10.1115/1.3641710.
Baron, M. L., and R. Parnes. 1962. “Displacements and velocities produced by the diffraction of a pressure wave by a cylindrical cavity in an elastic medium.” J. Appl. Mech. 29: 347.
Cao, H., and V. W. Lee. 1979. “Scattering and diffraction of plane P waves by circular cylindrical canyons with variable depth-to-width ratio.” Soil Dyn. Earthquake Eng. 9 (3): 141–150. https://doi.org/10.1016/S0301-2115(79)80003-2.
Cao, H., and V. W. Lee. 1990. “Scattering and differaction of plane P waves by circular cylindrical canyons with variable depth-to-width ratio.” Soil Dyn. Earthquake Eng. 9 (3): 141–150. https://doi.org/10.1016/S0267-7261(09)90013-6.
Davis, C. A., V. W. Lee, and J. P. Bardet. 2001. “Transverse response of underground cavities and pipes to incident SV waves.” Earthquake Eng. Struct. Dyn. 30 (3): 383–410. https://doi.org/10.1002/eqe.14.
Deng, X. F., J. B. Zhu, S. G. Chen, Z. Y. Zhao, Y. X. Zhou, and J. Zhao. 2014. “Numerical study on tunnel damage subject to blast-induced shock wave in jointed rock masses.” Tunnelling Underground Space Technol. 43: 88–100. https://doi.org/10.1016/j.tust.2014.04.004.
den Iseger, P. 2006. “Numerical transform inversion using Gaussian quadrature.” Probab. Eng. Inf. Sci. 20 (1): 1–44. https://doi.org/10.1017/S0269964806060013.
de Rosa, M. A., G. Giunta, and M. Rizzardi. 1995. “Parallel talbot's algorithm for distributed memory machines.” Parallel Comput. 21 (5): 783–801. https://doi.org/10.1016/0167-8191(94)00108-M.
Ding, H., L. H. Tong, C. Xu, and W. Hu. 2020. “Aseismic performance analysis of composite lining embedded in saturated poroelastic half space.” Int. J. Geomech. 20 (9): 04020156. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001787.
Fang, X.-Q., H.-X. Jin, J.-X. Liu, and M.-J. Huang. 2016. “Imperfect bonding effect on dynamic response of a non-circular lined tunnel subjected to shear waves.” Tunnelling Underground Space Technol. 56: 226–231. https://doi.org/10.1016/j.tust.2016.03.008.
Fang, X. Q., T. F. Zhang, B. L. Li, and R. J. Yuan. 2020. “Elastic-slip interface effect on dynamic stress around twin tunnels in soil medium subjected to blast waves.” Comput. Geotech. 119: 103301. https://doi.org/10.1016/j.compgeo.2019.103301.
Feng, F., X. Li, L. Luo, X. Zhao, S. Chen, N. Jiang, W. Huang, and Y. Wang. 2021a. “Rockburst response in hard rock owing to excavation unloading of twin tunnels at great depth.” Bull. Eng. Geol. Environ 80 (10): 7613–7631. https://doi.org/10.1007/s10064-021-02377-1.
Feng, Q., B. Jiang, G. Wang, and C. Hu. 2016. “Analytical solution for a circular roadway considering the transient effect of excavation unloading.” Int. J. Min. Sci. Technol. 26 (4): 543–549. https://doi.org/10.1016/j.ijmst.2016.05.002.
Feng, X.-T., P.-Z. Pan, and H. Zhou. 2006. “Simulation of the rock microfracturing process under uniaxial compression using an elasto-plastic cellular automaton.” Int. J. Rock Mech. Min. Sci. 43 (7): 1091–1108. https://doi.org/10.1016/j.ijrmms.2006.02.006.
Feng, X.-T., Z. Wang, Y. Zhou, C. Yang, P.-Z. Pan, and R. Kong. 2021b. “Modelling three-dimensional stress-dependent failure of hard rocks.” Acta Geotech. 16: 1647–1677. https://doi.org/10.1007/s11440-020-00998-6.
Gao, Y., X. Chen, N. Zhang, D. Dai, and X. Yu. 2018. “Scattering of plane SH waves induced by a semicylindrical canyon with a subsurface circular lined tunnel.” Int. J. Geomech. 18 (6): 06018012. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001137.
Garbow, B. S., G. Giunta, J. N. Lyness, and A. Murli. 1988. “Software for an implementation of Weeks’ method for the inverse Laplace transform.” ACM Trans. Math. Software 14 (2): 163–170. https://doi.org/10.1145/45054.45057.
Gatmiri, B., and H. Eslami. 2007. “Scattering of harmonic waves by a circular cavity in a porous medium: Complex functions theory approach.” Int. J. Geomech. 7 (5): 371–381. https://doi.org/10.1061/(ASCE)1532-3641(2007)7:5(371).
Halsted, D. J., and D. E. Brown. 1972. “Zakian’s technique for inverting Laplace transforms.” Chem. Eng. J. 3: 312–313. https://doi.org/10.1016/0300-9467(72)85037-8.
Jiang, L., X. Zhou, and J. Wang. 2009. “Scattering of a plane wave by a lined cylindrical cavity in a poroelastic half-plane.” Comput. Geotech. 36 (5): 773–786. https://doi.org/10.1016/j.compgeo.2009.01.001.
Lee, V. W., and J. Karl. 1992. “Diffraction of SV waves by underground, circular, cylindrical cavities.” Soil Dyn. Earthquake Eng. 11 (8): 445–456. https://doi.org/10.1016/0267-7261(92)90008-2.
Lee, V. W., and M. D. Trifunac. 1979. “Response of tunnels to incident SH waves.” J. Eng. Mech. 105: 643–659.
Li, C., and X. Li. 2018. “Influence of wavelength-to-tunnel-diameter ratio on dynamic response of underground tunnels subjected to blasting loads.” Int. J. Rock Mech. Min. Sci. 112: 323–338. https://doi.org/10.1016/j.ijrmms.2018.10.029.
Li, C., X. Li, and L. Liang. 2020a. “Dynamic response of existing tunnel under cylindrical unloading wave.” Int. J. Rock Mech. Min. Sci. 131: 104342. https://doi.org/10.1016/j.ijrmms.2020.104342.
Li, M., W. Mei, P.-Z. Pan, F. Yan, Z. Wu, and X.-T. Feng. 2020b. “Modeling transient excavation-induced dynamic responses in rock mass using an elasto-plastic cellular automaton.” Tunnelling Underground Space Technol. 96: 103183. https://doi.org/10.1016/j.tust.2019.103183.
Li, P.-X., X.-T. Feng, G.-L. Feng, Y.-X. Xiao, and B.-R. Chen. 2019. “Rockburst and microseismic characteristics around lithological interfaces under different excavation directions in deep tunnels.” Eng. Geol. 260: 105209. https://doi.org/10.1016/j.enggeo.2019.105209.
Li, X., W. Cao, M. Tao, Z. Zhou, and Z. Chen. 2016. “Influence of unloading disturbance on adjacent tunnels.” Int. J. Rock Mech. Min. Sci. 84: 10–24. https://doi.org/10.1016/j.ijrmms.2016.01.014.
Li, X., C. Li, W. Cao, and M. Tao. 2018a. “Dynamic stress concentration and energy evolution of deep-buried tunnels under blasting loads.” Int. J. Rock Mech. Min. Sci. 104: 131–146. https://doi.org/10.1016/j.ijrmms.2018.02.018.
Li, X., X.-F. Li, Q.-B. Zhang, and J. Zhao. 2018b. “A numerical study of spalling and related rockburst under dynamic disturbance using a particle-based numerical manifold method (PNMM).” Tunnelling Underground Space Technol. 81: 438–449. https://doi.org/10.1016/j.tust.2018.08.026.
Li, X., and L. Weng. 2016. “Numerical investigation on fracturing behaviors of deep-buried opening under dynamic disturbance.” Tunnelling Underground Space Technol. 54: 61–72. https://doi.org/10.1016/j.tust.2016.01.028.
Liu, D., B. Gai, and G. Tao. 1982. “Applications of the method of complex functions to dynamic stress concentrations.” Wave Motion 4 (3): 293–304. https://doi.org/10.1016/0165-2125(82)90025-7.
Liu, Q., and R. Wang. 2012. “Dynamic response of twin closely-spaced circular tunnels to harmonic plane waves in a full space.” Tunnelling Underground Space Technol. 32: 212–220. https://doi.org/10.1016/j.tust.2012.07.001.
Liu, Q., M. Zhao, and L. Wang. 2013. “Scattering of plane P, SV or Rayleigh waves by a shallow lined tunnel in an elastic half space.” Soil Dyn. Earthquake Eng. 49: 52–63. https://doi.org/10.1016/j.soildyn.2013.02.007.
Liu, W. W., Q. Feng, C. X. Wang, C. K. Lu, Z. Z. Xu, and W. T. Li. 2019a. “Analytical solution for three-dimensional radial heat transfer in a cold-region tunnel.” Cold Reg. Sci. Technol. 164: 1–12.
Liu, Z., C. He, H. Wang, and S. Shuaijie. 2019b. “Two-dimensional FM-IBEM solution to the broadband scattering of elastic waves in a fluid-saturated poroelastic half-space.” Eng. Anal. Boundary Elem. 104: 300–319. https://doi.org/10.1016/j.enganabound.2019.03.027.
Liu, Z., L. Huang, J. Liang, and C. Wu. 2019c. “A three-dimensional indirect boundary integral equation method for modeling elastic wave scattering in a layered half-space.” Int. J. Solids Struct. 169: 81–94. https://doi.org/10.1016/j.ijsolstr.2019.03.020.
Lu, S., C. Zhou, Z. Zhang, L. Ji, and N. Jiang. 2021. “Theoretical study on dynamic responses of an unlined circular tunnel subjected to blasting P-waves.” J. Mech. 37: 242–252. https://doi.org/10.1093/jom/ufaa029.
Lu, S., C. Zhou, Z. Zhang, and N. Jiang. 2019. “Particle velocity response of surrounding rock of a circular tunnel subjected to cylindrical P-waves.” Tunnelling Underground Space Technol. 83: 393–400. https://doi.org/10.1016/j.tust.2018.09.020.
Mei, W., M. Li, P. Pan, J. Pan, and K. Liu. 2021a. “Blasting induced dynamic response analysis in a rock tunnel based on combined inversion of Laplace transform with elasto-plastic cellular automaton.” Geophys. J. Int. 225 (1): 699–710. https://doi.org/10.1093/gji/ggaa615.
Mei, W., Y. Xia, G. Han, P.-Z. Pan, M. Li, and Z. Wang. 2021b. “Theoretical responses of shallow-buried circular cavity subjected to transient P wave.” Comput. Geotech. 139: 104411. https://doi.org/10.1016/j.compgeo.2021.104411.
Mei, W., Y. Xia, P.-Z. Pan, M. Li, S. Tan, and Y. Zhang. 2022. “Transient responses of deep-buried unlined tunnels subjected to blasting P wave.” Comput. Geotech. 146: 104729. https://doi.org/10.1016/j.compgeo.2022.104729.
Mow, C., and Y. Pao. 1973. Diffraction of elastic waves and dynamic stress concentrations. New York: Crane, Russak.
Pan, P., and X. Feng. 2013. “Numerical study on coupled thermo-mechanical processes in Äspö Pillar Stability Experiment.” J. Rock Mech. Geotech. Eng. 5 (2): 136–144. https://doi.org/10.1016/j.jrmge.2013.02.001.
Pan, P.-Z., X.-T. Feng, and J. A. Hudson. 2012. “The influence of the intermediate principal stress on rock failure behaviour: A numerical study.” Eng. Geol. 124: 109–118. https://doi.org/10.1016/j.enggeo.2011.10.008.
Pan, P.-Z., F. Yan, X.-T. Feng, and Z.-H. Wu. 2017. “Study on coupled thermo-hydro-mechanical processes in column bentonite test.” Environ. Earth Sci. 76: 618.
Pao, Y. H., and S. A. Thau. 1970. “A perturbation method for boundary-value problems in dynamid elasticity, part II.” Q. Appl. Math. 28 (2): 191–204. https://doi.org/10.1090/qam/99796.
Qiu, J., D. Li, X. Li, and Q. Zhu. 2020. “Numerical investigation on the stress evolution and failure behavior for deep roadway under blasting disturbance.” Soil Dyn. Earthquake Eng. 137: 106278. https://doi.org/10.1016/j.soildyn.2020.106278.
Shakeri, R., A. Mesgouez, and G. Lefeuve-Mesgouez. 2020. “Transient response of a concrete tunnel in an elastic rock with imperfect contact.” Int. J. Min. Sci. Technol. 30 (5): 605–612. https://doi.org/10.1016/j.ijmst.2020.05.008.
Stehfest, H. 1970a. “Algorithm 368: Numerical inversion of Laplace transforms [D5].” Commun. ACM 13 (1): 47–49. https://doi.org/10.1145/361953.361969.
Stehfest, H. 1970b. “Remark on algorithm 368: Numerical inversion of Laplace transforms.” Commun. ACM 13 (10): 624. https://doi.org/10.1145/355598.362787.
Talbot, A. 1979. “The accurate numerical inversion of Laplace transforms.” J. Inst. Math. Appl. 23 (1): 97–120. https://doi.org/10.1093/imamat/23.1.97.
Tao, M., Z. Li, W. Cao, X. Li, and C. Wu. 2019. “Stress redistribution of dynamic loading incident with arbitrary waveform through a circular cavity.” Int. J. Numer. Anal. Methods Geomech. 43 (6): 1279–1299. https://doi.org/10.1002/nag.2897.
Tao, M., A. Ma, W. Cao, X. Li, and F. Gong. 2017. “Dynamic response of pre-stressed rock with a circular cavity subject to transient loading.” Int. J. Rock Mech. Min. Sci. 99: 1–8. https://doi.org/10.1016/j.ijrmms.2017.09.003.
Tao, M., H. T. Zhao, Z. W. Li, and J. B. Zhu. 2020. “Analytical and numerical study of a circular cavity subjected to plane and cylindrical P-wave scattering.” Tunnelling Underground Space Technol. 95: 103143. https://doi.org/10.1016/j.tust.2019.103143.
Thau, S. A., and Y. H. Pao. 1967. “A perturbation method for boundary value problems in dynamid elasticity.” Q. Appl. Math. 25 (3): 243–260. https://doi.org/10.1090/qam/99899.
Toutain, J., J. L. Battaglia, C. Pradere, J. Pailhes, A. Kusiak, W. Aregba, and J. C. Batsale. 2011. “Numerical inversion of Laplace transform for time resolved thermal characterization experiment.” J. Heat Transfer 133 (4): 1–3. https://doi.org/10.1115/1.4002777.
Wang, X., and M. Cai. 2015. “Influence of wavelength-to-excavation span ratio on ground motion around deep underground excavations.” Tunnelling Underground Space Technol. 49: 438–453. https://doi.org/10.1016/j.tust.2015.06.004.
Weideman, J. A. C. 1999. “Algorithms for parameter selection in the weeks method for inverting the Laplace transform.” SIAM J. Sci. Comput. 21 (1): 111–128. https://doi.org/10.1137/S1064827596312432.
Weng, L., L. Huang, A. Taheri, and X. Li. 2017. “Rockburst characteristics and numerical simulation based on a strain energy density index: A case study of a roadway in Linglong gold mine, China.” Tunnelling Underground Space Technol. 69: 223–232. https://doi.org/10.1016/j.tust.2017.05.011.
Weng, L., X. Li, and M. Tao. 2015. “Influence of geostress orientation on fracture response of deep underground cavity subjected to dynamic loading.” Shock Vib. 2015: 575879. https://doi.org/10.1155/2015/575879.
Xia, X., H. B. Li, J. C. Li, B. Liu, and C. Yu. 2013. “A case study on rock damage prediction and control method for underground tunnels subjected to adjacent excavation blasting.” Tunnelling Underground Space Technol. 35: 1–7. https://doi.org/10.1016/j.tust.2012.11.010.
Yan, F., X.-T. Feng, J.-H. Lv, P.-Z. Pan, and S.-J. Li. 2018a. “Continuous-discontinuous cellular automaton method for cohesive crack growth in rock.” Eng. Fract. Mech. 188: 361–380. https://doi.org/10.1016/j.engfracmech.2017.09.007.
Yan, F., X.-T. Feng, P.-Z. Pan, and S.-J. Li. 2014. “Discontinuous cellular automaton method for crack growth analysis without remeshing.” Appl. Math. Modell. 38 (1): 291–307. https://doi.org/10.1016/j.apm.2013.06.017.
Yan, F., P.-Z. Pan, X.-T. Feng, and S.-J. Li. 2018b. “The continuous-discontinuous cellular automaton method for elastodynamic crack problems.” Eng. Fract. Mech. 204: 482–496. https://doi.org/10.1016/j.engfracmech.2018.10.025.
Yan, F., P.-Z. Pan, X.-T. Feng, J.-H. Lv, and S.-J. Li. 2017. “An adaptive cellular updating scheme for the continuous–discontinuous cellular automaton method.” Appl. Math. Modell. 46: 1–15. https://doi.org/10.1016/j.apm.2017.01.060.
Yan, F., H.-R. Yang, Q. Jiang, S.-J. Li, D.-P. Xu, and Z.-D. Tang. 2022. “Numerical simulation for T-stress for complex multiple branching and intersecting cracks based on continuous-discontinuous cellular automaton.” Theor. Appl. Fract. Mech. 118: 103234. https://doi.org/10.1016/j.tafmec.2021.103234.
Yan, F., W. Zhang, P.-Z. Pan, and S.-J. Li. 2021. “Dynamic crack propagation analysis combined the stable scheme and continuous-discontinuous cellular automaton.” Eng. Fract. Mech. 241: 107390. https://doi.org/10.1016/j.engfracmech.2020.107390.
Yang, J., W. Lu, Q. Jiang, C. Yao, S. Jiang, and L. Tian. 2016. “A study on the vibration frequency of blasting excavation in highly stressed rock masses.” Rock Mech. Rock Eng. 49 (7): 2825–2843. https://doi.org/10.1007/s00603-016-0964-6.
Yi, C. P., W. b. Lu, P. Zhang, D. Johansson, and U. Nyberg. 2016. “Effect of imperfect interface on the dynamic response of a circular lined tunnel impacted by plane P-waves.” Tunnelling Underground Space Technol. 51: 68–74. https://doi.org/10.1016/j.tust.2015.10.011.
Zhao, R., M. Tao, H. Zhao, W. Cao, X. Li, and S. Wang. 2020. “Dynamics fracture characteristics of cylindrically-bored granodiorite rocks under different hole size and initial stress state.” Theor. Appl. Fract. Mech. 109: 102702. https://doi.org/10.1016/j.tafmec.2020.102702.
Zhao, W., W. Chen, and D. Yang. 2018. “Effect of an imperfect interface on seismic response of a composite lining tunnel subjected to SH-waves.” Int. J. Geomech. 18 (12): 04018177. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001317.
Zhu, W. C., Z. H. Li, L. Zhu, and C. A. Tang. 2010. “Numerical simulation on rockburst of underground opening triggered by dynamic disturbance.” Tunnelling Underground Space Technol. 25 (5): 587–599. https://doi.org/10.1016/j.tust.2010.04.004.

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International Journal of Geomechanics
Volume 22Issue 10October 2022

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Received: Sep 5, 2021
Accepted: Apr 10, 2022
Published online: Jul 22, 2022
Published in print: Oct 1, 2022
Discussion open until: Dec 22, 2022

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Wanquan Mei
Ph.D. Candidate, School of Civil Engineering and Architecture, Wuhan Univ. of Technology, Wuhan, Hubei 430070, China.
Yuanyou Xia [email protected]
Professor, School of Civil Engineering and Architecture, Wuhan Univ. of Technology, Wuhan, Hubei 430070, China (corresponding author). Email: [email protected]
Professor, State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, Hubei 430071, China. ORCID: https://orcid.org/0000-0002-2833-4964
Mei Li
Associate Professor, School of Resources and Environmental Engineering, Wuhan Univ. of Technology, Wuhan, Hubei 430070, China.
Gaosheng Han
Ph.D. Candidate, School of Civil Engineering and Architecture, Wuhan Univ. of Technology, Wuhan, Hubei 430070, China.

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