Dynamic response of water-rich tunnel subjected to plane P wave considering excavation induced damage zone

Abstract

The stability analysis of a deep buried tunnel subjected to dynamic disturbance is an important issue. In this study, the transient response has been obtained by establishing a water-rich tunnel model considering excavation damage zone (EDZ). Based on Biot’s two-phase dynamic theory and wave function expansion method, the analytical solution of dynamic response around the water-rich tunnel containing EDZ subjected to P wave is derived. Moreover, Fourier transform and Duhamel’s integral technique is introduced to calculate the transient response, and the equivalent blasting curve is adopted to input excitation function. The dimensionless parameters thickness N and shear modulus ratio $ \widetilde{\mu}$ are defined to characterize the degree of damage in the surrounding rock, investigating the influencing factors, such as the parameters and the incident source frequencies. The results indicate that the dynamic stress concentration factor (DSCF) gradually decreases as the dimensionless parameters increase. Additionally, it is observed that the DSCF is more sensitive to changes in the thickness parameter N. Finally, the influence of the waveform parameters has been taken into account in the analysis of transient response, and the stress state and transfer process in each time stage of the EDZ are analyzed. This study establishes a theoretical foundation for comprehending the mechanical behavior and support design considerations associated with a deep-buried water-rich tunnel containing EDZ.

Keywords

Water-rich tunnel / Two-phase dynamic theory / Wave scattering / Transient response / Dynamic stress concentration

Declaration of competing 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.

Acknowledgment

The research presented in this paper was supported by the National Natural Science Foundation of China (Grant Nos. 12072376 and 52274105).

References

[1] Biot, M. A. (1956a). Theory of propagation of elastic waves in a fluidsaturated porous solid. I. low-frequency range. The Journal of the Acoustical Society of America, 28(2), 168-178.

[2] Biot, M. A. (1956b). Theory of propagation of elastic waves in a fluidsaturated porous solid. II. higher frequency range. The Journal of the Acoustical Society of America, 28(2), 179-191.

[3] Bobet, A. (2009). Elastic solution for deep tunnels. Application to excavation damage zone and rockbolt support. Rock Mechanics and Rock Engineering, 42(2), 147-174.

[4] Brown, E. (1980). Underground excavations in rock. CRC Press.

[5] Brown, E. T., Bray, J. W., Ladanyi, B., & Hoek, E. (1983). Ground response curves for rock tunnels. Journal of Geotechnical Engineering, 109(1), 15-39.

[6] Cho, W. J., Kim, J. S., Lee, C., & Choi, H.-J. (2013). Gas permeability in the excavation damaged zone at KURT. Engineering Geology, 164, 222-229.

[7] Feng, X. T., Guo, H. S., Yang, C.-X., & Li, S.-J. (2018). In situ observation and evaluation of zonal disintegration affected by existing fractures in deep hard rock tunneling. Engineering Geology, 242, 1-11.

[8] Gu, H. L., Lai, X. P., Tao, M., Cao, W. Z., & Yang, Z. K. (2023). The role of porosity in the dynamic disturbance resistance of water-saturated coal. International Journal of Rock Mechanics and Mining Sciences, 166, 105388.

[9] Hasheminejad, S. M., & Avazmohammadi, R. (2007). Harmonic wave diffraction by two circular cavities in a poroelastic formation. Soil Dynamics and Earthquake Engineering, 27, 29-41.

[10] Hasheminejad, S. M., & Hosseini, H. (2002). Radiation loading of a cylindrical source in a fluid-filled cylindrical cavity embedded within a fluid-saturated poroelastic medium. Journal of Applied Mechanics, 69 (5), 675-683.

[11] Jiang, L. F., Zhou, X. L., & Wang, J. H. (2009). Scattering of a plane wave by a lined cylindrical cavity in a poroelastic half-plane. Computers and Geotechnics, 36, 773-786.

[12] Kaiser, P., Yazici, S., & Maloney, S. (2001). Mining-induced stress change and consequences of stress path on excavation stability—a case study. International Journal of Rock Mechanics and Mining Sciences, 38(2), 167-180.

[13] Lai, J., Wang, Y. C., & Liu, Y. (2021). Blasting excavation induced damage caused to the rock mass surrounding tunnels. IOP Conference Series: Earth and Environmental Science, 814(1), 012013.

[14] Li, W. H., Zhu, S. N., Lee, V. W., Shi, P. X., & Zhao, C. G. (2022). Scattering of plane SV-waves by a circular lined tunnel in an undersea saturated half-space. Soil Dynamics and Earthquake Engineering, 153, 107064.

[15] Li, X. B., Cao, W. Z., Zhou, Z. L., & Zou, Y. (2014). Influence of stress path on excavation unloading response. Tunnelling and Underground Space Technology, 42, 237-246.

[16] Li, X. B., Li, C. J., Cao, W. Z., & Tao, M. (2018). Dynamic stress concentration and energy evolution of deep-buried tunnels under blasting loads. International Journal of Rock Mechanics and Mining Sciences, 104, 131-146.

[17] Li, X. B., & Weng, L. (2016). Numerical investigation on fracturing behaviors of deep-buried opening under dynamic disturbance. Tunnelling and Underground Space Technology, 54, 61-72.

[18] Luo, S., Gong, F. Q., Peng, K., & Liu, Z. X. (2023). Influence of water on rockburst proneness of sandstone: Insights from relative and absolute energy storage. Engineering Geology, 323, 107172.

[19] Martino, J. B., & Chandler, N. A. (2004). Excavation-induced damage studies at the underground research laboratory. International Journal of Rock Mechanics and Mining Sciences, 41(8), 1413-1426.

[20] Mitaim, S., & Detournay, E. (2004). Damage around a cylindrical opening in a brittle rock mass. International Journal of Rock Mechanics and Mining Sciences, 41(8), 1447-1457.

[21] Mow, C. C., & Pao, Y. H. (1971). The diffraction of elastic waves and dynamic stress concentrations. Santa Monica, CA: RAND Corporation.

[22] Pao, Y. H., Mow, C. C., & Achenbach, J. D. (1973). Diffraction of elastic waves and dynamic stress concentrations. Journal of Applied Mechanics, 40(4), 872.

[23] Read, R. S. (2004). 20 years of excavation response studies at AECL’s underground research laboratory. International Journal of Rock Mechanics and Mining Sciences, 41(8), 1251-1275.

[24] Senjuntichai, T., & Rajapakse, R. (1993). Transient response of a circular cavity in a poroelastic medium. International Journal for Numerical and Analytical Methods in Geomechanics, 17(6), 357-383.

[25] Siren, T., Kantia, P., & Rinne, M. (2015). Considerations and observations of stress-induced and construction-induced excavation damage zone in crystalline rock. International Journal of Rock Mechanics and Mining Sciences, 73, 165-174.

[26] Su, G., Feng, X., Wang, J., Jiang, J., & Hu, L. (2017). Experimental study of remotely triggered rockburst induced by a tunnel axial dynamic disturbance under true-triaxial conditions. Rock Mechanics and Rock Engineering, 50(8), 2207-2226.

[27] Tao, M., Li, X., & Wu, C. (2013). 3D numerical model for dynamic loading-induced multiple fracture zones around underground cavity faces. Computers and Geotechnics, 54, 33-45.

[28] Tao, M., Li, Z., Cao, W., Li, X., & Wu, C. (2019). Stress redistribution of dynamic loading incident with arbitrary waveform through a circular cavity. International Journal for Numerical and Analytical Methods in Geomechanics, 43(6), 1279-1299.

[29] Tao, M., Luo, H., Wu, C., Cao, W., & Zhao, R. (2023a). Dynamic analysis of the different types of elliptic cylindrical inclusions subjected to plane SH-wave scattering. Mathematical Methods in the Applied Sciences, 46(2), 2773-2800.

[30] Tao, M., Xiang, G. L., Zhao, R., & Wu, C. Q. (2023b). Scattering of Pwave and transient response around a fluid-filled cavity in an elastic medium. Journal of Central South University, 30(2), 568-583.

[31] Tao, M., Zhao, H. T., Li, Z. W., & Zhu, J. B. (2020a). Analytical and numerical study of a circular cavity subjected to plane and cylindrical P-wave scattering. Tunnelling and Underground Space Technology, 95, 103143.

[32] Tao, M., Zhao, R., Du, K., Cao, W., & Li, Z. (2020b). Dynamic stress concentration and failure characteristics around elliptical cavity subjected to impact loading. International Journal of Solids and Structures, 191-192, 401-417.

[33] Tsang, C.-F., Bernier, F., & Davies, C. (2005). Geohydromechanical processes in the Excavation Damaged Zone in crystalline rock, rock salt, and indurated and plastic clays—in the context of radioactive waste disposal. International Journal of Rock Mechanics and Mining Sciences, 42(1), 109-125.

[34] Xu, L., Gong, F. Q., & Liu, Z. X. (2022). Experiments on rockburst proneness of pre-heated granite at different temperatures: Insights from energy storage, dissipation and surplus. Journal of Rock Mechanics and Geotechnical Engineering, 14(5), 1343-1355.

[35] Xu, P., Xia, T.-D., & Han, T.-C. (2006). Scattering of elastic wave by a cylindrical shell deeply embedded in saturated soils. Acta Seismologica Sinica, 19(2), 191-198.

[36] Yan, P., Lu, W.-B., Chen, M., Hu, Y.-G., Zhou, C.-B., & Wu, X.-X. (2015). contributions of in-situ stress transient redistribution to blasting excavation damage zone of deep tunnels. Rock Mechanics and Rock Engineering, 48(2), 715-726.

[37] Yi, C. P., Lu, W. B., Zhang, P., Johansson, D., & Nyberg, U. (2016). Effect of imperfect interface on the dynamic response of a circular lined tunnel impacted by plane P-waves. Tunnelling and Underground Space Technology, 51, 68-74.

[38] Yin, T., Yang, Z., Wu, Y., Tan, X., & Li, M. (2022). Experimental investigation on the effect of open fire on the tensile properties and damage evolution behavior of granite. International Journal of Damage Mechanics, 31(8), 1139-1164.

[39] Zhao, R., Tao, M., Wu, C. Q., Wang, S. F., & Zhu, J. B. (2023a). Spallation damage of underground openings caused by excavation disturbance of adjacent tunnels. Tunnelling and Underground Space Technology, 132, 104892.

[40] Zhao, R., Tao, M., Zhao, H. T., Wu, C. Q., & Cao, W. Z. (2023b). Theoretical study on dynamic stress redistribution around circular tunnel with different unloading paths. Computers and Geotechnics, 163, 105737.

[41] Zhou, Z. L., Wang, P. Y., Cai, X., & Cao, W. Z. (2023). Influence of water content on energy partition and release in rock failure: implications for water-weakening on rock-burst proneness. Rock Mechanics and Rock Engineering, 56, 6189-6205.