Numerical Study of P-Waves Propagating across Deep Rock Masses Based on the Hoek–Brown Model
Publication: International Journal of Geomechanics
Volume 20, Issue 2
Abstract
Strong dynamic disturbances constitute an important problem threatening the safety of deep underground engineering projects. The mechanical mechanisms responsible for such disturbances in deep rock masses can be revealed by studying stress waves propagating across them. In this study, the propagation of P-waves across a deep rock mass was investigated both numerically and theoretically. The Hoek–Brown (HB) model, which is able to account for the stress state and nonlinear failure of the rock mass, was employed. In particular, the time-domain recursive method was extended to analyze the propagation of P-waves across the rock mass following the HB failure criterion. Good agreement is found between the theoretical results and simulations, which demonstrates that using the Universal Distinct Element Code (UDEC) with the HB model to study the transmission of P-waves across rock masses is eminently feasible. The effects of the disturbance factor, confining pressure, incident amplitude, and coupling of joints and rock mass quality on wave propagation were also studied using the UDEC in a systematic manner. The results show that for an incident P-wave of given amplitude, the greater the rock mass quality and smaller the disturbance factor, the greater the transmission coefficient. In addition, there is an upper limit to the effect the confining pressure has on the transmission coefficient. The amplitude of the incident wave also has an important influence on the transmission coefficient. Finally, if the quality of the rock mass is good and the disturbance slight, then the attenuation of the wave is primarily caused by the joints.
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Data Availability Statement
Some or all data, models, or code generated or used during the study are available from the corresponding author by request. Specific items are as follows:
1.
The original data for Figs. 3–9 and 11–13.
2.
The UDEC code used in this work.
Acknowledgments
The research was financially supported by National Natural Science Foundation of China (Grant Nos. 11602284, 51609183, and 41807280) and the Open Research Fund of the State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences (Grant No. Z015005).
References
Alejano, L. R., I. Gómez-Márquez, and R. Martínez-Alegría. 2010. “Analysis of a complex toppling-circular slope failure.” Eng. Geol. 114 (1–2): 93–104. https://doi.org/10.1016/j.enggeo.2010.03.005.
Babanouri, N., H. Mansouri, S. K. Nasab, and M. Bahaadini. 2013. “A coupled method to study blast wave propagation in fractured rock masses and estimate unknown properties.” Comput. Geotech. 49 (Apr): 134–142. https://doi.org/10.1016/j.compgeo.2012.11.008.
Cai, J. G., and J. Zhao. 2000. “Effects of multiple parallel fractures on apparent attenuation of stress waves in rock mass.” Int. J. Rock Mech. Min. Sci. 37 (4): 661–682. https://doi.org/10.1016/S1365-1609(00)00013-7.
Chen, S. G., and J. Zhao. 1998. “A study of UDEC modelling for blast wave propagation in jointed rock masses.” Int. J. Rock Mech. Min. Sci. 35 (1): 93–99. https://doi.org/10.1016/S0148-9062(97)00322-7.
Cheng, G. W., C. X. Chen, L. C. Li, W. C. Zhu, T. H. Yang, F. Dai, and B. Ren. 2018. “Numerical modelling of strata movement at footwall induced by underground mining.” Int. J. Rock Mech. Min. Sci. 108 (Aug): 142–156. https://doi.org/10.1016/j.ijrmms.2018.06.013.
Cheng, G. W., T. H. Ma, C. A. Tang, H. Y. Liu, and S. J. Wang. 2017. “A zoning model for coal mining-induced strata movement based on microseismic monitoring.” Int. J. Rock Mech. Min. Sci. 94 (Apr): 123–138. https://doi.org/10.1016/j.ijrmms.2017.03.001.
Cook, N. G. W., and K. Hodgson. 1965. “Some detailed stress-strain curves for rock.” J. Geophys. Res.-Atmos. 70 (12): 2883–2888. https://doi.org/10.1029/JZ070i012p02883.
Fu, X. D., Q. Sheng, Y. H. Zhang, and J. Chen. 2017. “Time-frequency analysis of seismic wave propagation across a rock mass using the discontinuous deformation analysis method.” Int. J. Geomech. 17 (8): 04017024. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000892.
Hoek, E., and E. T. Brown. 1997. “Practical estimates of rock mass strength.” Int. J. Rock Mech. Min. Sci. 34 (8): 1165–1186. https://doi.org/10.1016/S1365-1609(97)80069-X.
Huang, X., S. Qi, A. Williams, Y. Zou, and B. Zheng. 2015. “Numerical simulation of stress wave propagating through filled joints by particle model.” Int. J. Solids Struct. 69–70 (Sep): 23–33. https://doi.org/10.1016/j.ijsolstr.2015.06.012.
Itasca. 2004. UDEC version 4.0 user’s manual. Minneapolis: Itasca.
Kolsky, H. 1953. Stress waves in solids. Oxford, UK: Clarendon Press.
Konicek, P., K. Soucek, L. Stas, and R. Singh. 2013. “Long-hole destress blasting for rock-burst control during deep underground coal mining.” Int. J. Rock Mech. Min. Sci. 61 (Jul): 141–153. https://doi.org/10.1016/j.ijrmms.2013.02.001.
Li, H. B., T. T. Liu, Y. Q. Liu, J. C. Li, X. Xia, and B. Liu. 2015a. “Numerical modeling of wave transmission across rock mass with nonlinear joints.” Rock Mech. Rock Eng. 49 (3): 1115–1121.
Li, J. C., H. B. Li, G. W. Ma, and J. Zhao. 2012. “A time-domain recursive method to analyse transient wave propagation across rock joints.” Geophys. J. Int. 188 (2): 631–644. https://doi.org/10.1111/j.1365-246X.2011.05286.x.
Li, J. C., T. T. Liu, H. B. Li, Y. Q. Liu, B. Liu, and X. Xia. 2015b. “Shear wave propagation across filled Joints with the effect of interfacial shear strength.” Rock Mech. Rock Eng. 48 (4): 1547–1557. https://doi.org/10.1007/s00603-014-0662-1.
Li, J. C., G. W. Ma, and J. Zhao. 2011. “Analysis of stochastic seismic wave interaction with a slippery rock fault.” Rock Mech. Rock Eng. 44 (1): 85–92. https://doi.org/10.1007/s00603-010-0109-2.
Liu, T. T., X. P. Li, J. C. Li, H. B. Li, Y. Zheng, and Y. Luo. 2017. “Numerical study on S-wave transmission across a rough, filled discontinuity.” Arab. J. Geosci. 10 (11): 249. https://doi.org/10.1007/s12517-017-3030-0.
Meng, F. Z., L. N. Y. Wong, H. Zhou, J. Yu, and G. T. Cheng. 2019. “Shear rate effects on the post-peak shear behaviour and acoustic emission characteristics of artificially split granite joints.” Rock Mech. Rock Eng. 52 (7): 2155–2174.
Pyrak-Nolte, L. J., L. R. Myer, and N. G. W. Cook. 1990. “Transmission of seismic waves across single natural fractures.” J. Geophys. Res. 95 (B6): 8617. https://doi.org/10.1029/JB095iB06p08617.
Schoenberg, M. 1980. “Elastic wave behavior across linear slip interfaces.” J. Acoust. So. Am. 68 (5): 1516–1521. https://doi.org/10.1121/1.385077.
Sebastian, R., and T. G. Sitharam. 2016. “Transformations of obliquely striking waves at a rock joint: Numerical simulations.” Int. J. Geomech. 16 (3): 04015079. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000575.
Yan, C. Z., Y. Y. Jiao, and S. Yang. 2019. “A 2D coupled hydro-thermal model for the combined finite-discrete element method.” Acta Geotech. 14 (2): 403–416. https://doi.org/10.1007/s11440-018-0653-6.
Zhao, J., J. G. Cai, X. B. Zhao, and H. B. Li. 2008a. “Dynamic model of fracture normal behaviour and application to prediction of stress wave attenuation across fractures.” Rock Mech. Rock Eng. 41 (5): 671–693. https://doi.org/10.1007/s00603-006-0127-2.
Zhao, J., X. B. Zhao, and J. G. Cai. 2006. “A further study of P-wave attenuation across parallel fractures with linear deformational behaviour.” Int. J. Rock Mech. Min. Sci. 43 (5): 776–788. https://doi.org/10.1016/j.ijrmms.2005.12.007.
Zhao, X. B., J. Zhao, J. G. Cai, and A. M. Hefny. 2008b. “UDEC modelling on wave propagation across fractured rock mass.” Comput. Geotech. 35 (1): 97–104. https://doi.org/10.1016/j.compgeo.2007.01.001.
Zhao, X. B., J. B. Zhu, J. Zhao, and J. G. Cai. 2012. “Study of wave attenuation across parallel fractures using propagator matrix method.” Int. J. Numer. Anal. Methods Geomech. 36 (10): 1264–1279. https://doi.org/10.1002/nag.1050.
Zheng, Y., C. X. Chen, T. T. Liu, D. R. Song, and F. Meng. 2019. “Stability analysis of anti-dip bedding rock slopes locally reinforced by rock bolts.” Eng. Geol. 251: 228–240. https://doi.org/10.1016/j.enggeo.2019.02.002.
Zheng, Y., C. X. Chen, T. T. Liu, H. N. Zhang, K. Z. Xia, and F. Liu. 2018. “Study on the mechanisms of flexural toppling failure in anti-inclined rock slopes using numerical and limit equilibrium models.” Eng. Geol. 237 (Apr): 116–128. https://doi.org/10.1016/j.enggeo.2018.02.006.
Zhu, J. B., X. F. Deng, X. B. Zhao, and J. Zhao. 2013. “A numerical study on wave transmission across multiple intersecting joint sets in rock mass with UDEC.” Rock Mech. Rock Eng. 46 (6): 1429–1442. https://doi.org/10.1007/s00603-012-0352-9.
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Published In
International Journal of Geomechanics
Volume 20 • Issue 2 • February 2020
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©2019 American Society of Civil Engineers.
History
Received: Jan 29, 2019
Accepted: Jul 12, 2019
Published online: Nov 29, 2019
Published in print: Feb 1, 2020
Discussion open until: Apr 29, 2020
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