Abstract
Open joints have significantly different effects on stress wave propagation across them as compared to closed and filled joints. In the present study, a theoretical model is developed based on the analysis of interaction process between stress waves and a single open joint. The analytical solutions to the energy transmission coefficient are mathematically derived for stress waves across an open joint. Parametric studies are conducted to evaluate the effects of various parameters on the energy transmission coefficient. It is found that the energy transmission coefficient follows a similar trend for all types of stress waves, but stress waves with different waveforms have different values. The energy transmission coefficient increases with the increase in the wave amplitude and duration, but decreases with the gap width. It also increases at the outset, and then decreases gradually with the increase in the incident angle for rectangle, symmetric triangle and ascending triangle waves, but it decreases with the incident angle for sine and descending triangle waves. Furthermore, different-shaped stress waves have different critical gap widths for wave transmission. The optimal incident angle and the critical gap width increase as the wave duration increases, but the critical stress amplitude decreases.
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References
Cai JG, Zhao J (2000) Effects of multiple parallel fractures on apparent attenuation of stress wave in rock masses. Int J Rock Mech Min Sci 37(4):661–682
Ewing WM, Jardetzky WS, Press F (1957) Elastic waves in layered media. McGraw-Hill, New York
Fourney WL, Dick RD, Wang XJ et al (1997a) Effects of weak layers on particle velocity measurements. Rock Mech Rock Eng 30(1):1–18
Fourney WL, Dick RD, Fordyce DF et al (1997b) Effects of open gaps on particle velocity measurements. Rock Mech Rock Eng 30(2):95–111
Li JC, Ma GW (2009) Experimental study of stress wave propagation across a filled rock joint. Int J Rock Mech Min Sci 46(3):471–478
Li JC, Ma GW (2010) Analysis of blast wave interaction with a rock joint. Rock Mech Rock Eng 43(6):777–787
Li JC, Ma GW, Huang X (2010) Analysis of wave propagation through a filled rock joint. Rock Mech Rock Eng 43(6):789–798
Li YX, Zhu ZM, Li XB, Deng JH, Xie HP (2011) Study on the transmission and reflection of stress waves across joints. Int J Rock Mech Min Sci 48(3):364–371
Li JC, Wu W, Li HB, Zhu JB, Zhao J (2013) A thin-layer interface model for wave propagation through filled rock joints. J Appl Geophys 91:31–38
Li JC, Li HB, Jiao YY, Liu YQ, Xia X, Yu C (2014) Analysis for oblique wave propagation across filled joints based on thin-layer interface model. J Appl Geophys 102:39–46
Pyrak-Nolte LJ (1996) The seismic response of fractures and the interrelation among fracture properties. Int J Rock Mech Min Sci 33(8):787–802
Pyrak-Nolte LJ, Myer LR, Cook NGW (1990) Transmission of seismic waves across single natural fractures. J Geophys Res 95(6):8617–8638
Schoenberg M (1980) Elastic wave behavior across linear slip interfaces. J Acoust Soc Am 68(5):1516–1521
Wang WH, Li XB, Zuo YJ (2006) Effect of non-linearly normal deformational joint on elastic P-wave propagation. Chin J Rock Mech Eng 25(6):1218–1225 (in Chinese)
Yu J, Qian QH, Lin CM, Zhao XB (2009) Transmission of elastic P-wave across one fracture with improved nonlinear normal deformation behaviors. Chin J Geotech Eng 31(8):1156–1164 (in Chinese)
Zhao J, Cai JG (2001) Transmission of elastic P-wave across single fractures with a nonlinear normal deformational behavior. Rock Mech Rock Eng 34(1):3–22
Zhao J, Zhao XB, Cai JG (2006a) A further study of P-wave attenuation across parallel fractures with linear deformational behavior. Int J Rock Mech Min Sci 43(5):776–788
Zhao XB, Zhao J, Cai JG (2006b) P-wave transmission across fractures with nonlinear deformational behavior. Int J Numer Anal Methods Geomech 30(11):1097–1112
Zhu JB, Zhao XB, Wu W, Zhao J (2012) Wave propagation across rock joints filled with viscoelastic medium using modified recursive method. J Appl Geophys 86:82–87
Acknowledgments
This work was supported by the National Natural Science Foundation of China (41372278, 41472269, 41102170), the China Scholarship Council and the freedom explore Program of Central South University.
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Wang, W., Hao, H., Li, X. et al. Effects of a Single Open Joint on Energy Transmission Coefficients of Stress Waves with Different Waveforms. Rock Mech Rock Eng 48, 2157–2166 (2015). https://doi.org/10.1007/s00603-014-0684-8
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DOI: https://doi.org/10.1007/s00603-014-0684-8