Transformations of Obliquely Striking Waves at a Rock Joint: Numerical Simulations
Publication: International Journal of Geomechanics
Volume 16, Issue 3
Abstract
Knowledge of wave propagation across rock joints is necessary for understanding distinctions between wave attenuation and lithology. Whenever a propagating seismic wave strikes a rock joint at an angle not normal to the joint, wave transformation occurs. The rock joints existing in the field are not oriented in the condition for normal incidence of the wave; hence, wave transformations are very common. In this paper, transformations of P and Sv waves have been modeled numerically with the help of a distinct element method. Validation of the numerical model has been carried out by comparing the wave velocities obtained from bender/extender elements. The dependence of the transformation of obliquely striking waves on the frequency of incident waves and stiffness of the joint has been studied. The velocities of propagating waves and the ratios of stress amplitudes of propagating waves with respect to the incident wave have been obtained and compared for all the possible angles of incidence. The wave velocities and amplitudes of propagating stress waves are found to be dependent on the angle of incidence of the waves at the rock joint. It was observed that the transformed waves that are of the same type as the incident wave contain more energy.
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References
Aki, K., and Richards, P. G. (1980). Quantitative seismology: Theory and methods, Vol.1, W. H. Freeman, San Francisco.
Arroyo, M., Pineda, J. A., and Romero, E. (2010). “Shear wave measurements using bender elements in argillaceous rocks.” Geotech. Test. J., 33(6), 1–11.
Arulnathan, R., Boulanger, R., and Riemer, M. F. (1998). “Analysis of bender element tests.” Geotech. Test. J., 21(2), 120–131.
Cha, M., Cho, G., and Santamarina, J. C. (2009). “Long wavelength P-wave and S-wave propagation in jointed rock masses.” Geophysics, 74(5), E205–E214.
Chan, C. (2010). “Bender element test in soil specimens: Identifying the shear wave arrival time.” Electron. J. Geotech. Eng., 15, 1263–1276.
Chen, S. G., Cai, J. G., Zhao, J., and Zhou, Y. X. (2000). “Discrete element modelling of underground explosions in jointed rock mass.” Geotech. Geol. Eng., 18, 59–78.
Cook, K. L., Algermissen, S. T., and Costain, J. K. (1962). “The status of PS converted waves in crustal studies.” J. Geophys. Res., 67(12), 4769–4778.
Cundall, P. A., and Hart, R. D. (1992). “Numerical modeling of discontinua.” Eng. Comp., 9(2), 101–113.
Deng, X. F., Zhu, J. B., Chen, S. G., and Zhao, J. (2012). “Some fundamental issues and verification of 3DEC in modeling wave propagation in jointed rock masses.” Rock Mech. Rock Eng., 45(5), 943–951.
Fratta, D., and Santamarina, J. C. (2002). “Shear wave propagation in jointed rock: State of stress.” Géotechnique, 52(7), 495–505.
Gu, B., Nihei, K. T., Myer, L. R., and Pyrak-Nolte, L. J. (1996). “Fracture interface waves.” J. Geophys. Res., 101(B1), 827–835.
King, M. S., Chaudhary, N. A., and Shakeel, A. (1995). “Experimental ultrasonic velocities and permeability of sandstones with aligned cracks.” Int. J. Rock Mech. Miner. Sci. Geomech. Abstr., 32(2), 155–163.
Kramer, S. (1996). Geotechnical earthquake engineering, Prentice Hall, Upper Saddle River, NJ.
Kuhlemeyer, R. L., and Lysmer, J. (1973). “Finite element accuracy for wave propagation problems.” J. Soil Mech. Found. Div., 99(SM5), 421–427.
Kurtuluş, C., Üςkardeş, M., Sari, U., and Güner, Ş. O. (2012). “Experimental studies in wave propagation across a jointed rock mass.” Bull. Eng. Geol. Environ., 71(2), 231–234.
Miller, R. K. (1977). “An approximate method of analysis of the transmission of elastic waves through a frictional boundary.” J. Appl. Mech., 44(4), 652–656.
Miller, R. K. (1978). “The effects of boundary friction on the propagation of elastic waves.” Bull. Seismol. Soc. Am., 68(4), 987–998.
Mohd-Nordin, M. M., Song, K., Cho, G., and Mohamed, Z. (2014). “Long-wavelength elastic wave propagation across naturally fractured rock masses.” Rock Mech. Rock Eng., 47(2), 561–573.
Nihei, K. T., Yi, W., Myer, L. R., and Cook, N. G. W. (1999). “Fracture channel waves.” J. Geophys. Res., 104(3), 4769–4781.
Olsson, S. (2007). “Analyses of seismic wave conversion in the crust and upper mantle beneath the Baltic shield,” Ph.D. thesis, Uppsala Univ., Uppsala, Sweden.
Perino, A. (2011). “Wave propagation through discontinuous media in rock engineering,” Ph.D. thesis, Polytechnic Univ. of Turin, Turin, Italy.
Pyrak-Nolte, L. J., Myer, L. R., and Cook, N. G. W. (1990a). “Transmission of seismic waves across single natural fractures.” J. Geophys. Res., 95(B6), 8617–8638.
Pyrak-Nolte, L. J., Myer, L. R., and Cook, N. G. W. (1990b). “Anisotropy in seismic velocities and amplitudes from multiple parallel fractures.” J. Geophys. Res., 95(B7), 11345–11358.
Schoenberg, M. (1980). “Elastic wave behavior across linear slip interfaces.” J. Acoust. Soc. Am., 68(5), 1516–1521.
Sebastian, R., and Sitharam, T. G. (2014). “Numerical simulation of transformation of an obliquely incident shear wave at rock joint.” Proc., Int. Symp. on Geomechanics from Micro to Macro (IS-Cambridge 2014), Soga et al., eds., Taylor & Francis, London, 801–805.
Stewart, R. R., Gaiser, J. E., Brown, R. J., and Lawton, D. C. (2003). “Converted-wave seismic exploration: Applications.” Geophysics, 68(1), 40–57.
UDEC [Computer software]. Itasca, Minneapolis.
Viggiani, G., and Atkinson, J. H. (1995). “Interpretation of bender element tests.” Géotechnique, 45(1), 149–154.
Zhao, X. B., Zhao, J., Cai, J. G., and Hefny, A. M. (2008). “UDEC modelling on wave propagation across fractured rock masses.” Comput. Geotech., 35(1), 97–104.
Zhao, X. B., Zhao, J., Hefny, A. M., and Cai, J. G. (2006). “Normal transmission of S-wave across parallel fractures with Coulomb slip behavior.” J. Eng. Mech., 641–650.
Zhu, J. B., and Zhao, J. (2013). “Obliquely incident wave propagation across rock joints with virtual wave source method.” J. Appl. Geophys., 88, 23–30.
3DEC [Computer software]. Version 4.1. Itasca Consulting Group, Inc., Minneapolis.
Information & Authors
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Published In
International Journal of Geomechanics
Volume 16 • Issue 3 • June 2016
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Dec 22, 2014
Accepted: Jun 29, 2015
Published online: Jan 5, 2016
Published in print: Jun 1, 2016
Discussion open until: Jun 5, 2016
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