Propagation of Torsional Surface Wave in an Anisotropic Porous Medium over a Dry Sandy Half-Space
Publication: International Journal of Geomechanics
Volume 16, Issue 2
Abstract
The present paper deals with the propagation of torsional surface waves in an anisotropic porous layer over an inhomogeneous dry sandy half-space. The shear modulus of elasticity and density has been considered as variable in a porous layer, and the modulus of rigidity remains variable in a sandy half-space. The Whittaker function and its derivative give the result of the phase velocity equation using suitable boundary conditions. The effect of a dimensionless wave number on a dispersion curve has been found numerically, and a graphical representation of porosity and sandiness has been given. The derived dispersion equation found that the velocity of a torsional wave is influenced because of the presence of porosity, inhomogeneity, and sandy half-space. The study may be useful to understand the nature of seismic-wave propagation during earthquakes.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors convey their sincere thanks to the Council of Scientific and Industrial Research (CSIR), New Delhi, for awarding the research Project No.: 25(0227)/13/EMR-II Dated: 05.09.2013 entitled “Study of Torsional Wave in Anisotropic and Nonhomogeneous Media.”
References
Akbarov, S. D., Kepceler, T., and Egilmez, M. M. (2011). “Torsional wave dispersion in a finitely pre-strained hollow sandwich circular cylinder.” J. Sound Vib., 330(18–19), 4519–4537.
Biot, M. A. (1956). “Theory of propagation of elastic waves in a fluid-saturated porous solid.” J. Acoust. Soc. Am., 28(2), 168–178.
Biot, M. A. (1965). Mechanics of incremental deformation, John Wiley and Sons, New York.
Chattaraj, R., and Samal, S. K. (2013). “Love waves in the fiber-reinforced layer over a gravitating porous half-space.” Acta Geophys., 61(5), 1170–1183.
Chattopadhyay, A., Gupta, S., Kumari, P., and Sharma, V. K. (2013). “Torsional wave propagation in non-homogeneous layer between non-homogeneous half-spaces.” Int. J. Numer. Anal. Methods Geomech., 37(10), 1280–1291.
Chattopadhyay, A., Gupta, S., Sahu, S. A., and Singh, A. K. (2012). “Torsional surface waves in a self-reinforced medium over a heterogeneous half-space.” Int. J. Geomech., 193–197.
Chattopadhyay, A., Gupta, S., Samal, S. K., and Sharma, V. K. (2009). “Torsional waves in self-reinforced medium.” Int. J. Geomech., 9–13.
Dey, S., Gupta, A. K., and Gupta, S. (1998). “Propagation of torsional surface waves in dry sandy medium under gravity.” Math. Mech. Solids, 3(2), 227–235.
Dey, S., and Sarkar, M. G. (2002). “Torsional surface waves in an initially stressed anisotropic porous medium.” J. Eng. Mech., 184–189.
De Barros, L., Dietrich, M., and Valette, B. (2010). “Full waveform inversion of seismic waves reflected in a stratified porous medium.” Geophys. J. Int., 182(3), 1543–1556.
Ewing, W. M., Jardetzky, W. S., and Press, F. (1957). Elastic wave in layered media, McGraw-Hill, New York.
Georgiadis, H. G., Vardoulakis, I., and Lykotrafitis, G. (2000). “Torsional surface waves in a gradient-elastic half-space.” Wave Motion, 31(4), 333–348.
Ghorai, A. P., Samal, S. K., and Mahanti, N. C. (2010). “Love waves in a fluid-saturated porous layer under a rigid boundary and lying over an elastic half-space under gravity.” Appl. Math. Modell., 34(7), 1873–1883.
Gubbins, D. (1990). Seismology and plate tectonics, Cambridge University Press, Cambridge.
Gupta, A. K., and Gupta, S. (2011). “Torsional surface waves in gravitating anisotropic porous half space.” Math. Mech. Solids, 16(4), 445–450.
Gupta, S., Chattopadhyay, A., Kundu, S., and Gupta, A. K. (2010a). “Propagation of torsional surface wave in gravitating anisotropic porous half-space with rigid boundary.” Int. J. Appl. Math. Mech., 6(11), 17–25.
Gupta, S., Chattopadhyay, A., and Majhi, D. K. (2010b). “Effect of initial stress on propagation of Love wave in an anisotropic porous layer.” J. Solid Mech., 2(1), 50–62.
Iesan, D., and Nappa, L. (2003). “Axially symmetric problems for a porous elastic solid.” Int. J. Solids Struct., 40(20), 5271–5286.
Ke, L. L., Wang, Y. S., and Zhang, Z. M. (2006). “Love waves in an inhomogeneous fluid saturated porous layered half-space with linearly varying properties.” Soil Dyn. Earthquake Eng., 26(6–7), 574–581.
Kończak, Z. (1989). “The propagation of Love waves in a fluid-saturated porous anisotropic layer.” Acta Mech., 79(3–4), 155–168.
Kundu, S., Gupta, S., and Manna, S. (2014a). “SH-type waves dispersion in an isotropic medium sandwiched between an initially stressed orthotropic and heterogeneous semi-infinite media.” Meccanica, 49(3), 749–758.
Kundu, S., Gupta, S., and Manna, S. (2014b). “Propagation of G-type seismic wave in heterogeneous layer lying over an initially stressed heterogeneous half-space.” Appl. Math. Comput., 234(3), 1–12.
Pal, A. K. (1985). “The propagation of love wave in a dry sandy layer.” Acta Geophys., 33(2), 183–188.
Shearer, T., Abraham, D., and Parenell, W. J. (2013). “Torsional wave propagation in a prestressed hyperelastic annual circular cylinder.” Q. J. Mech. Appl. Math., 66(4), 465–687.
Uenishi, K. (2010). “On a possible role of Rayleigh surface waves in dynamic slope failures.” Int. J. Geomech., 153–160.
Wang, C. D., Lin, Y. T., Jeng, Y. S., and Ruan, Z. W. (2010). “Wave propagation in an inhomogeneous cross-anisotropic medium.” Int. J. Numer. Anal. Methods Geomech., 34(7), 711–732.
Wang, H., and Tian, J. (2014). “Acoustoelastic theory for fluid-saturated porous media.” Acta Mech. Sol. Sin., 27(1), 41–53.
Wang, Y. S., and Zhang, Z. M. (1998). “Propagation of Love waves in a transversely isotropic fluid saturated porous layered half-space.” J. Acoust. Soc. Am., 103(2), 695–701.
Information & Authors
Information
Published In
Copyright
© 2015 American Society of Civil Engineers.
History
Received: Oct 18, 2014
Accepted: Feb 19, 2015
Published online: Jun 30, 2015
Discussion open until: Nov 30, 2015
Published in print: Apr 1, 2016
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.