Technical Notes
May 27, 2013

Torsional Wave Propagation in a Substratum over a Dry Sandy Gibson Half-Space

Publication: International Journal of Geomechanics
Volume 14, Issue 3

Abstract

The propagation of torsional surface waves in a transversely isotropic substratum lying over a dry sandy gibson half-space in the presence of initial stress (compressive and tensile) and gravity have been studied analytically and computed numerically. The dispersion equation has been derived in a closed form. The effect of various inhomogeneity parameters on the torsional wave propagation has been exhibited by means of graphs. The influence of initial stress (compressive and tensile), Biot’s gravity parameter, and the sandy parameter have also been shown on the phase velocity of the torsional surface wave. Dispersion equations are in perfect agreement with the standard results when derived for some particular cases. Graphical user interface software has been developed to generalize the effect of various parameter discussed.

Get full access to this article

View all available purchase options and get full access to this article.

References

Biot, M. A. (1965). Mechanics of incremental deformation, Wiley, New York.
Bullen, K. E. (1940). “The problem of the Earth’s density variation.” Bull. Seismol. Soc. Am., 30(3), 235–250.
Chammas, R., Abraham, O., Cote, P., Pedersen, H. A., and Semblat, J. F. (2003). “Characterization of heterogeneous soils using surface waves: Homogenization and numerical modeling.” Int. J. Geomech., 55–63.
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.
Chapman, C. (2004). Fundamentals of seismic wave propagation, Cambridge University Press, Cambridge, U.K.
Ewing, W. M., Jardetzky, W. S., and Press, F. (1957). Elastic waves in layered media, McGraw Hill, New York.
Georgiadis, H. G., Vardaulakis, I., and Lykotrafitis, G. (2000). “Torsional surface wave in gradient-elastic half-space.” Wave Motion, 31(4), 333–348.
Golamhossen, F. R. (2000). “Propagation of waves in an elastic cylinder with voids.” Sci. Technol.-Res. J., 5, 43–52.
Gupta, S., Majhi, D. K., and Vishwakarma, S. K. (2012). “Torsional surface wave propagation in an initially stressed non-homogeneous layer over a non-homogeneous half-space.” Appl. Math. Comput., 219(6), 3209–3218.
Iesan, D., and Nappa, L. (2003). “Axially symmetric problems for a porous elastic solid.” Int. J. Solids Struct., 40(20), 5271–5286.
Jones, J. P. (1964). “Wave propagation in a two layered medium.” J. Appl. Mech., 31(2), 213–222.
Klein, K., and Santamarina, J. C. (2005). “Soft sediments: Wave-based characterization.” Int. J. Geomech., 147–157.
Love, A. E. H. (1944). A treatise on mathematical theory of elasticity, 4th Ed., Dover Publications, New York.
Midya, G. K. (2004). “On Love-type surface waves in homogeneous micropolar elastic media.” Int. J. Eng. Sci., 42(11–12), 1275–1288.
Nayfeh, A. H., and Abdelrahman, W. G. (2000). “An approximate model for wave propagation in rectangular rods and their geometric limits.” J. Vib. Control, 6, 3–17.
Ponnusamy, P., and Rajagopal, M. (2010). “Wave propagation in a homogeneous transversely isotropic thermoelastic solid cylinder of polygonal cross-sections.” J. Vib. Control, 16, 647–664.
Pujole, J. (2003). Elastic wave propagation and generation in seismology, Cambridge University Press, Cambridge, U.K.
Quintanilla, R. (2001). “On uniqueness and continuous dependence in the nonlinear theory of mixtures of elastic solids with voids.” Math. Mech. Solids, 6(3), 281–298.
Tomar, S. K. (2005). “Wave propagation in a micropolar elastic plate with voids.” J. Vib. Control, 11, 849–863.
Uenishi, K. (2010). “On a possible role of Rayleigh surface waves in dynamic slope failures.” Int. J. Geomech., 153–160.
Vardoulakis, I. (1984). “Torsional surface waves in inhomogeneous elastic media.” Int. J. Numer. Anal. Methods Geomech., 8(3), 287–296.
Whittaker, E. T., and Watson, G. N. (1990). A course in modern analysis, Cambridge University Press, Cambridge, U.K.

Information & Authors

Information

Published In

Go to International Journal of Geomechanics
International Journal of Geomechanics
Volume 14Issue 3June 2014

History

Received: Jul 2, 2012
Accepted: May 24, 2013
Published online: May 27, 2013
Published in print: Jun 1, 2014
Discussion open until: Aug 10, 2014

Permissions

Request permissions for this article.

Authors

Affiliations

Sumit Kumar Vishwakarma [email protected]
Assistant Professor, Dept. of Mathematics, Birla Institute of Technology and Science-Pilani, Hyderabad Campus, Hyderabad 500078, India (corresponding author). E-mail: [email protected]
Shishir Gupta
Professor, Dept. of Applied Mathematics, Indian School of Mines, Dhanbad 826004, India.
Samapti Kundu
Research Scholar, Dept. of Applied Mathematics, Indian School of Mines, Dhanbad 826004, India.

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.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share