Love-Wave Propagation in an Inhomogeneous Orthotropic Medium Obeying the Exponential and Generalized Power Law Models
Publication: International Journal of Geomechanics
Volume 17, Issue 7
Abstract
Based on the theory of elasticity, the analytical solutions of the Love-wave dispersion equation are generated for the inhomogeneous orthotropic medium, for which the Young’s modulus (Ex, Ey, Ez), shear modulus (Gxy, Gyz, Gxz), and medium density (ρ) are obeying the exponential law model (Exeαz, Eyeαz, Ezeαz, Gxyeαz, Gyzeαz, Gxzeαz, and ρeαz) and the generalized power model [Ex(a + bz)m, Ey(a + bz)m, Ez(a + bz)m, Gxy(a + bz)m, Gyz(a + bz)m, Gxz(a + bz)m, and ρ(a + bz)m]; however, three Poisson’s ratios (υxy, υyz, υxz) are constants regardless of depth. In other words, the aforementioned moduli and density of the upper orthotropic layer [with thickness (H)] and lower orthotropic half-space are assumed to vary exponentially and generalized power laws as depth increased. To explore the influence of the inhomogeneous characteristics of the orthotropic materials on Love-wave velocity, a parametric study was conducted by utilizing the granite’s parameters. The results reveal that the Love-wave velocity is markedly influenced by the inhomogeneity parameters (α, a, b, and m) but is unaffected by the presented isotropic/orthotropic rock types. Hence, it is imperative to consider the effect of inhomogeneities when investigating the behaviors of Love-wave propagation in the orthotropic medium.
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Acknowledgments
The corresponding author thanks the Ministry of Science and Technology (MOST) for supporting this research under Contracts MOST 105-2625-M-239-004 MY2.
References
Abd-Alla, A. M., and Ahmed, S. M. (1999). “Propagation of Love waves in a non-homogeneous orthotropic elastic layer under initial stress overlying semi-infinite medium.” Appl. Math. Comput., 106(2–3), 265–275.
Chakraborty, S. K., and Dey, S. (1982). “The propagation of Love waves in water-saturated soil underlain by a heterogeneous elastic medium.” Acta Mech., 44(3), 169–176.
De, S. (1972). “On the propagation of Love waves in a non-homogeneous isotropic layer of finite depth lying on an infinite non-isotropic layer.” Pure Appl. Geophys., 101(1), 90–101.
Gupta, S., Chattopadhyay, A., and Majhi, D. K. (2010). “Effect of initial stress on propagation of Love waves in an anisotropic porous layer.” J. Solid Mech., 2(1), 50–62.
Gupta, S., Chattopadhyay, A., Vishwakarma, S. K., and Majhi, D. K. (2011). “Influence of rigid boundary and initial stress on the propagation of Love wave.” Appl. Math., 2(5), 586–594.
Gupta, S., Majhi, D. K., Kundu, S., and Vishwakarma, S. K. (2012). “Propagation of torsional surface waves in a homogeneous layer of finite thickness over an initially stressed heterogeneous half-space.” Appl. Math. Comput., 218(9), 5655–5664.
Gupta, S., Majhi, D. K., Kundu, S., and Vishwakarma, S. K. (2013). “Propagation of Love waves in non-homogeneous substratum over initially stressed heterogeneous half-space.” Appl. Math. Mech., 34(2), 249–258.
Kakar, R. (2015). “Love waves in Voigt-type viscoelastic inhomogeneous layer overlying a gravitational half-space.” Int. J. Geomech., 04015068.
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), 155–168.
Kundu, S., Manna, S., and Gupta, S. (2015). “Propagation of SH-wave in an initially stressed orthotropic medium sandwiched by a homogeneous and an inhomogeneous semi-infinite media.” Math. Methods Appl. Sci., 38(9), 1926–1936.
Love, A. E. H. (1911). Some problems of geodynamics, Cambridge Univ. Press, Cambridge, U.K.
Madan, D. K., Kumar, R., and Sikka, J. S. (2014). “Love wave propagation in an irregular fluid saturated porous anisotropic layer with rigid boundary.” J. Appl. Sci. Res., 10(4), 281–287.
Mahmoud, S. R. (2010). “Effect of the non-homogeneity on wave propagation on orthotropic elastic media.” Int. J. Contemp. Math. Sci., 5(45–48), 2211–2224.
Pal, P. C., Kumar, S., and Bose, S. (2014). “Propagation of plane SH-wave in inhomogeneous monoclinic layer overlying self-reinforced elastic solid half-space.” Int. J. Appl. Math. Mech., 10(3), 58–68.
Pal, P. K., and Acharya, D. (1998). “Effects of inhomogeneity on surface waves in anisotropic media.” Sadhana, 23(3), 247–258.
Pan, U. C., and Chakrabarty, S. K. (1973). “On Love waves in inhomogeneous anisotropic elastic solids.” Pure Appl. Geophys., 102(1), 29–36.
Pradhan, A., Samal, S. K., and Mahanti, N. C. (2003). “Influence of anisotropy on the Love waves in a self-reinforced medium.” Tamkang J. Sci. Eng., 6(3), 173–178.
Rowe, R. K., and Booker, J. R. (1981). “The behaviour of footings resting a non-homogeneous soil mass with a crust, part I. Strip footings.” Can. Geotech. J., 18(2), 250–264.
Sano, O., and Kudo, Y. (1992). “Relation of fracture resistance to fabric for granitic rocks.” Pure Appl. Geophys., 138(4), 657–677.
Sethi, M., Gupta, K. C., Kakar, R., and Gupta, M. P. (2011). “Propagation of Love waves in a non-homogeneous orthotropic layer under compression ‘P’ overlying semi-infinite non-homogeneous medium.” Int. J. Appl. Math. Mech., 7(10), 97–110.
Thapliyal, V. (1971a). “Love waves in a sedimentary layer lying over an anisotropic inhomogeneous half space.” Pure Appl. Geophys., 88(1), 53–59.
Thapliyal, V. (1971b). “Love waves in inhomogeneous and anisotropic earth—I.” Pure Appl. Geophys., 91(1), 40–50.
Ting, T. C. T. (2011). “Surface waves in an exponentially graded, general anisotropic elastic material under the influence of gravity.” Wave Motion, 48(4), 335–344.
Upadhyay, S. K. (1970). “Love wave propagation in anisotropic inhomogeneous medium: Elastic parameters for equivalent isotropic case.” Pure Appl. Geophys., 81(1), 45–50.
Upadhyay, S. K. (1971). “Separation of equation of motion of Love waves in curvilinearly anisotropic inhomogeneous medium.” Pure Appl. Geophys., 86(1), 63–68.
Wang, C. D., Wang, W. J., Lin, Y. T., and Ruan, Z. W. (2012). “Wave propagation in an inhomogeneous transversely isotropic material obeying the generalized power law model.” Arch. Appl. Mech., 82(7), 919–936.
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Published In
International Journal of Geomechanics
Volume 17 • Issue 7 • July 2017
Copyright
© 2017 American Society of Civil Engineers.
History
Received: Mar 12, 2016
Accepted: Oct 25, 2016
Published online: Jan 13, 2017
Discussion open until: Jun 13, 2017
Published in print: Jul 1, 2017
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