Response of anisotropic porous layered media with uncertain soil parameters to shear body-and Love-waves

  • Sadouki, Amina ;
  • Harichane, Zamila ;
  • Elachachi, Sidi Mohammed ;
  • Erken, Ayfer
  • Received : 2017.09.25
  • Accepted : 2018.02.23
  • Published : 2018.04.25


The present study is dedicated to investigate the SH body-as well as Love-waves propagation effects in porous media with uncertain porosity and permeability. A unified formulation of the governing equations for one-dimensional (1-D) wave propagation in anisotropic porous layered media is presented deterministically. The uncertainties around the above two cited parameters are taken into account by random fields with the help of Monte Carlo Simulations (MCS). Random samples of the porosity and the permeability are generated according to the normal and lognormal distribution functions, respectively, with a mean value and a coefficient of variation for each one of the two parameters. After performing several thousands of samples, the mathematical expectation (mean) of the solution of the wave propagation equations in terms of amplification functions for SH waves and in terms of dispersion equation for Love-waves are obtained. The limits of the Love wave velocity in a porous soil layer overlaying a homogeneous half-space are obtained where it is found that random variations of porosity change the zeros of the wave equation. Also, the increase of uncertainties in the porosity (high coefficient of variation) decreases the mean amplification function amplitudes and shifts the fundamental frequencies. However, no effects are observed on both Love wave dispersion and amplification function for random variations of permeability. Lastly, the present approach is applied to a case study in the Adapazari town basin so that to estimate ground motion accelerations lacked in the fast-growing during the main shock of the damaging 1999 Kocaeli earthquake.


SH wave;Love wave;dispersion;Monte Carlo simulations;amplification;acceleration


  1. Assimaki, D., Pecker, A., Popescu, R. and Prevost, J. (2003), "Effects of spatial variability of soil properties on surface ground motion", J. Earthq. Eng., 7, 1-44.
  2. Bansal, S.R. and Kuldeepak. (2011), "Study of propagation of shear waves in a multilayer medium including a fluid-saturated porous stratum", Int. J. Theor. Appl. Sci., 3, 57-61.
  3. Bezih, K., Chateauneuf, A., Kalla, M. and Bacconnet, C. (2015), "Effect of soil-structure interaction on the reliability of reinforced concrete bridges", Ain Shams Eng. J., 1, 2090-4479.
  4. Biot, M.A. (1956a), "Theory of propagation of elastic waves in fluid-saturated porous solid. I. Low-frequency range", J. Acoust. Soc. Am., 28, 168-178.
  5. Biot, M.A. (1956b), "Theory of propagation of elastic waves in a fluid-saturated porous solid. II. Higher frequency range", J. Acoust. Soc. Am., 28, 179-191.
  6. Celebi, M., Toprak, S. and Holzer, T. (2000), "Strong-motion, siteeffects and Hazard Issues in rebuilding Turkey: in light of the 17 August 1999 earthquake and its aftershocks", Int. J. Hous. Sci. Its Appl., 24, 21-38.
  7. Cetin, K.O., Youd, T.L., Seed, R.B., Bray, J.D., Sancio, R., Lettis, W., ... & Durgunoglu, H.T. (2002), "Liquefaction-induced ground deformations at Hotel Sapanca during Kocaeli (Izmit), Turkey earthquake", Soil Dyn. Earthq. Eng., 22, 1083-92.
  8. Crampin, S. (1970), "The dispersion of surface waves in multilayered anisotropic media", Geophys. J. Int., 21, 387-402.
  9. Erdik, M. (2000), "Report on 1999 kocaeli and duzce (turkey) earthquakes", Bogazici University, Turkey.
  10. 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. Model., 34, 1873-1883.
  11. Guellil, M.E., Harichane, Z., Berkane, H.D. and Sadouki, A. (2017), "Soil and structure uncertainly on the Foundation Structure dynamic response", Earthq. Struct., 12, 153-163.
  12. Gupta, S., Vishwakarma, S.K., Majhi, D.K. and Kundu, S. (2013), "Possibility of Love wave propagation in a porous layer under the effect of linearly varying directional rigidities", Appl. Math. Model., 37, 6652-6660.
  13. Kakar, R. (2015)," SH-wave propagation in a heterogeneous layer over an inhomogeneous isotropic elastic half-space", Earthq. Struct., 9(2), 305-320.
  14. Khellafi, M.A., Harichane, Z., Afra, H. and Erken, A. (2016), "Prediction of parameters of soil stratums and earthen dams from free field acceleration records", Int. J. Geotech. Earthq. Eng. (IJGEE), 7, 33-56.
  15. Kielczynski, P. (2018), "Surface Love waves in a lossy layered planar waveguide with a viscoelastic guiding layer", Appl. Math. Model., 53, 419-432.
  16. Kielczynski, P., Szalewski, M., Balcerzak, A. and Wieja, K. (2015), "Group and phase velocity of Love waves propagating in elastic functionally graded materials", Arch. Acoust., 40, 273-281.
  17. Komazawa, M., Morikawa, H., Nakamura, K., Akamatsu, J., Nishimura, K., Sawada, S., Erken, A. and Onalp, A. (2002), "Bedrock structure in Adapazari, Turkey - a possible cause of severe damage by the 1999 Kocaeli earthquake", Soil Dyn. Earthq. Eng., 22, 829-836.
  18. Kudo, K., Kanno, T., Okada, H., O zel, O., Erdik, M., Takahashi, M., Sasatani, T., Higashi, S. and Yoshida, K. (2000) "Site specific issues on strong ground motion during the Kociaeli, Turkey earthquake of August 17, 1999, as Inferred from Array Observations of Microtremors and Aftershocks", Bull. Seismol. Soc. Am., 92, 448-465.
  19. Pallavika, V.K.K., Chakraborty, S.K. and Amalendu, S. (2008), "Finite difference modeling of SH-wave propagation in multilayered porous crust", J. Ind. Geophys. Union., 12, 165-172.
  20. Rao Rama, Y.V. and Sarma, K.S. (1984), "Generation of SH type of waves due to stress discontinuity in a poroelastic-layered medium", Ind. Inst. Sci., 64, 21-28.
  21. Ren, H., Goloshubin, G. and Hilterman, F.J. (2009), "Poroelastic analysis of amplitude-versus-frequency variations", Geophys., 74, 41-48.
  22. Rohan, E. (2013), "Homogenization of acoustic waves in strongly heterogeneous porous structures", Wave Motion, 50, 1073-1089.
  23. Saha, A., Kundu, S., Gupta, S. and Vaishnav, P.K. (2015), "Love waves in a heterogeneous orthotropic layer under initial stress overlying a gravitating porous half-space", Proc. Ind. Natn. Sci. Acad., 81, 1193-1205.
  24. Sharma, M.D. and Gogna, M.L. (1993), "Reflection and transmission of SH waves in an initially stressed medium consisting of a sandy layer lying over a fluid-saturated porous solid", Pageoph, 140, 613-628.
  25. Sidhu, R.S. (1971), "Propagation of love waves in a two-layered heterogeneous half space", Pageoph., 91(1), 76-94.
  26. Son, M.S. and Kang, Y.J. (2012), "Propagation of shear waves in a poroelastic layer constrained between two elastic layers", Appl. Math. Model., 36, 3685-3695.
  27. Wang, S. and Hao, H. (2002), "Effect of random variations of soil properties on site amplification of seismic ground motions", Soil Dyn. Earthq. Eng., 22, 551-64.