Technical Notes
Sep 28, 2022

Propagation of Love-Type Wave in an Imperfectly Bonded Double-Porous Composite Rock Structure Impacted by Liquid Loading

Publication: International Journal of Geomechanics
Volume 22, Issue 12

Abstract

Construction of a large water reservoir can trigger an earthquake. The event of the earthquake can lead to the propagation of a destructive Love-type waves (LT-wave). Therefore, the area near the reservoir is prone to the propagation of LT-waves. Due to this, it is crucial to examine the propagation of LT-wave propagation in the geological structure found in these areas. The present analysis adduces the propagation of LT-waves in the anisotropic double-porous rock structure that is generally found the area of water reservoirs. The said rock structure consists of three different regions: the uppermost viscous liquid region, transversely isotropic double-porous (TIDP) rock layer in the middle, and the lowermost half-space region comprised of isotropic double-porous (IDP) rock medium. The expressions for the dispersion and damping characteristics have been derived for parabolicalal and rectangular interfacial irregularity. The profound efficacy of distinct physical parameters, such as irregularity parameter, interfacial bonding parameter, porosity parameter of said middle double-porous layer, and porosity parameter of said lowermost double-porous half-space on the phase velocity and attenuation coefficient of LT-waves, are also discussed.

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Data Availability Statement

The data, models, or code that used in the present study are available by the corresponding author upon reasonable request.

Acknowledgments

The authors convey their sincere thanks to University Grants Commission (UGC) for providing a senior research fellowship to Mr. Mukesh Kumar Pal with UGC-JRF award and Ref. No: 416141 & 19/06/2016(i)EU-V for carrying out this research work.

References

Agersborg, R., T. A. Johansen, and M. Jakobsen. 2009. “Velocity variations in carbonate rocks due to dual porosity and wave-induced fluid flow.” Geophys. Prospect. 57 (1): 81–98. https://doi.org/10.1111/j.1365-2478.2008.00733.x.
Ba, J., J. M. Carcione, and J. X. Nie. 2011. “Biot-Rayleigh theory of wave propagation in double-porosity media.” J. Geophys. Res. 116 (B6): B06202. https://doi.org/10.1029/2010JB008185.
Bai, P., P. Wu, Z. Yan, and X. S. Zhao. 2009. “A reverse cation–anion double hydrolysis approach to the synthesis of mesoporous γ-Al2O3 with a bimodal pore size distribution.” Microporous Mesoporous Mater. 118 (1–3): 288–295. https://doi.org/10.1016/j.micromeso.2008.08.047.
Barenblatt, G. I. 1971. “Filtration of two nonmixing fluids in a homogeneous porous medium.” Fluid Dyn. 6 (5): 857–864. https://doi.org/10.1007/BF01013869.
Barenblatt, G. I., I. P. Zheltov, and I. N. Kochina. 1960. “Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks [strata].” J. Appl. Math. Mech. 24 (5): 1286–1303. https://doi.org/10.1016/0021-8928(60)90107-6.
Berryman, J. G. 2002. “Extension of poroelastic analysis to double-porosity materials: New technique in microgeomechanics.” J. Eng. Mech. 128 (8): 840–847. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:8(840).
Berryman, J. G., and H. F. Wang. 1998. “Double-porosity modeling in elastic wave propagation for reservoir characterization.” In Mathematical methods in geophysical imaging V, Vol. 3453, edited by S. Hassanzadeh, 58–69. Washington, DC: International Society for Optics and Photonics.
Beskos, D. E., and E. C. Aifantis. 1986. “On the theory of consolidation with double porosity—II.” Int. J. Eng. Sci. 24 (11): 1697–1716. https://doi.org/10.1016/0020-7225(86)90076-5.
Biot, M. A. 1956a. “Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low-frequency range.” J. Acoust. Soc. Am. 28: 168–178. https://doi.org/10.1121/1.1908239.
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 (2): 179–191. https://doi.org/10.1121/1.1908241.
Biot, M. A. 1962a. “Generalized theory of acoustic propagation in porous dissipative media.” J. Acoust. Soc. Am. 34 (9A): 1254–1264. https://doi.org/10.1121/1.1918315.
Biot, M. A. 1962b. “Mechanics of deformation and acoustic propagation in porous media.” J. Appl. Phys. 33 (4): 1482–1498. https://doi.org/10.1063/1.1728759.
Boutin, C., and P. Royer. 2015. “On models of double porosity poroelastic media.” Geophys. J. Int. 203 (3): 1694–1725. https://doi.org/10.1093/gji/ggv378.
Chattaraj, R., S. K. Samal, and N. C. Mahanti. 2013. “Dispersion of love wave propagating in irregular anisotropic porous stratum under initial stress.” Int. J. Geomech. 13 (4): 402–408. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000230.
Chattopadhyay, A. 1975. “On the dispersion equation for love wave due to irregularity in the thickness of non-homogeneous crustal layer.” Acta Geophys Polonica 23: 307–317.
Chattopadhyay, A., and R. K. De. 1983. “Love type waves in a porous layer with irregular interface.” Int. J. Eng. Sci. 21 (11): 1295–1303. https://doi.org/10.1016/0020-7225(83)90126-X.
Chattopadhyay, A., and A. K. Singh. 2012. “Propagation of magnetoelastic shear waves in an irregular self-reinforced layer.” J. Eng. Math. 75 (1): 139–155. https://doi.org/10.1007/s10665-011-9519-8.
Choquet, C. 2004. “Derivation of the double porosity model of a compressible miscible displacement in naturally fractured reservoirs.” Appl. Anal. 83 (5): 477–499. https://doi.org/10.1080/00036810310001643194.
Dai, Z.-j., and Z.-B. Kuang. 2006. “Love waves in double porosity media.” J. Sound Vib. 296 (4–5): 1000–1012. https://doi.org/10.1016/j.jsv.2006.03.029.
Dai, Z.-J., Z.-B. Kuang, and S.-X. Zhao. 2006. “Reflection and transmission of elastic waves from the interface of a fluid-saturated porous solid and a double porosity solid.” Transp. Porous Media 65 (2): 237–264. https://doi.org/10.1007/s11242-005-6084-5.
Galeş, C., and S. Chiriţă. 2020. “Wave propagation in materials with double porosity.” Mech. Mater. 149: 103558. https://doi.org/10.1016/j.mechmat.2020.103558.
Gupta, H. K. 2002. “A review of recent studies of triggered earthquakes by artificial water reservoirs with special emphasis on earthquakes in Koyna, India.” Earth Sci. Rev. 58 (3–4): 279–310. https://doi.org/10.1016/S0012-8252(02)00063-6.
Izadi, A., R. Jamshidi Chenari, S. Javankhshdel, and F. Hemmati Masouleh. 2022. “Effect of love wave propagation on the equivalent seismic bearing capacity of shallow foundations using 3D Coulomb failure mechanism.” Geotech. Geol. Eng. 40 (5): 2781–2797. https://doi.org/10.1007/s10706-022-02061-5.
Kiełczyński, P., M. Szalewski, and A. Balcerzak. 2012. “Effect of a viscous liquid loading on love wave propagation.” Int. J. Solids Struct. 49 (17): 2314–2319. https://doi.org/10.1016/j.ijsolstr.2012.04.030.
Love, A. E. H. 1944. A treatise on the mathematical theory of elasticity. Vol. 1. New York: Dover Publications.
Lyu, D.-D., J.-T. Wang, F. Jin, and C.-H. Zhang. 2014. “Reflection and transmission of plane waves at a water–porous sediment interface with a double-porosity substrate.” Transp. Porous Media 103 (1): 25–45. https://doi.org/10.1007/s11242-014-0286-7.
Mal, A. K. 1962. “On the frequency equation for love waves due to abrupt thickening of the crustal layer.” Geofisica Pura e Applicata 52 (1): 59–68. https://doi.org/10.1007/BF01996000.
Mistri, K. C., A. K. Singh, and A. Das. 2018. “Attenuation and dispersion of SH-waves in a loosely bonded sandwiched fluid saturated porous layer.” Soil Dyn. Earthquake Eng. 107: 350–362. https://doi.org/10.1016/j.soildyn.2018.01.037.
Murty, G. S. 1975. “A theoretical model for the attenuation and dispersion of Stoneley waves at the loosely bonded interface of elastic half spaces.” Phys. Earth Planet. Inter. 11 (1): 65–79. https://doi.org/10.1016/0031-9201(75)90076-X.
Murty, G. S. 1976. “Reflection, transmission and attenuation of elastic waves at a loosely-bonded interface of two half spaces.” Geophys. J. Int. 44 (2): 389–404. https://doi.org/10.1111/j.1365-246X.1976.tb03663.x.
Negi, A., A. K. Singh, and R. P. Yadav. 2020. “Analysis on dynamic interfacial crack impacted by SH-wave in bi-material poroelastic strip.” Compos. Struct. 233: 111639. https://doi.org/10.1016/j.compstruct.2019.111639.
Nield, D. A., and A. Bejan. 2017. “Mechanics of fluid flow through a porous medium.” In Convection in porous media, 1–35. Cham, Switzerland: Springer.
Pal, J., and A. P. Ghorai. 2015. “Propagation of love wave in sandy layer under initial stress above anisotropic porous half-space under gravity.” Transp. Porous Media 109 (2): 297–316. https://doi.org/10.1007/s11242-015-0519-4.
Sharma, M. D. 2014. “Effect of local fluid flow on Rayleigh waves in a double porosity solid.” Bull. Seismol. Soc. Am. 104 (6): 2633–2643. https://doi.org/10.1785/0120140014.
Sharma, M. D. 2015a. “Effect of local fluid flow on the propagation of elastic waves in a transversely isotropic double-porosity medium.” Geophys. J. Int. 200 (3): 1423–1435. https://doi.org/10.1093/gji/ggu485.
Sharma, M. D. 2015b. “Constitutive relations for wave propagation in a double porosity solids.” Mech. Mater. 91: 263–276. https://doi.org/10.1016/j.mechmat.2015.08.005.
Simpson, D. W. 1986. “Triggered earthquakes.” Annu. Rev. Earth Planet. Sci. 14 (1): 21–42. https://doi.org/10.1146/annurev.ea.14.050186.000321.
Singh, A. K., A. Negi, A. Chattopadhyay, and A. K. Verma. 2017. “Analysis of different types of heterogeneity and induced stresses in an initially stressed irregular transversely isotropic rock medium subjected to dynamic load.” Int. J. Geomech. 17 (8): 04017022. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000891.
Tranter, C. J. 1966. Integral transforms in mathematical physics. London: Methuen and Co. Ltd.
Vashisth, A. K., M. D. Sharma, and M. L. Gogna. 1991. “Reflection and transmission of elastic waves at a loosely bonded interface between an elastic solid and liquid-saturated porous solid.” Geophys. J. Int. 105 (3): 601–617. https://doi.org/10.1111/j.1365-246X.1991.tb00799.x.
Willis, H. F. 1948. “LV. A formula for expanding an integral as a series.” London Edinburgh Dublin Philos. Mag. J. Sci. 39 (293): 455–459. https://doi.org/10.1080/14786444808521694.
Wilson, R. K., and E. C. Aifantis. 1982. “On the theory of consolidation with double porosity.” Int. J. Eng. Sci. 20 (9): 1009–1035. https://doi.org/10.1016/0020-7225(82)90036-2.
Wilson, R. K., and E. C. Aifantis. 1984. “A double porosity model for acoustic wave propagation in fractured-porous rock.” Int. J. Eng. Sci. 22 (8–10): 1209–1217. https://doi.org/10.1016/0020-7225(84)90124-1.
Zheng, P., B. Ding, and X. Sun. 2017. “Elastic wave attenuation and dispersion induced by mesoscopic flow in double-porosity rocks.” Int. J. Rock Mech. Min. Sci. 91: 104–111. https://doi.org/10.1016/j.ijrmms.2016.11.018.

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Go to International Journal of Geomechanics
International Journal of Geomechanics
Volume 22Issue 12December 2022

History

Received: Jul 1, 2021
Accepted: Jun 12, 2022
Published online: Sep 28, 2022
Published in print: Dec 1, 2022
Discussion open until: Feb 28, 2023

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Mukesh Kumar Pal [email protected]
Dept. of Mathematics & Computing, Indian Institute of Technology (Indian School of Mines), Dhanbad, Jharkhand, India. Email: [email protected]
Dept. of Mathematics, School of Advanced Sciences, VIT-AP, Univ., Amaravati, Andhra Pradesh, India (corresponding author). ORCID: https://orcid.org/0000-0002-5463-6173. Email: [email protected]
Abhishek Kumar Singh [email protected]
Dept. of Mathematics & Computing, Indian Institute of Technology (Indian School of Mines), Dhanbad, Jharkhand, India. Email: [email protected]

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