Abstract
Took into consideration the coupling effect of thermo, hydraulics and mechanics, a set of thermo–hydro-mechanical coupled wave equations for fluid–saturated soil are developed. In these wave equations, the \(P_{3}\)-wave in solid phase and \(P_{4}\)-wave in fluid phase are coupled into \(T\)-wave in fluid–saturated soil by the assumption that the temperature of the solid phase is equal to the temperature of liquid phase at the same position. The dispersion equations for the thermo-elastic wave, which can be degraded to the equations for elastic wave in fluid–saturated soil, are derived from the above equations by introducing four potential functions. Then, these equations are solved numerically. The characteristics of wave phase velocity, attenuation and the effect of thermal expansion, initial temperature and porosity, etc., on phase velocities of \(P_{1}\)-, \(P_{2}\)-, and \(T\)-wave are discussed. As a reference, the characteristics of the propagation of elastic waves in fluid–saturated soil are also studied. The computation results show that (1) the phase velocity of \(P_{1}\)-wave obtained by the theory of thermoporoelascity (THM) is faster than that by the theory of poroelasticity (HM); (2) the attenuation of \(P_{1}\)-wave obtained by either the theory of THM or HM are consistent; (3) the dissemination characteristics of \(P_{2}\)-wave are almost consistent; (4) the phase velocity of \(T\)-wave is the slowest among the three compressional waves; and (5) The attenuation versus frequency characteristic of \(T\)-wave is similar to that of \(P_{2}\)-wave.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aoudi, M.: A problem for an infinite elastic body with a spherical cavity in the theory of generalized thermoelastic diffusion. Int. J. Solids Struct. 44(17), 5711–5722 (2007)
Belotserkovets, A., Prevost, J.H.: Thermoporoelastic response of a fluid–fluid-saturated porous sphere: an analytical solution. Int. J. Eng. Sci. 49(2), 1415–1423 (2011)
Biot, M.A.: Theory of propagation of elastic waves in a fluid fluid–saturated porous solid. I. Low frequency range. II. Higher frequency range. J. Acoust. Soc. Am. 28(2), 168–191 (1956)
Biot, M.A.: Thermoelasticity and irreversible thermo-dynamics. J. Appl. Phys. 27(3), 240–253 (1956)
Coussy, O.: Poromechanics. Wiley, Chichester (2004)
Eringen, A.C.: Mechanics of Continua. Robert E. Krieger Publishing Co., New York (1980)
Gajo, A., Fedel, A., Mongiovi, L.: Experimental analysis of the effects of fluid–solid couplings on the velocity of elastic waves in fluid–saturated porous medium. Geotechnique 47(5), 993–1008 (1997)
Green, A.E., Lindsay, K.A.: Thermoelasticity. J. Elast. 2(1), 1–7 (1972)
Khashan, S.A., Al-nimr, M.A.: Validation of the local thermal equilibrium assumption in forced convection of non-newtonian fluids through porous channels. Transp. Porous Med. 61(3), 291–305 (2005)
Liu, G.B., Xie, K.H., Zheng, R.Y.: Model of nonlinear coupled thermo–hydro-elastodynamics response for a fluid–saturated poroelastic medium. Sci. China (Ser. E) 52(8), 2373–2383 (2009)
Liu, G.B., Xie, K.H., Ye, R.H.: Mode of a spherical cavity’s thermo-elastodynamic response in a fluid–saturated porous medium for non-torsional loads. Comput. Geotech. 37(3), 381–390 (2010)
Liu, G.B., Liu, X.H., Ye, R.H.: The relaxation effects of a fluid–saturated porous medium using the generalized thermoviscoelasticity theory. Int. J. Eng. Sci. 48(9), 795–808 (2010)
Lord, H.W., Shulman, Y.: A generalised dynamical theory of thermoelasticity. J. Mech. Phys. Solids 15(5), 299–309 (1967)
Lykotrafitis, G., Georgiadis, H.G., Brock, L.M.: Three-dimensional thermoelastic wave motions in a half-space under the action of a buried source. Int. J. Solids Struct. 38(28–29), 4857–4878 (2001)
Pecker, C., Deresiewicz, H.: Thermal effects on waves in liquid filled porous medium. Acta Mech. 16(1–2), 45–64 (1973)
Plona, T.J.: Observation of a second bulk compressional wave in a porous medium at ultrasonic frequencies. Appl. Phys. Lett. 36(4), 259–261 (1980)
Sharma, M.D.: Wave propagation in a general anisotropic poroelastic medium: Biot’s theories and homogenization theory. J. Earth Syst. Sci. 116(4), 357–367 (2007)
Sherief, H.H., Saleh, H.A.: A problem for an infinite thermoelastic body with a spherical cavity. Int. J. Eng. Sci. 36(4), 473–487 (1998)
Singh, B.: Reflection of SV waves from the free surface of an elastic solid in generalized thermoelastic diffusion. J. Sound Vib. 291(3–5), 764–778 (2006)
Singh, B.: Wave propagation in a generalized thermoelastic material with voids. Appl. Math. Comput. 189(1), 698–709 (2007)
Singh, B.: Reflection of plane waves at the free surface of a monoclinic thermoelastic solid half-space. Eur. J. Mech. A Solid 29(5), 911–916 (2010)
Singh, B.: On propagation of plane waves in generalized porothermoelasticity. B. Seismol. Soc. Am. 101(2), 756–762 (2011)
Wenzlau, F., Müller, T.: Finite-difference modeling of wave propagation and diffusion in poroelastic media. Geophysics 74(4), T55–T66 (2009)
Yang, J., Wu, S.M., Chai, Y.Q.: Characteristics of propagation of elastic waves in fluid–saturated soils. Chin. J. Vib. Eng. 9(2), 128–137 (1996)
Youssef, H.M.: Theory of generalized porothermoelasticity. Int. J. Rock Mech. Min. Sci. 44(2), 222–227 (2007)
Zhou, Y., Rajapakse, R.K.N.D., Graham, J.: A coupled thermoporoelastic model with thermo-osmosis and thermal-filtration. Int. J. Solid Struct. 35(34–35), 4659–4683 (1998)
Acknowledgments
The present research is supported by the National Natural Science Foundation of China (NSFC) under the approved Grant No. 51278256, and No. 51178227, to which the authors are very grateful.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Haibing, T., Ganbin, L., Kanghe, X. et al. Characteristics of Wave Propagation in The Saturated Thermoelastic Porous Medium. Transp Porous Med 103, 47–68 (2014). https://doi.org/10.1007/s11242-014-0287-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11242-014-0287-6