Generalized Porothermoelasticity of Asphaltic Material
Mohammad H. Alawi
DOI: 10.4236/eng.2011.311138   PDF    HTML     4,097 Downloads   7,006 Views   Citations


In this work, a mathematical model of generalized porothermoelasticity with one relaxation time for poroelastic half-space saturated with fluid will be constructed in the context of Youssef model (2007). We will obtain the general solution in the Laplace transform domain and apply it in a certain asphalt material which is thermally shocked on its bounding plane. The inversion of the Laplace transform will be obtained numerically and the numerical values of the temperature, stresses, strains and displacements will be illustrated graphically for the solid and the liquid.

Share and Cite:

M. Alawi, "Generalized Porothermoelasticity of Asphaltic Material," Engineering, Vol. 3 No. 11, 2011, pp. 1102-1114. doi: 10.4236/eng.2011.311138.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] C. Pecker and H. Deresiewiez, “Thermal Effects on Wave in Liquid-Filled Porous Media,” Journal of Acta Mecha- nica, Vol. 16, No. 1-2, 1973, pp. 45-64. doi:10.1007/BF01177125
[2] M. A. Biot, “General Theory of Three-Dimensional Consolidation,” Journal of Applied Physics, Vol. 12, No. 2, 1941, pp. 155-164. doi:10.1063/1.1712886
[3] M. A. Biot, “Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid. I. Low-Frequency Range,” Journal of Acoustical Society America, Vol. 28, No. 2, 1956, pp. 168-178. doi:10.1121/1.1908239
[4] F. Gassmann, “Uber die Elastizitat Poroser Medien,” Veirteljahrsschrift der Naturforschenden Gesellschaft in Zzirich, Vol. 96, 1951, pp. 1-23.
[5] M. A. Biot and D. G. Willis, “The Elastic Coefficients of the Theory of Consolidation,” Journal of Applied Mechanics, Vol. 24, No. 4, 1957, pp. 594-601.
[6] M. A. Biot, “Mechanics of Deformation and Acoustic Propagation in Porous Media,” Journal of Applied Physics, Vol. 33, No. 4, 1962, pp. 1482-1498. doi:10.1063/1.1728759
[7] H. Deresiewicz and R. Skalak, “On Uniqueness in Dynamic Poroelasticity,” Bulletin of the Seismological Society of America, Vol. 53, No. 4, 1963, pp. 783-788.
[8] G. Mandl, “Change in Skeletal Volume of a Fluid-Filled Porous Body under Stress,” Journal of Applied Physics, Vol. 12, No. 5, 1964, pp. 299-315. doi:10.1016/0022-5096(64)90027-4
[9] A. Nur and J. D. Byerlee, “An Exact Effective Stress Law for Elastic Deformation of Rock with Fluids,” Journal of Geophysical Research, Vol. 76, No. 26, 1971, pp. 6414- 6419. doi:10.1029/JB076i026p06414
[10] R. J. S. Brown and J. Korringa, “On the Dependence of the Elastic Properties of a Porous Rock on the Compressibility of the Pore Fluid,” Geophysics, Vol. 40, 1975, pp. 608-616. doi:10.1190/1.1440551
[11] J. R. Rice and M. P. Cleary, “Some Basic, Stress Diffusion Solutions for Fluid-Saturated Elastic Porous Media with Compressible Constituents,” Review of Geophysics, Space Physics, Vol. 14, No. 2, 1976, pp. 227-241. doi:10.1029/RG014i002p00227
[12] R. Burridge and J. B. Keller, “Poroelasticit, y Equations Derived from Microstructure,” Journal of Acoustical Society America, Vol. 70, No. 4, 1981, pp. 1140-1146. doi:10.1121/1.386945
[13] R. W. Zimmerman, W. H. Somerton and M. S. King, “Compressibility of Porous Rocks,” Journal of Geophysical Research, Vol. 91, No. B12, 1986, pp. 12765- 12777. doi:10.1029/JB091iB12p12765
[14] R. W. Zimmerman, L. R. Myer and N. G. W. Cook, “Grain and Void Compression in Fractured and Porous Rock,” International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, Vol. 31, No. 2, 1994, pp. 179-184. doi:10.1016/0148-9062(94)92809-6
[15] J. G. Berryman and G. W. Milton, “Exact Results for Generalized Gassmann’s Equations in Composite Porous Media with Two Constituents,” Geophysics, Vol. 56, 1991, pp. 1950-1960. doi:10.1190/1.1443006
[16] M. Thompson and J. R. Willis, “A Reformation of the Equations of Anisotropic Poroelasticity,” Journal of Applied Mechanics, Vol. 58, No. 3, 1991, pp. 612-616. doi:10.1115/1.2897239
[17] S. R. Pride, A. F. Gangi and F. D. Morgan, “Deriving the Equations of Motion for Porous Isotropic Media,” Journal of Acoustical Society America, Vol. 92, No. 6, 1992, pp. 3278-3290. doi:10.1121/1.404178
[18] J. G. Berryman and H. F. Wang, “The Elastic Coefficients of Double-Porosity Models for Fluid Transport in Jointed Rock,” Journal of Geophysical Research, Vol. 100, No. B12, 1995, pp. 24611-24627. doi:10.1029/95JB02161
[19] K. Tuncay and M. Y. Corapcioglu, “Effective Stress Principle for Saturated Fractured Porous Media,” Water Resources Research, Vol. 31, No. 12, 1995, pp. 3103-3106. doi:10.1029/95WR02764
[20] A. H. D. Cheng, “Integral Equation for Poroelasticity in Frequency Domain with BEM solution,” Journal of Engineering Mechanics, Vol. 117, No. 5, 1991, pp. 1136- 1157. doi:10.1061/(ASCE)0733-9399(1991)117:5(1136)
[21] P. A.Charlez and O. Heugas, “Measurement of Thermoporoelastic Properties of Rocks: Theory and Applications,” Ed. J.A. Hudson, 1992, pp. 42-46.
[22] Y. Abousleiman and L. Cui, “Poroelastic Solutions in Transversely Isotropic Media for Wellbore and Cylinder,” International Journal of Solids Structures, Vol. 35, No. 34-35, 1998, pp. 4905-4903. doi:10.1016/S0020-7683(98)00101-2
[23] A. Ghassemi and A. Diek, “Porothermoelasticity for Swelling Shales,” Journal of Petroleum Science & Engineeing, Vol. 34, 2002, pp. 123-135.
[24] S. R. Tod, “An Anisotropic Fractured Poroelastic Effective Medium Theory,” Geophysical Journal International, Vol. 155, No. 3, 2003, pp. 1006-1020.
[25] H. Lord and Y. Shulman, “A Generalized Dynamical Theory of Thermoelasticity,” Journal of the Mechanics and Physics of Solids, Vol. 15, No. 5, 1967, pp. 299-309. doi:10.1016/0022-5096(67)90024-5
[26] H. M. Youssef, “Theory of Generalized Porothermoelasticity,” International Journal of Rock Mechanics and Mining Sciences, Vol. 44, No. 2, 2007, pp. 222-227. doi:10.1016/j.ijrmms.2006.07.001
[27] G. Honig and U. Hirdes, “A Method for the Numerical Inversion of Laplace Transform,” Journal of Computational and Applied Mathematics, Vol. 10, No. 1, 1984, pp. 113-132. doi:10.1016/0377-0427(84)90075-X
[28] G.-B. Liu, S.-R. Ding, R.-H. Ye and X.-H. Liu, “Relaxation Effects of a Saturated Porous Media Using the Two- Dimensional Generalized Thermoelastic Theory,” Trans- port in Porous Media, Vol. 86, No. 1, 2011, pp. 283-303. doi:10.1007/s11242-010-9621-9
[29] Y. Zhong and L. Geng, “Thermal Stresses of Asphalt Pavement under Dependence of Material Characteristics on Reference Temperature,” Mechanics of Time-Dependent Materials, Vol. 13, No. 1, 2009, pp. 81-91. doi:10.1007/s11043-008-9073-6

Copyright © 2023 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.