Consolidation Solutions of a Saturated Porothermoelastic Hollow Cylinder with Infinite Length

B. BAI
DOI: 10.4236/eng.2010.21005                

Abstract

An analytical method is derived for the thermal consolidation of a saturated, porous, hollow cylinder with infinite length. The solutions in Laplace transform space are first obtained and then numerically inverted by Stehfest method. Two cases of boundary conditions are considered. First, variable thermal loadings are applied on the inner and outer pervious lateral surfaces of the hollow cylinder, and a variable mechanical loading with time is applied on the outer surface; while the displacement of the inner surface remains fixed. Secondly, variable thermal and mechanical loading are applied on the outer pervious surface, and the inner surface remains fixed, impervious and insulated. As two special problems, a solid cylinder with infinite length and a cylindrical cavity in a half-space body are also discussed. Finally, the evolutions of temperature, pore pressure and displacement with time along radial direction are analyzed by a numerical example.

Keywords

Porothermoelastic Media, Hollow Cylinder, Variable Thermal Loading, Consolidation Solutions, Stehfest Method

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	M. Kurashige, “A thermoelastic theory of fluid-filled porous materials,” International Journal of Solids and Structures, Vol. 25, No. 9, pp. 1039?1052, 1989.
[2]	X. Li, “A generalized theory of thermoelasticity for an anisotropic medium,” International Journal of Engineering Science, Vol. 30, No. 5, pp. 571?577, 1992.
[3]	H. N. Seneviratne, J. P. Carter, D. W. Airey, and J. R. Booker, “A review of models for predicting the thermomechanical behavior of soft clays,” International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 17, No. 10, pp. 715?733,1993.
[4]	M. Bai and Y. Abousleiman, “Thermoporoelastic coupling with application to consolidation,” International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 21, No. 2, pp. 121?132, 1997.
[5]	R. W. Zimmerman, “Coupling in poroelasticity and thermoelasticity,” International Journal of Rock Mechanics and Mining Sciences, Vol. 37, No. 1, pp. 79?87, 2000.
[6]	J. R. Booker and C. Savvidou, “Consolidation around a spherical heat source,” International Journal of Solids and Structures, Vol. 20, No. 5, pp. 1079?1090, 1984.
[7]	D. F. McTigue, “Flow to a heated borehole in porous, thermoelastic rock: Analysis,” Water Resources Research, Vol. 26, No. 8, pp. 1763?1774, 1990.
[8]	D. W. Smith and J. R. Booker, “Green’s function for a fully coupled thermoporoelastic materials,” International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 17, No. 2, pp. 139?163, 1993.
[9]	A. Giraud, F. Homand, and G. Rousset, “Thermoelastic and thermoplastic response of a double-layer porous space containing a decaying heat source,” International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 22, No. 2, pp. 133?149, 1998.
[10]	Y. Wang and E. Papamichos, “An analytical solution for conductive heat flow and the thermally induced fluid flow around a wellbore in a poroelastic medium,” Water Resource Research, Vol. 36, No. 5, pp. 3375?3384, 1994.
[11]	Y. Wang and E. Papamichos, “Thermal effects on fluid flow and hydraulic fracturing from wellbores and cavities in low-permeability formations,” International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 23, No. 15, pp. 1819?1834, 1999.
[12]	E. Blond, N. Schmitt, and F. Hild, “Response of saturated porous media to cyclic thermal loading,” International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 27, No. 11, pp. 883?904, 2003.
[13]	B. Bai, “Response of saturated porous media subjected to local thermal loading on the surface of semi-infinite space,” Acta Mechanica Sinica, Vol. 22, No. 1, pp. 54?61, 2006.
[14]	B. Bai, “Fluctuation responses of saturated porous media subjected to cyclic thermal loading,” Computers and Geotechnics, Vol. 33, No. 4, pp. 396?403, 2006.
[15]	Y. Abousleiman and S. Ekbote, “Solutions for the inclined borehole in a porothermoelastic transversely isotropic medium,” Journal of applied Mechanics, Vol. 72, No. 2, pp. 102?114, 2005.
[16]	M. Kanj, Y. Abousleiman, and R. Ghanem, “Poromechanics of anisotropic hollow cylinders,” Journal of Engineering Mechanics, Vol. 129, No. 11, pp. 1277?1287, 2003.
[17]	M. Kanj and Y. Abousleiman, “Porothermoelastic analyses of anisotropic hollow cylinders with applications,” International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 29, No. 1, pp. 103?126, 2005.
[18]	B. Bai, “Thermal consolidation of layered porous half- space to variable thermal loading,” Applied Mathematics and Mechanics, Vol. 27, No. 11, pp. 1531?1539, 2006.