Linear theory for porous thermoelastic materials

Technical Report · Tue Sep 10 04:00:00 EDT 1985

OSTI ID:5174832

McTigue, D F

A linear theory for fluid-saturated, porous, thermoelastic media is developed. The theory allows for compressibility and thermal expansion of both the fluid and solid constituents. An approach to solving boundary value problems is presented, in which a diffusion equation with a temperature-dependent source term governs a combination of the mean total stress and the fluid pore pressure. In certain special cases, this reduces to a diffusion equation for the pressure alone. In addition, when convective heat transfer can be neglected, the temperature field can be determined independently, and the source term in the pressure equation is known. Drained and undrained limits are identified, in which fluid flow plays no role in the deformation. In the drained case, the medium behaves as a simple thermoelastic body with the properties of the porous skeleton with no fluid present. In the undrained limit, the fluid is trapped in the pores, and the material responds as a thermoelastic body with effective compressibility and thermal expansivity determined in part by the fluid properties. The theory is further specialized to plane and one-dimensional deformations, and several illustrative problems are solved. In particular, the one-dimensional heating of a half-space is explored for constant-temperature and constant-flux boundary conditions on the thermal field, and for drained (zero pressure) and impermeable (zero flux) conditions on the fluid pressure field. Finally, solutions are presented for constant heat flux delivered to a borehole for both drained and impermeable boundaries. The behavior of all of these solutions depends critically upon the ratio of the fluid and thermal diffusivities, with very large and very small values of this parameter corresponding to drained and undrained responses, respectively.

• Research Organization: Sandia National Labs., Albuquerque, NM (USA)
• DOE Contract Number: AC04-76DP00789
• OSTI ID: 5174832
• Report Number(s): SAND-85-1149; ON: DE86000222
• Country of Publication: United States
• Language: English

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