ABSTRACT
The classical problem in geomechanics dealing with the stress-induced isothermal “ow of a “uid through a deformable porous medium, usually referred to as the process of soil consolidation, is a cornerstone in the development of the subject of soil mechanics and is generally regarded as the start of multiphasic treatment of the mechanics of porous media. Although the development of the theory of 1D soil consolidation is generally attributed to Terzaghi [1], the important contributions of others, Fillunger [2] in particular, are now being recognized [3,4]. The 1D theory certainly provides an explanation of the processes involved in soil consolidation but does not constitute a formal theory. The formal theory of isothermal soil consolidation presented by Biot [5] is a generalization of the 1D theory to three dimensions. This is a complete theory, which is rigorous in the sense of a continuum formulation applicable to a medium with voids. It is also an elegantly simple theory that continues to “ourish after seven decades. The theory employs linear elasticity to characterize the mechanical behavior of the porous skeleton, and Darcy’s law governs “uid “ow through the accessible porous space. Extensive expositions of both the fundamental aspects of Biot’s theory of isothermal poroelasticity and its applications to the analytical solution of problems in geomechanics are documented by Mandel [6], de Josselin de Jong [7], McNamee and Gibson [8],
20.1 Introduction ..........................................................................................................................663 20.2 Thermohydromechanical Modeling and Governing Equations ...........................................665 20.3 One-Dimensional Problems in Thermoporoelasticity .......................................................... 671
20.3.1 Axial Loading and Boundary Heating of the 1D Element ....................................... 671 20.3.2 Thermomechanical Problem: Formulation ............................................................... 673 20.3.3 Hydromechanical Problem ....................................................................................... 675 20.3.4 Hydromechanical Problem: The Effect of Solid Phase and Fluid Compressibility .....677 20.3.5 Thermohydromechanical Problem: Formulation ..................................................... 679 20.3.6 Thermohydromechanical Problem: The Effects of Solid Phase and Fluid Phase
Compressibility .........................................................................................................684 20.3.7 Thermohydromechanical Problem: Numerical Results............................................686 20.3.8 Thermohydromechanical Problem: Computational Estimates ................................. 688
20.4 Spherically Symmetric Problems in Thermoporoelasticity .................................................694 20.4.1 Boundary Heating of a Poroelastic Sphere ............................................................... 695 20.4.2 Computational Results for the Boundary Heating of a Poroelastic Sphere ..............697
