Thermo-Poromechanics: Applications and Developments

Geomechanics is a well-established area of geotechnique and the geosciences that involves the application of the principles of mathematics, mechanics and physics to describe the response of geomaterials subjected to thermal, mechanical and physical effects. The development of the subject of geomechanics evolved largely through the separate applications of classical theories of continuum mechanics as defined by elasticity, plasticity, fluid flow through porous media and heat conduction to the study of geomaterials that includes soils, rocks and other multiphasic materials. What distinguishes modern developments in geomechanics of multiphasic materials is the consideration of an extensive range of couplings between the dependent variables that characterize the deformation, thermal and flow fields and, on occasions, chemical transport. For example, the consideration of coupling of thermal and elastic behavior forms the basis of the coupled theory of classical thermoelasticity introduced by Duhamel (1837) and further developed in the works of Hopkinson (1879), Neumann (1885), Almansi (1897), Tedone (1906) and Voigt (1910). The classical theory of thermoelasticity developed in these works represents the complete coupling of the deformation and heat conduction processes within the framework of classical continuum mechanics. References to the numerous developments in thermoelasticity are given by Boley and Wiener (1960), Nowacki (1962), Carlson (1972) and Nowinski (1978). In the context of geomechanics, the need to consider coupling effects in geomaterials dates back to the elementary one-dimensional theory of soil consolidation developed by Terzaghi (1925). This has been an important starting point for the multiphasic treatment of fluid-saturated porous media. Karl Terzaghi (1925) is considered to be the main developer of the theory of one-dimensional consolidation, but important contributions by others, particularly Fillunger (1936), should not be overlooked (de Boer, 2000a, b). Terzaghi's one-dimensional theory can explain the processes that occur during soil consolidation, but this cannot be considered as a “formal theory”. Biot (1941) developed a complete theory of isothermal soil consolidation; this theory is exact in its continuum formulation applicable to a medium with voids and is a generalization of Terzaghi's (1925) one-dimensional theory to three dimensions. Because of the elegance and ease of use, Biot's theory of soil consolidation continues to be used more than seven decades later.