Analytical study of the thermo-osmosis effect in porothermoelastic responses of saturated porous media under axisymmetric thermal loadings

Abstract

Thermo-osmosis effect is defined as the additional fluid flux caused by the thermal gradient in the porous medium and has recently received much attention in thermally coupled processes of soils and rocks, such as the geological disposal of nuclear waste. However, majority of research studies on thermo-osmosis flow have considered plane-strain conditions which disregard the local thermal expansion and contraction due to finite-dimension loadings. In this paper, we have extended the three-dimensional porothermoelastic model with the thermo-osmosis effect under axisymmetric thermal loadings. With the Laplace-Hankel transform, we obtain the explicit expressions of the temperature, pore pressure, stresses and displacements in the transformed domain. After the verification of this model against analytical and experimental results, we carry out the case study of a disk thermal loading placed at the surface of half space. The thermo-osmosis effect can increase the maximum value of the non-uniform pore pressure caused by the finite-dimension thermal loading. After the dissipation of pore pressure, the driving force from the thermo-osmosis effect can maintain the osmotic flux near the thermal loading. These results show that the thermo-osmosis effect is important to the porothermoelastic behaviors of porous media but is mainly limited to the vicinity of the finite-dimension loading.