A two-stage analytical extension for porothermoelastic model under axisymmetric loadings

Porothermoelastic responses of saturated porous media find wide applications in geotechnical engineering. However, the coupled partial differential equations describing the conservation of momentum, mass, and energy in the porous medium posed mathematical difficulties in obtaining analytical solutions. In this paper, we provided a two-stage porothermoelastic model for comprehensive solutions under axisymmetric loadings. At the first stage, the governing equations were decoupled by the Laplace–Hankel transform, which yielded the explicit expressions of the temperature, pore pressure, displacements, and the vertical and shear stresses. At the second stage, the radial and tangential strains were obtained after the numerical inversion of the volumetric strain and displacements. We also found that the volumetric strain played an important role in this model: (1) coupled displacements with the pore pressure and temperature at the first stage; (2) combined the vertical, radial, and tangential strains at the second stage. Results of a finite layer under a disk thermal loading showed that this model could capture the thermal expansion and contraction in terms of displacements, strains and stresses, and such mechanical interactions could give rise to the buildup and dissipation of pore pressures during the thermal conduction.