General steady-state solution for thermo-poroelastic material

This study established a general steady-state solution in the z-convex domain (the domain boundary must have at most two points of intersection with any straight line parallel to the z-axis) for thermo-poroelastic materials. Two displacement functions to simplify the equations governing elasticity, pressure, and temperature fields into one Laplace equation and four eighth-order partial–differential governing equations are introduced. The general solutions of displacement, pressure, and temperature are derived in terms of five harmonic functions using the generalized Almansi’s theorem and considering equivalent substitution. The relationship between the Boussinesq–Galerkin general solutions and the general solution proposed in this paper is discussed without considering the changes in pore pressure and temperature to prove the completeness of the latter.