Linear coupled analysis of desiccation shrinkage: Explicit and semi-explicit solutions

Solutions are presented for the problem of the dessiccation shrinkage in a porous partially saturated medium. The rheological model taken into account is linear poroelastic (Lassabatere 1994, Coussy & Lassabatere 1995, Coussy 1995) so the analysis is mainly focused on hydromechanical coupling effects. Three ideal structures, each characterized by one spatial variable, are taken into account: a wall of finite thickness (cartesian geometry), a thick cylinder and a thick sphere. The solution of the time-dependent problem is carried out by applying Laplace transformation to the field variables. Exact solutions are obtained in Laplace transforms space using Mathematica to solve the field equations taking into account the symmetry and boundary conditions. Talbot's algorithm modified by Piessens and al. (Piessens et al. 1983) is performed to invert the Laplace transform solutions. A bibliographical and numerical study shows that this method is remarkably precise, stable and close to the analytical inversion. Results are presented using poroelastic data representative of a concrete to evaluate saturation, volumetric strain and mean stress.