Analytical solutions are derived for one-dimensional consolidation, free swelling and electrical loading of a saturated charged porous medium. The governing equations describe infinitesimal deformations of linear elastic isotropic charged porous media saturated with a mono-valent ionic solution. From the governing equations a coupled diffusion equation in state space notation is derived for the electro-chemical potentials, which is decoupled introducing a set of normal parameters, being a linear combination of the eigenvectors of the diffusivity matrix. The magnitude of the eigenvalues of the diffusivity matrix correspond to the time scales for Darcy flow, diffusion of ionic constituents and diffusion of electrical potential.
Meerveld, van, J., Molenaar, M. M., Huyghe, J. M. R. J., & Baaijens, F. P. T. (2003). Analytical solution of compression, free swelling and electrical loading of saturated charged porous media. Transport in Porous Media, 50(1-2), 111-126. https://doi.org/10.1023/A:1020641329225