In this paper, the analytical solution of porous medium consolidation with the rheological Kelvin-Voigt frame is presented. The rheological model is a model which elements are four basic physical features: elasticity, viscosity, plasticity and strength. One-dimensional problem insist on solving equations for porous column filed with liquid and being a subject of one-dimensional compression with load through porous plate (allowing fluid flow), pressure gradient and weight of column itself. Results obtained may be used also for determination of effective parameters of the Biot model. According to the types of equations, in the range of analytical solutions we will make a use of techniques based on double integral transformation of Laplace and Fourier. Within the range of boundary issues solutions of porous media consolidation the use will be made of a finite element method.
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