Abstract
A three-phase mathematical model of a partially saturated porous medium, based on Biot's model, with five basic functions for describing wave processes is considered. Based on the theorem of operational computation of integrating the original, a stepped method of numerical inversion of Laplace transform is presented. A modification of the stepped method of numerical inversion of Laplace transform is introduced, and its effectivity is analyzed, using the example of a piecewise-linear function. The modification made it possible to reduce the number of points necessary for achieving a required accuracy. The problem of a load acting on a one-dimensional partially saturated poroelastic bar is analyzed. Dynamic responses of displacements and pore pressures for different values of the saturation coefficient of the model of a poroelastic material are presented. The effect of the saturation coefficient on the dynamic responses of displacement and pore pressures is demonstrated. The results are compared with the data published by other authors. Keywords: porous medium, Biot's model, Laplace transform, stepped scheme, prismatic body, analytical solution.
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