Numerical modeling of the non-stationary wave processes occurring at pulse action on nonlinear fluid-saturated porous media is discussed. The problem under study serves an illustration to the earlier offered case of a nonlinear two-velocity model of heterophase media. The equations of the model obtained by method of conservation laws are uniquely defined and, in contrast to the Biot model, the introduction of additional material parameters is not required. Physical properties of a medium are defined by the equation of state and kinetic parameters. The equations of the model are hyperbolic in a wide range of values of thermodynamic and hydrodynamic parameters of the model. That is way for the numerical model Godunov’s scheme with parallel algorithms was used. The problem of pulsed action on a fluid-saturated porous semi-infinite layer, into which a saturating fluid is pumped, was considered. The pulse action was set spatially distributed, with a strong maximum at the center of the boundary. Numerical modeling for various values of physical parameters and various forms of a shock pulse was carried out. Fields of velocities, deformations, stresses in a porous matrix, distribution of a saturating fluid, and areas of dilatancy have been constructed. Results of the calculation show that in elastic-deformed porous matrix saturated with the Newtonian fluid a very weak dispersion of compact pulse action is observed: the original boundary pulse is propagating to large distances almost without modification of its form, and only with a weak attenuation. Results of the calculation also show the correlation of distribution of partial density of a saturating fluid (that is, the degree of porosity of a solid matrix) and the fields of dilatancy. The model of a saturated porous media can be considered as a filtration-dilatation model that can be used for analysis of non-stationary processes in the earthquake-prone zones.

The work was supported by the RFBR (grant 03-05-64403), by the Presidium of SB RAS (grant 106), and by the President's Grants (NSh-2118.2003.5, NSh-1573.2003.5).