# Porous materials

#### Elastic porous media saturated by a fluid (liquid or a gas) are an example of materials with microstructure. Such material is double phase medium consisted of elastic continuum and matrix of voids that filled by fluid. The necessity of investigation of wave processes in such media is due to applied problems of soil mechanics, geophysics, and vibroseismic exploration; the construction and oil and gas industries; and the occurrence of new granular–powder and sponge materials used, for example, for thermal and vibroinsulation of aerospace elements.

#### At present, the commonly accepted tool for theoretical study of propagation of linear waves in porous fluid saturated media is the Biot–Frenkel equations generalizing the equations of the classical theory of elasticity to the case of two-phase media. In the frame of this project integral approach are developed and studied disperse curves and influence of porosity on surface wave in half-spaces and tube waves in the structures consisted of borehole embedded in the poroelastic medium saturated by fluid. Using numerical examples it is demonstrated that the amplitude of additional modes occurring due to the presence of a microstructure can be essentially larger than the amplitudes of principal modes present in the waveguide with purely elastic layers.

*Porous multilayered half-space*

*Dispersion curves for the three-layered half-space for different combinations of porosity ε1, ε2 of two upper layers (influence of porosity on surface waves of the half-space) *