| Popis: |
The review of a number of scientific works in the field of modeling wave processes in partially saturated porous media is proposed. Review consists of three parts. In the first part of overview, classification of porous media according to the degree of saturation with a wetting filler is stated. The fundamental works of the modern theory of porous continuums, which resulted in the Biot's theory and the mixture theory, are considered. The advantages, disadvantages, as well as the conditions for the correspondence between the two approaches are indicated. The second part is devoted to scientific publications of an applied and academic nature, which are mostly devoted to the study of the features of wave processes in poroelastic media by analytical and semi-analytical methods. Special attention is paid to the works devoted to the modeling of slow longitudinal waves as a distinctive feature of wave processes in partially saturated poroelastic media. The third part gives an overview of the application of boundary element and finite element methods to study the stress-strain state of saturated and partially saturated porous media, the behavior of waves during their propagation in the media under consideration, and the analysis of local dynamic effects. The two methods are compared. Experimental works confirming theoretical results obtained within the Biot's theory are indicated. A brief analysis of modern achievements in the problems of numerical simulation of dynamic effects in semi-infinite porous media with a layered structure such as the seabed is carried out. Works on the derivation of fundamental solutions for systems of poroelasticity equations and the construction of the corresponding integral equations in time and space of the Fourier and Laplace integral transformations are considered. Works are given that consider various aspects of boundary element modeling of unsaturated porous media and the application of boundary and finite element methods on specific examples. |
