Mathematical modeling of the filtration consolidation of water-saturated randomly inhomogeneous soil masses

Abstract

The filtration consolidation of water-saturated randomly inhomogeneous soil masses is studied. The field of excess head in a soil mass with random inclusions is obtained in the case of random consolidation coefficients.

Nonclassical differential dynamic models of space-time consolidation processes

“…(4)) formally coincides with the consolidation equation (obtained earlier in [8]) for a porous medium with relaxed filtration process; however, in the case under study, it is additionally possible to calculate the relaxation parameters t t 1 2 and according to relations (5), which determine also the physical meaning of these parameters.…”

“…Relations (6), (7), (8), and (1) yield a system of equations of filtration-convective diffusion in a fractured porous medium as s n 1 1 1…”

“…In contrast to the case of relaxation filtration in a porous medium [8], the equations for concentration fields are not integro-differential, which greatly simplifies the modeling.…”

“…In practice, such sewage ponds are often filled with concentrated salt solutions, which made it necessary to search and develop efficient techniques for the mathematical modeling of the dynamics of consolidation processes, taking into account salt transfer and some other factors [2][3][4]. Such factors include relaxation phenomena accompanying some filtration processes in deformable media and are due to various reasons [2] such as the necessity of accounting for the complex microstructure of solutions and pore space [6][7][8]. In the studies known to date (see, e.g., [1][2][3][4][5][6][7][8]) the dynamics of consolidation processes in deformable media saturated with salt solutions was simulated using the classical porous medium as a mathematical model [9].…”

“…Such factors include relaxation phenomena accompanying some filtration processes in deformable media and are due to various reasons [2] such as the necessity of accounting for the complex microstructure of solutions and pore space [6][7][8]. In the studies known to date (see, e.g., [1][2][3][4][5][6][7][8]) the dynamics of consolidation processes in deformable media saturated with salt solutions was simulated using the classical porous medium as a mathematical model [9]. We will develop a mathematical model to describe the dynamics of the consolidation of process of a porous fractured [10] medium saturated with a salt solution in view of interphase mass exchange, which makes it possible to model the dynamics of this process in, for example, artificially fractured (mine burst, explosions) rock.…”