Abstract
To study the peculiarities of anomalous consolidation processes in saturated porous (soil) media in the conditions of salt transfer, we present a new mathematical model developed on the base of the fractional-fractal approach that allows considering temporal non-locality of transfer processes in media of fractal structure. For the case of the finite thickness domain with permeable boundaries, a finite-difference technique for numerical solution of the corresponding one-dimensional non-linear boundary value problem is developed. The paper also presents a fractional-fractal model of a filtration-consolidation process in clay soils of fractal structure saturated with salt solutions. An analytical solution is found for the corresponding one-dimensional boundary value problem in the domain of finite thickness with permeable upper and impermeable lower boundaries.
Highlights
The determination of the conditions for the safe functioning of industrial and domestic wastewater storage facilities, as well as numerous other engineering facilities that pollute soils and groundwater, are among the most important and relevant, primarily in the connection with environment protection issues
Considering a non-local in time isothermal filtration-consolidation process in a soil of fractal structure saturated with a salt solution, we start from the following generalizations of the Darcy’s and
Within the framework of such non-classical mathematical model, the fractional-differential dynamics of a non-local in time filtration-consolidation process in a soil of fractal structure saturated with a salt solution in the case of the domain of finite thickness l with permeable boundaries is described in the domain Ω = {(x, t) : 0 < x < l, t > 0} by the system of Equations (6) and (7) with the following boundary conditions: H(0, t) = 0, H(l, t) = 0, H(x, 0) = H0, (8)
Summary
The determination of the conditions for the safe functioning of industrial and domestic wastewater storage facilities, as well as numerous other engineering facilities that pollute soils and groundwater, are among the most important and relevant, primarily in the connection with environment protection issues. Considering a non-local in time isothermal filtration-consolidation process in a soil of fractal structure saturated with a salt solution, we start from the following generalizations of the Darcy’s and
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