On One Class of Boundary Value Problems of the Steady-State Filtration Theory in Porous Grounds

Abstract

:In the framework of Darcy's law of filtration the investigation results of one class of boundary value problems of the steady-state filtration theory in porous ground base are presented. The plane mixed bounadry value problems on the structural analysis of hydrotechnical con­struction of dam type on filtrating ground base in the form of a layer of finite or infinite thickness are considered. The coefficient of filtration is assumed to be constant, piecewise constant, or changing by the depth of base according to the exponential law, the property of anisotropy of filtration is also taken into account. Axis-symmetric and three-dimentional boundary value problems of the theory of steady-state fluid filtration in a three-dimentional layer of a finite or infinite thickness are discussed. These problems are of the type of Lamb well-known hydrodynamic problems in the theory of steady-state flow of the ideal fluid, when through the circular or rectangular openeing of a rigid screen on the upper bound of the layer the liquid with a definite vertical velocity or with a definite pressure is injected into porous ground base. Here, the fields of velocities and pressures in the layer, as well as flow rates of liquid through the certain sections of the ground base are determined.