The paper considers one of the approaches to the modeling of spill liquid viscous hydrocarbons, followed by pressureless infiltration into the soil in the approximation of "shallow water"

All kinds of hydrodynamic processes in the overwhelming majority of cases can have adverse consequences from the point of view of ecology and economics.This requires the development of adequate measures to organize the elimination of the consequences of such events. Mathematical modeling of spills has applied importance for the development of technological equipment designed to reduce the impact of consequences of spills and its prevention.

A mathematical model is proposed that allows, on the basis of quasi-one-dimensional equations, to illustrate the process of spreading a liquid above the surface of a soil and impregnating this liquid into the ground. The rate of impregnation is assumed constant.

Based on the shallow water theory, the problem on radial spreading of incompressible liquid over a horizontal surface with account for the presence of vegetation has been studied. Some exact as well as approximate analytical solutions have been obtained that describe various cases, stages, and possible regimes of the process of spreading. A comparison of the results obtained with experimental data is made.Introduction. The phenomenon of liquid spreading over the earth′s surface is of interest from the viewpoint of assessing the possible contaminations caused by emergency ejections of liquid-containing media [1]. The extent of contamination depends on the amount of ejected mass and the rapidity of ejection, as well as on the imbibing ability of ground and the characteristics of vegetative cover. Various aspects of the spread of liquid and gaseous ejections, as well as of mudfl ows and landslides over a horizontal surface, are considered in [2][3][4][5][6][7][8]. The results of theoretical and experimental investigations of axisymmetric fl ows above porous and permeable surfaces are presented in [9][10][11][12]. Regimes of the spreading of ejections are possible when the rapidity of the propagation of a pool is governed by inertia effects. It seems that the main stage of such spreading takes place in an inertialess regime when the head gradient determined by the thickness of the liquid layer on the ground surface is balanced out by the forces of the hydraulic resistance produced by a ground covered with vegetation.