Flow in unsaturated porous media is commonly described by the Richards equation. This equation is strongly nonlinear due to interrelationships between water pressure head (negative in unsaturated conditions), water content and hydraulic conductivity. The accuracy of numerical solution of the Richards equation often depends on the method used to estimate average hydraulic conductivity between neighbouring nodes or cells of the numerical grid. The present paper discusses application of the computer simulation code VS2DI to three test problems concerning infiltration into an initially dry medium, using various methods for inter-cell conductivity calculation (arithmetic mean, geometric mean and upstream weighting). It is shown that the influence of the averaging method can be very large for coarse grid, but that it diminishes as cell size decreases. Overall, the arithmetic average produced the most reliable results for coarse grids. Moreover, the difference between results obtained with various methods is a convenient indicator of the adequacy of grid refinement.

The paper presents a 2D upward infiltration experiment performed on a model porous medium consisting of fine sand background with two inclusions made of coarser sands. The purpose of the experiment was to investigate the effects of structural air trapping, which occurs during infiltration as a result of heterogeneous material structure. The experiment shows that a significant amount of air becomes trapped in each of the inclusions. Numerical simulations were carried out using the two-phase water-air flow model and the Richards equation. The experimental results can be reproduced with good accuracy only using a two-phase flow model, which accounts for both structural and pore-scale trapping. On the other hand, the Richards equation was not able to represent the structural trapping caused by material heterogeneity.

Abstract. Numerical models are often used to describe flow and deformation processes occurring in dikes during flood events. Modeling of such phenomena is a challenging task, due to the complexity of the system, consisting of three material phases: soil skeleton, pore water and pore air. Additional difficulties are transient loading caused by variable in time water levels, heterogeneity of the soil or air trapping. This paper presents a brief review of the influence of the air phase in soil on water flow and pore pressure generation, with focus on applications related to stability of dikes, earth dams and similar structures. Numerical simulations are carried out to investigate the differences between the Richards equation and the two-phase flow model, using an in-house code based on the finite volume method. A variety of boundary problems are considered, including seepage through flood dikes, dike overtopping and water level fluctuations. Special attention is paid to the problem of air trapping, which occurs when water flows over the top of a dike. Such a phenomenon occurred during experiments on model dikes reported in the literature, ultimately leading to development of cracks and damages in dike structure.

Flow in flood dikes, earth dams, and embankments occurs in variably saturated conditions, with pores of the earth material filled partly with water and partly with air. In routine engineering analysis, the influence of pore air is neglected and the air pressure is assumed equal to atmospheric. In some circumstances, for example, during overtopping of the dike by water, the effect of pore air on water flow and stability of the structure can be important. These features cannot be captured with the commonly used Richards equation. In this paper, we analyze earlier experiments on the overtopping of a model dike made of fine sand. During the experiments, a significant amount of air was trapped near the outer slope of the dike, which later escaped through a fracture formed in wet sand. The observations were compared with numerical simulations using the Richards equation and the two-phase immiscible flow model. The deformation and damage of the dike were not modelled, but the initial evolution of the entrapped air pressure (before damage occurred) was in a good agreement with two-phase flow simulations.

The process of flow modeling in unsaturated porous medium is often found in many fields of sciences: geology, fluid mechanics, thermodynamics, microbiology or chemistry. Problem is relatively complicated due to complexity of the system which contains three phases: water, air and soil skeleton. The flow of water in such a medium can be described using two-phase (2PH) flow formulation, which accounts the inflow of air and water phases, or with simplified model known as Richards (RE) equation where only water flow is taken into account. In many well known programs available in the market (like SeepW, STOMP) the primary interest is only the water flow and the flow of air is omitted. As a result Richard equation in used more often. It's main assumption is that pore air is continuous and has connection with atmospheric air which is equivalent to infinite mobility of the air phase during all simulation. This paper presents a brief review of the influence of the air phase in soil on water flow and pore pressure generation, with focus on applications related to infiltration process occurring in the large areas. An irrigation effect of rice fields with shallow water table has been investigated. To assess the impact of the gas phase various lengths of the infiltration zone have been considered. Numerical simulations are carried out to investigate the differences between the Richards equation and the two-phase flow model, using an in-house code based on the finite volume method.