On the Application of the Lattice Boltzmann Method to Predict Soil Meso Seepage Characteristics

In this study, a two-dimensional approach is elaborated to study with the lattice Boltzmann method (LBM) the seepage of water in the pores of a soil. Firstly, the D2Q9 model is selected to account for the discrete velocity distribution of water flow. In particular, impermeability is considered as macroscopic boundary condition for the left and right domain sides, while the upper and lower boundaries are assumed to behave as pressure boundaries controlled by different densities. The micro-boundary conditions are implemented through the standard rebound strategy and a non-equilibrium extrapolation scheme. Matlab is used for the development of the related algorithm. Finally, the influence of porosity, permeability, osmotic pressure and other factors is assessed with regard to seepage characteristics and the ensuing results are compared with Darcy's law. The computations show that, for fixed initial conditions, the pore structure has a certain influence on the local velocity of seepage, but the overall state is stable, and the average velocity of each layer is the same. The larger the pore passage is, the faster the flow velocity is, and vice versa. For low permeability, the numerical results are consistent with the Darcy's law. The greater the pressure difference between the inlet and outlet of seepage, the greater the seepage rate. The relationship between them is linear (yet in good agreement with Darcy's law).