Two-dimensional steady flow rate equation for loess joints

The problem of jointed loess flows is a two-dimensional one including the flows both along the joint and perpendicular to the joint direction. This matter lacks research. Considering the vertical flows into the loess and the flow speed in the loess itself, a two-dimensional model for loess joints is established. By using this model, a seepage differential equation of flow velocity is derived by means of the Eulerian variational method. A two-dimensional steady flow equation for loess joints is further derived based on the flow characteristics and the boundary conditions of loess joints. This equation can be treated as an extension of the cubic law in the research field of rock joints. What’s more, based on the Darcy's law, a permeability coefficient for loess joints is also derived.