The role of capillary forces in steady-state and transient seepage flows

Steady and transient seepage problems were investigated numerically using a dimensionless formulation for water flow in variably saturated, two-dimensional anisotropic and homogenous porous media. The dimensionless formulation combines the aspect ratio and the anisotropy ratio in one dimensionless parameter, M, and accounts for capillarity effects using the ratio of the domain height to the height of capillary fringe as another dimensionless parameter, α. Two domain geometries were considered: rectangular and trapezoidal. It was found that M and α play major roles in the development and the height of the seepage face. The height of the steady-state seepage face increased with the decreasing value of α. The effects of capillarity on the development of the transient seepage face were investigated by lowering the open water level on one side of the domain at various uniform velocities while the other side was kept at a constant value. It was found for most scenarios that decoupling between the water table and the open water level first occurred for domains with large α. In other words, the seepage face heights of these systems were larger than those with a small α. These results are the opposite of the steady-state results and are due to the fact that drainage of the pores was the major mechanism controlling the drop of the transient water table, especially at earlier times. A criterion for the decoupling of the water table from the falling open water level (i.e., the formation of the transient seepage face) was developed by Dracos (1965). It states that decoupling does not occur as long as the falling speed, VF, of the open water level is less than V_d = K_o sin² B/φ where K_o is the saturated hydraulic conductivity of the soil, φ is the porosity, and β is the angle of the exit face with the horizontal (i.e., β = π/2 implies a vertical face). Our investigation revealed that decoupling occurs for smaller falling velocities than Vd, and is caused by, among others, the fact that the water table is not tangent to the exit face but rather intersects it at a nonzero angle.