Effect of nonuniform boundary conditions on steady flow in saturated homogeneous cylindrical soil columns
Laboratory column experiments involving steady flow in homogeneous soil are often analyzed assuming that the flow is spatially uniform in any plane transverse to the longitudinal axis aligned with the column centerline. Axisymmetric steady flow in such a column was analyzed to determine the impact of radially nonuniform boundary conditions at the column entrance and exit planes. A general solution to the governing Laplace equation was derived taking into account arbitrary functional forms of the imposed head and flux boundary conditions. Specific solutions were deduced for smoothly varying and abrupt disturbances at the boundaries. The solutions were used to derive expressions for the length scale over which the induced flow nonuniformities are dissipated within the column. For soil columns with an aspect ratio (column radius/length) less than about 1/3, the maximum dissipation length scale is in all cases less than (3/2) R, where R is the column radius. For practical purposes it is sufficient to take R as the dissipation length scale. Consequently, no matter what the radial variation in the boundary condition, flow will be uniform within the column if at each end a baffle zone with length equal to R is incorporated into the soil column design. The results can be applied to homogeneous anisotropic soil via a simple scaling. Published experimental results showing nonuniform flow near the entrance and exit boundaries were found to be consistent with the theoretical results.
Keywords: Bessel functions ; Axisymmetric flow ; Laplace’s equation ; Baffle ; Orifice ; Dissipation length scale ; Analytical solutions ; Stokes stream function ; Hydraulic potential ; Darcy’s law ; Streamlines ; Fourier-Bessel series
Record created on 2009-01-07, modified on 2016-08-08