Behavior of Porous Bed Near Flow Singularity

The behavior of a porous bed in the vicinity of a flow singularity that was imposed by the nonorthogonality of a potential line and a streamline was studied theoretically and experimentally. Flow of water under a circular cylinder that is partially imbedded in sand results in nonorthogonality at the intersection of sand and cylinder unless the cylinder is half imbedded. The analytical solution indicates that the seepage force can be theoretically infinite at the singular point. Experiments were conducted that led to boiling, heaving, and piping for the partially-imbedded cylinder. Results of the experiment indicate that the flow singularity of nonorthogonality is not very serious because nature apparently corrects for this anomaly by a readjustment of the flow in the vicinity of the singularity. Furthermore, a more detailed investigation of the analytical solution in the vicinity of the singularity shows that, if the hydraulic gradient is evaluated in terms of the sand diameter in the vicinity of the singularity point, the seepage force may not actually be very large.