Mathematical Model for Piping

Abstract

In the technical note, a two-dimensional mathematical model for piping under a dam on a granular material is reported. No details of the calculation are given, but the results are communicated. The key feature of the model is the treatment of a piping channel, thus incorporating and unifying apparently conflicting hypotheses made in the past by Lane and Koshla. The result is a map of steady-state equilibrium situations that are possible for the length of the piping channel under the dam as a function of the water-level difference on both sides of the dam and the particle grain size. The latter parameter arises because of the necessary treatment of the stability of the channel walls. The results show that stable states are possible as long as the piping channel does not exceed half the length of the structure. A formula linking the relevant parameters to obtain a necessary condition for equilibrium is presented. Implications for model tests and centrifuge tests are discussed.