Modelling water flow through railway ballast with random permeability and a free boundary

Floodwaters can damage railway tracks by scouring the ballast, and this can, in turn, lead to dire consequences, including train accidents. Therefore, the accurate prediction of water flow through railway ballast is of significant importance to assess and mediate the risk of ballast damage. In particular, ballast permeability is an important parameter because it controls the flow rate through the ballast. Here we develop a model that includes the random permeability effect using the Karhunen-Loeve expansion. We also allow for the free boundary. The computation is carried out using the finite element method, and it is shown that the same elements can compute the Karhunen-Loeve expansion as are used in the numerical solution of the fluid flow. All calculations are carefully validated against either analytic solutions or results from the literature. It is shown that randomness in the permeability increases the outward flow compared to the constant permeability case. It is also shown that allowing for the free boundary changes significantly the flow characteristics.