Criteria for modelling flow movement in filtering structures of railway earthworks

The article presents the derivation of similarity criteria for laminar, turbulent, and transitional regimes of filtration flow in pipeless French drain systems. In recent years, coarse-grained materials have been widely used in the construction of railway embankments to protect slopes from erosion and wash-outs and to build filter trenches. The patterns of filtration flows in both cases are the same as in pipeless French drainage systems; however, not all of the calculation dependencies required for practical use can be obtained theoretically, and it is then necessary to use either mathematical methods or, more often, physical modelling. In particular, it is not possible to theoretically obtain dependencies for determining flow depths when there is no water level at the downstream end of the outlets. Until now, research has been conducted primarily by hydraulic engineers for filtration flows through embankment dams. In this case, the filtration usually behaves as a laminar flow. In the outlet sections of filter trenches and pipeless drains, the flow is generally turbulent, while at the section just before the outlet the flow is transitional. Until recently, these cases remained outside the focus of filtration specialists. There were no criteria for modelling. In this article, these criteria are derived from the equations of filtration flow motion in drains for all three regimes: laminar, transitional, and turbulent. Verification of the obtained similarity criteria was carried out for a 14 metre long pipeless French drain laid in a trough. The article presents a water surface profile designed using a theoretically justified calculation relationship. The same figure also shows points obtained by measurements in specific sections of the filtration flow in the trough. As can be seen from the figure, the agreement of the results is quite satisfactory.

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