Numerical modelling of the erosion and deposition of sand inside a filter layer

Niels Gjøl Jacobsen, Marcel R. A. van Gent, Jørgen Fredsøe

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This paper treats the numerical modelling of the behaviour of a sand core covered by rocks and exposed to waves. The associated displacement of the rock is also studied. A design that allows for erosion and deposition of the sand core beneath a rock layer in a coastal structure requires an accurate prediction method to assure that the amount of erosion remains within acceptable limits. This work presents a numerical model that is capable of describing the erosion and deposition patterns inside of an open filter of rock on top of sand. The hydraulic loading is that of incident irregular waves and the open filters are surface piercing. Due to the few experimental data sets on sediment transport inside of rock layers, a sediment transport formulation has been proposed based on a matching between the numerical model and experimental data on the profile deformation inside an open filter. The rock layer on top of a sand core introduces a correction term in the Exner equation (the continuity equation for sediment and change in bed level). The correction term originates from the fact that the sand can only be deposited in the pores of the filter material. The numerical model is validated against additional data sets on the erosion and deposition patterns inside of an open filter. A few cases are defined to study the effect of the sinking of the filter into the erosion hole. The numerical model is also applied to several application cases. The response of the core material (sand) to changes in the wave period and wave height is considered. The effect of different layouts of the filter is studied in order to investigate the effect of different filter profiles on the resulting erosion. Finally, it is studied how much the design of a hydraulically closed filter can be relaxed to obtain a reduction in the design requirements of the filter thickness, while the deformation to the sand core remains acceptably small.
Original languageEnglish
JournalCoastal engineering
Pages (from-to)47-63
Publication statusPublished - 2017

Bibliographical note

© 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (


  • Modified Exner equation
  • Numerical modeling
  • Open filters
  • Sediment transport


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