Infiltration of fine sediment mixtures through poorly sorted immobile coarse beds

Percolation of fine sediment is a common process in gravel bed rivers, which often exhibit extended and overlapping grain size distributions of the bed and the supplied fine sediment. Yet existing sediment infiltration theory assumes well-sorted fine material with smaller grain size than the bed pores, and as such, is not suitable for many situations encountered in gravel bed streams. Previous developments for infiltration of uniform material are here generalized to consider poorly sorted sediment mixtures. Governing equations and a numerical solution to model the vertical distribution of infiltrating sediment are presented. The equations are solved as a function of a trapping coefficient, dependent on the relative size of infiltrating fines in relation to bed material. A method is developed to generate equivalent grain size distributions to calculate the trapping coefficient, when grain sizes of the infiltrating and bed materials overlap. Moreover, a bed cutoff size is defined and computed with a semiempirical packing-porosity model, to distinguish particles smaller than the bed pores. Published experimental data are used to test the new model and calibrate the trapping coefficient. It is shown that this coefficient is highly sensible to the fine and coarse tails of fine and coarse materials grain size distributions. Accordingly, calibrated values of the coefficient are set as a function of a mean size ratio, computed from the geometric mean of the tails of the size distributions. Incorporating this relation, the model performed well in reproducing indirect observations of sediment infiltration from experiments reported in the literature.