1. Instituto de Mecánica de Fluidos UNEXPO / Universidad Nacional Politécnica Antonio José de Sucre Fractionally-Integrated Sediment-Transport rate over a Non-Uniform Sediment Bed Oscar Sarmiento and Marco Falcón UNEXPO / Universidad Nacional Politécnica Antonio José de Sucre Instituto de Mecánica de Fluidos UNEXPOUNEXPO UNEXPOUNEXPO

2. UNEXPO / Universidad Nacional Politécnica Antonio José de Sucre Objective  To obtain the bedload sediment transport rate over a non-uniform sediment bed calculating the P article E rosion P robability by C alibrating the: PDF of the I nstantaneous F luid S hear- S tress. PDF (uniform) of the C ritical S hear- S tress for each particle size. N on- H iding P article P robability.

3. Instituto de Mecánica de Fluidos UNEXPO / Universidad Nacional Politécnica Antonio José de Sucre Method  Calibration of a probabilistic, non-mechanistic sediment transport model with data reported by Brownlie. Minimization of the sums of the squares of the deviations between observed and predicted rates, by varying systematically the C alibration P arameters, some of which determine the F luid S hear- S tress and the B ed, C ritical S hear- S tress D ensity, P robabilistic F unctions

4. Instituto de Mecánica de Fluidos UNEXPO / Universidad Nacional Politécnica Antonio José de Sucre A  ),(At   P p  p Instantaneous spatially averaged fluid shear stress

5. Instituto de Mecánica de Fluidos UNEXPO / Universidad Nacional Politécnica Antonio José de Sucre PDF´s averaged area

6. Instituto de Mecánica de Fluidos UNEXPO / Universidad Nacional Politécnica Antonio José de Sucre Erosion Probability

7. Instituto de Mecánica de Fluidos UNEXPO / Universidad Nacional Politécnica Antonio José de Sucre Probability of erosion

8. Instituto de Mecánica de Fluidos UNEXPO / Universidad Nacional Politécnica Antonio José de Sucre PDF of the shear stresses ; Bed critical: Fluid:

9. Instituto de Mecánica de Fluidos UNEXPO / Universidad Nacional Politécnica Antonio José de Sucre PDF of the fluid shear stresses

10. Instituto de Mecánica de Fluidos UNEXPO / Universidad Nacional Politécnica Antonio José de Sucre Non dimensional expression for the unit weight rate of bedload transport of non- uniform sediment particles

11. Instituto de Mecánica de Fluidos UNEXPO / Universidad Nacional Politécnica Antonio José de Sucre Application of the non uniform sediment formula with data sets not used for its calibration

12. Instituto de Mecánica de Fluidos UNEXPO / Universidad Nacional Politécnica Antonio José de Sucre Sd = 5.7547 Dimensionless transport rates for uniform sediment data, calculated with the calibrated non-uniform formula

13. Instituto de Mecánica de Fluidos UNEXPO / Universidad Nacional Politécnica Antonio José de Sucre Conclusion and Recommendations  The computed transport rates, for uniform sediment, deviate somewhat from observed results, when calculated with the non-uniform sediment calibrated formula.  The smaller and larger rates could be normalized by their mean value in order that all measurements have more or less equal influence on the calibration parameters and on the minimization procedure of the squares of the deviations between theory and experiments

14. Instituto de Mecánica de Fluidos UNEXPO / Universidad Nacional Politécnica Antonio José de Sucre Recommendations  Uniform sediment data should be included in the calibration for non-uniform sediment experiments.

15. Instituto de Mecánica de Fluidos UNEXPO / Universidad Nacional Politécnica Antonio José de Sucre Weigth particles per unit bed area Probable weight of the eroded particles per unit bed area Time for a particle to be eroded (Einstein, Yalin) Rate of Erosion

16. Instituto de Mecánica de Fluidos UNEXPO / Universidad Nacional Politécnica Antonio José de Sucre Average weigth of the particles being deposited by unit width and unit of time of the weight fraction Rate of Deposition Unit bedload weight rate Weight grain- size density of the material transported in the bedload layer Average distance achieved by a particle until to stop (Einstein, 1950)

17. Instituto de Mecánica de Fluidos UNEXPO / Universidad Nacional Politécnica Antonio José de Sucre Probability of erosion: three experiments reported by Brownlie (1981)