The effect of grain roughness and bed-load transport on the friction resistance of erodible beds in steep slopes

This study aimed at investigating the effect of grain roughness and bed-load transport on erodible beds friction coefficient (f) in a laboratory flume of 8 m long and 25.5 cm wide. Experiments were carried out at slopes 2, 3 and 5% for an erodible bed consisting of uniform grains with the median diameter of 1.7, 3.3 and 8.2 mm. The maximum dimensionless discharge of the bed-load transport was obtained equal to 0.30. Conducting the experiments in uniform bed material and with the use of empirical relations, friction factor caused by bed roughness (f_c) was obtained and the resistance coefficient caused by the bed-load transport (f_m) was calculated using the linear theory. By analyzing 130 data from the experimental results of this research and experimental data gathered by Recking et al. (J Hydraul Eng 134(9):1302–1310, 2008) it was realized that at the slopes 5% or more, the frictional resistance caused by the bed-load transport (f_m) had more contribution on the total friction resistance f. Also the resistance friction caused by the grains roughness had more contribution at small slope so that in the range of f_c/f > 0.6, about 90% of the data was placed at slopes 2–3%, while in the range of f_c/f< 0.3, about 90% of the data was placed at slopes of 5–9%. By dimensional analysis, non-dimensional parameters influencing f_m were identified and an empirical equation was proposed for f_m and validated by experimental results of the previous studies. The accuracy of the relation proposed for prediction of f_m was acceptable. The sensitivity analysis of the effective parameters in the proposed equation showed that the Froude number and slope had the greatest effect on the frictional resistance caused by the bed erosion (f_m), respectively.