Graf W.H. (1991) Flow resistance over a gravel bed: Its consequence on initial sediment movement. In: Armanini A., Di Silvio G. (eds) Fluvial Hydraulics of Mountain Regions. Lecture Notes in Earth Sciences, vol 37. Springer, Berlin, Heidelberg
The first part concerns itself with the friction factor of a gravel bed. Velocity distributions are measured in a gravel-bed flume having large slopes of 0.2<So (%)<2 and total water depths of 7<D(cm)<23. Two uniform gravel sizes of ds=2.35 cm and ds=1.35 cm are investigated. It is shown that : (i) the velocity distribution (see Fig.1) can be described by the logarithmic law, eqn (2) (see Fig.2a) in the inner region and by a parabolic law, eqn (4) (see Fig.2b) in the outer region; (ii) the friction velocities are reasonably equal to the ones computed from the energy slope; (iii) the position of the reference level, yo, can be established. The flow-resistance relations, eqns (6) and (6a), were researched and rendered : (i) the numerical constants, Br (see Fig.3) and \(\bar B\)r, depend upon the relative roughness (see Fig.4); (ii) where 3 zones can be identified; (iii) zone 1 being for small relative roughness with \(\bar B\)r≈6.25, proposed by Keulegan (1938); (iv) zone 3 being for large relative roughness with \(\bar B\)r≈3.25, proposed by Graf (1984). Two independent laboratory experiments and one set of field data (see Fig.6) are used to demonstrate the validity of the proposed flow-resistance relation.
The second part deals with the consequence of the above-developed flow-resistance relation on the initiation of grain movement on the bed. The results for steep-sloped and gravel-bed channels do not seem to agree with the well-accepted Shields diagram (see Fig.8). The understanding of the hydrodynamics of the turbulent flow over rough surfaces, expressed with the flow resistance, eqn (6a), and an appropriate constant, \(\bar B\)r (see Fig.4), help to explain the deviation from the Shields diagram if relative roughness are of importance, i.e. : (ds/D)>0.04. Data, now available in the literature, are used (see Fig.10) to present in a simple way for the determination of initial sediment movement.