Vízügyi Közlemények, 1970 (52. évfolyam)

4. füzet - Rövidebb közlemények és beszámolók

Shields as well. Some investigators followed individualistic approaches, thus e. g. Bogárdi defined the condition immediately preceding the critical situation as one in which a sediment grain of a diameter identical to that of the bed material, thrown into the water and sinking to the bottom continues to move over it, while in the critical stage a few stationary particles are also set into motion [14]. From among the fluid forces mentioned above attention is focused by most theoretical investigators of the mechanism of bed-load transportation on the tractive force alone, while the uplift force is not incorporated in an explicit form in their formulae. Thus the author of one of the most familiar theories, White, reduced the equilibrium problem of a particle at rest to the consideration of the moments due to the tractive force and the submerged particle weight [15]. The constants involved in the formulae are, however, determined experimentally by the authors, so that these include implicitly the influence of the uplift forces as well. Considerably less reference is made to the experimental study of these latter in the literature []6] and no generally accepted theoretical relationships are as yet available. According to experimentally more, or less verified estimates the uplift force is two-and-a half to five times as great as the tractive force [15, 17]. Another group of investigators discarded the physical-analytical approach, forming dimensionless groups of the parameters considered most important and attempting to correlate these with experimental results. One of the pioneers of this method was Shields [11], who expressed the dimensionless shear-velocity parameter later named after him in terms of the boundary layer shear velocity Reynolds number: In the above expression r

0 — у Ц S is the shear stress developed on the channel bottom [g/sq.cm]; y

s and y are the specific gravities of sediment and water, respectively, [g/cu.cm]; d is the mean bed-load diameter: U, = V t

0/q the shear velocity [cm/sec]; q the density of water [g.sec

2/cm

4]; y the kinematic viscosity of water [cm

2/sec], S the slope of the energy gradient line and D the waterdepth [cm], The relationship of Shields and the graphical representation thereof became widely familiar, although several investigators, to mention only Egiazaroff [18], published slightly different data on the critical condition. According to Egiazaroff the critical shear stress is where Сд is the resistance coefficient, which in the case of a quartz sphere settling in water may be taken as 0,4; a^ is the function of R„ and its magnitude determined experimentally for coarse-grained bottom material (y

8 — y)d 3 C

D (a

r + 5,75 log 0,63)

2 45