Page 256 - Handbook of Gold Exploration and Evaluation

Sedimentation and detrital gold 227

4.18 Definition diagram for calculating the initiation of grain motion on a
horizontal bed (after Slingerland and Smith, 1986). (Reprinted, with
permission, from the Annual Review of Earth and Planetary Sciences, Volume
14, ß 1986 by Annual Reviews www.annualreviews.org).

assumed to be cohesionless, all particles in the bed are equant in size and are at
rest. For a grain to rotate about a pivot point A, a moment balance shows that the
ratio of the fluid forces F to the gravity forces G is:

F=G a G sin =a f cos ÿ † 4.18
where a G and a f are the moment arms about A, is the angle between the fluid
force vector and the horizontal, and the point of application is assumed to be
along the normal to the pivot line.
Figure 4.18 is a definition diagram for calculating the initiation of grain
motion on a horizontal bed. A sub-spherical particle of diameter D and density
p , protruding above the bed a distance P, must pivot about point A on a
downward flow grain of diameter K. The resultant of the lift and drag forces (in
magnitude and direction) is a fluid force vector F, which acts at a distance a f
away from a pivot line through A and at an angle , from the horizontal to rotate
the grain about a pivot point P. A grain weight vector G acts through the grain
centre of gravity CG at a distance a g away from the pivot line. At the moment of
entrainment, the fluid torque must be greater than the resisting torque.

4.4.2 Transport

Fundamental principles governing the nature of stream channels and the shapes
of streams in cross-section map view and longitudinal profile have been