SPILLWAYS 229
due to the difficulties in the definition of the onset of skimming flow as
well as to possible scale effects.
The same as for any rough spillway surface, the point of inception of
self-aeration on stepped spillways is closer to the crest than in the case of
smooth spillways due to the faster growth of the turbulent boundary layer
thickness (equation (4.37)). According to Boes and Hager (2003a) the
blackwater distance Lifrom the crest to the air entrainment inception
point is
Li5.9yc6/5/((sin)7/5h1/5) (4.67)(this can be compared with equation (4.23) for smooth spillways).
Equation 4.67 demonstrates again the great importance of the unit
dischargeqand the relatively small influence of the step height h.
The uniform equivalent clear water depth ywcan be computed from
(Boes and Hager 2003b):
yw/h0.215 (sin )^ 1/3 (4.68)i.e.ywis independent of the step height.
The uniform flow depth for the mixture of air and water y 90 (import-
ant for spillway side wall height) as given by the authors is:
y 90 /h0.5Fr*(0.1 tan 0.5) (4.69)whereFr*qw/(gsinh^3 )1/2
Although the enhanced aeration and earlier air inception point on
stepped spillway surfaces act as cavitation protection, there still is a risk of
cavitation (due to negative pressures on the vertical step faces) in the
region of blackwater flow upstream of the inception point and particularly
downstream of it before sufficient entrained air reaches the spillway
surface. According to the discussion of the Boes and Hager (2003a) paper
the velocity at the inception point should not exceed about 15 m/s to avoid
risk of cavitation.
For further details of the design of stepped spillways and their flow
structure see Chanson (1995, 2001), Chanson and Toombes (2002), Boes
and Hager (2003a, 2003b) and Chanson (2004). For energy dissipation on
stepped spillways see Section 5.2.
Although superficially similar in terms of type of flow, spillways
using prefabricated blocks have lower steps, smaller slopes and present
additional design problems to stepped spillways on large (RCC) dams.
Gabion stepped spillways may have a rather limited life, but earth dam
spillways protected by prefabricated interlocking concrete blocks have been
used quite extensively. Russian engineers pioneered the design of concrete
wedge blocks and Pravdivets and Bramley (1989) described in some detail