Geoscience Reference
In-Depth Information
b
Y c ð
X 2
0
:
1
Þ¼ð
0
:
047 log X 2
0
:
023
Þb 2
b
Y c ð
0
:
1
<
X 2
0
:
25
Þ¼ð
0
:
01 log X 2 þ
0
:
034
Þb 2
(12)
Y c ð
X 2 >
0
:
25
Þ¼ð
0
:
0517 log X 2 þ
0
:
057
Þb 2
10 3 [ Dg /( u 2
b 2 )] 1/3 d ; and
where X 2
4.67
b 2 (0.265
M
1)
¼
( M + 2)/
(1
2 M ).
Egiazaroff ( 1965 ) gave yet another derivation for Y c ( R ). He assumed that
the velocity at an elevation of 0.63 d (above the bottom of particle) equals the fall
velocity w ss of particle. His equation is
þ
1
:
33
Y c ¼
(13)
C D ½
a r þ
5
:
75 log
ð
0
:
63
Þ
where a r ¼
0.4 for large R . Both a r and C D
increase for low R . His results do not correspond with the Shields diagram.
Mantz ( 1977 ) proposed the extended Shields diagram to obtain the condition
of maximum stability (Fig. 2 ). Yalin and Karahan ( 1979 ) presented a curve of Y c
versus R , using a large volume of data collected from literature (Fig. 2 ). Their
curve is regarded as a superior curve to the commonly used Shields curve.
Cao et al. ( 2006 ) derived the explicit equation for the curve of Yalin and
Karahan ( 1979 ). It is:
8.5; and C D ¼
drag coefficient
¼
b
R 0 : 23
d
Y c ð
R d
6
:
61
Þ¼
0
:
1414
=
0 : 35
2 : 84
Þ¼ ½
1
þð
0
:
0223 R b Þ
b
(14)
Y c ð
6
:
61
<
R d
282
:
84
09 R 0 : 68
d
3
:
r
Y c ð
R d
282
:
84
Þ¼
0
:
045
1
Yalin and Karahan
Upper curve of Mantz
0.1
Low curve of Mantz
0.01
0.01
0.1
1
10
100
1000
10000
R *
Fig. 2 Curves ( Y c vs. R ) of Mantz (1977) and Yalin and Karahan ( 1979 )
Search WWH ::




Custom Search