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i
56 4 5712 2
18 2 9
26 8 20 1 26 11 10 2 27 2 4 3
ii
2
2
FL
ABC
m
mm
1
2
3
m min
4
a
c
e
b
d
FWL FWL
FWL FWL
FWL
5
6
7
8
m
m
9
10
PS
m
11
m
mm mm
m
m
m
12
mm
m
mm
13
JIS A 1202
1204 1203 1205 1214 1210 1218 1216 JGS 0524 JIS A 1217 JGS 0523 0541 0542
Dd max
D
wwet
wdry wf wwet
wdry Dwwet
wf
wf
14
dmax
d max
wd r y
ww
et
wf
wop
t
D
(UU)
(CU) (CD)
1.2
(CU) (CD)
(CU) (CD)
(CU) (CD)
)
Wf
15
D
D
D
w
wdry
woptw
wopt w
w
w
w w
dmax
dmax
d
cm s
k
S r
wwet
UU CU CD
w2 w3 wopt
w3
c U
c
16
n
n
ii
m1
mnmmn 1
mds
ds
n m n
2
17
cm scm s
2.6 ( 2.6)
5 10-5cm/s5 10-6cm/s
mmmm
mmmm
18
mm
1)
mm
1)
( ) 25 3
19
20
m m
m m
m m ha ha ha ha m s m s m m
21
22
YesNo
END
START
HWL
HWL
H m
H m
FWL
23
24
25
26
NEPA
27
5
avoidance
minimization
rectification
reduction elimination
compensation
28
IUCN6
better worse
29
30
31
1.2
200 1 200 A B
C
20
200 100
1.2 200
A
QA Are ················································································································· (3.2.1)
QA m3/s re mm/h A km2
(1) A
A
40km2
(2)
tp
ep rACt ··················································································································· (3.2.2)
A km2 re tp mm/h C tp C
32
CC
2 3
karbey
rziha kraven
C
C 250 350 290 C 190 210 200
C 130 150 140 C 90 120 100
C 60 90 70 (3)
re rfp
rfr pe ········································································································································· (3.2.3)
r 200 mm/h fp
fp
fp fp
0.75 0.90 0.70 0.80 0.50 0.75 0.45 0.60
0.70 0.80 0.75 0.85 0.45 0.75 0.50 0.75
fp
0.6 0.7 0.8 0.9
70 40 40
33
B
C
Creager 20km2
)1( 05.0ACAq ··············································································································································· (3.2.4)
q m3/s/ km2 A km2 C
34
C
/ 30
35
15 4 57 5
45 10 ( ) 11 11
Yes
No
Q2 1.2 Q1
Yes
Yes
No
No
START
30, 60, 120 200 r
fp
tp C A0.22 re 0.35 re fp r
re tp
A
AQ re A
Q1 max(QA, QB, QC)
1.2 Q1
Q 2
END END
B QB C QC
36
37
FS
No
Yes
Yes
No
No
START
q
END
No YesYes
No
Yes
FS 1.2
q 60 min100 m
38
39
40
L L
10 m
L
B B
HWL FWL
H1 H2Ha H
d
Hb
d 10 m H Hb d 10 m H Ha
H1 H2
h1
HWLFWL
h2h1 h2
41
B HWL
FWL
H1 H2 h1 h2
(1)
qc 500 kN/m2 k 1 10 4 cm/s 1 10 6 m/s
N 4
a.
42
1/3
b.
43
(a)
xr
xr
kkdt
······································································································································· (3.3.1)
t (m) d (m) k1 (m/s) k (m/s)
xr ( hb)xr
qf
qf
dr xxdhk
··········································································································································· (3.3.2)
qf (m3/s) h (m) xr (m) xd (m)
xr xd
h t
d
hb
(b)
x
xr
)( ax
ax
eae ···································································································· (3.3.3)
a
dktk
x (m) xr (m)
q f xr
x 1/10 1.0 3.0m
44
k
k
x xdd
t h
c.
(2)
(HWL) (FWL) h1 ························································· (3.3.4)
a. FWL
b. h1
0.3 1.2m
45
(a) h1 b h1 b h1 b
(b)
h1 v h1 v h1 v
(c)
(d)
(3)
R 1.0 m h2 0.05 H2 1.0 ··································································································································· (3.3.5)
5.0 m1 m
R 1.0 m h2 0.05 H2 R ······································································································································· (3.3.6) R m
h2 m H2 m
R F (m) V (m/s)
a.
(a) F F
( a )
( b )
ab
46
(b) F F
(c) F
(d)
F'F'
Fa
b
cd
F'
F F''
F'
F F F
F'
b.
30 m/s20 m/s
1999 30 m/s
47
m s
48
c.
Rm
V m s
V m s
V m s
V m s
V m sV m s
F(m)
Severdrup-Munk-Bretschneider S.M.B Wilson Saville (4)
B 0.2H 2.0 ····································································································· (3.3.7)
B m H m
5.0 m 2.0 m
3.0 m
49
(5)
B
HH
HWL FWL h
h
d d
h
b
h
d d
n
n nn
n
n n n
n
H (m)
H1 (m)
h1 (m)
h2 (m)
B (m)
n4 ( )n1 ( ) b (m)h3 (m)
d1 (m) d4 (m)
d2 (m)
d3 (m)
h4 (m)
0.3 1.0 3.0
1.5 0 0.3 1.51.5
1.1 1.5
5 3.3 0.5 1.2 1.8 1.5 0.5 1.8 1.3 1.85 3.3 0.5 1.2 3.0 1.8
1.5 0.5
1.81.5
1.3 1.8
10 7.8 0.8 1.4 4.0 2.1 2.4 2.1 2.110 7.8 0.8 1.4 4.0 2.1
2.0 0.5
2.41.5
2.1 2.1 15 12.2 1.2 1.6 5.0 3.0 3.5 3.2 2.5
(3.3.5) (3.3.6)
(3.3.7) 1.5
3 1
m
0.3
1.5 3.5m
1.5 m
n2 n1 0.1 n3 n2 0.2
d3 1/2 d2
1.5 2.5
1) 2) 3)
(6)
(a)
100m
60 / min
50
10.05
(b) .
15 4
khHb
hHqsinsinCM
·········································································· (3.3.8)
q m3/s b PQ m H1 m k m/s CM M L
MQ M LP C
cossinCM B ······················································································································· (3.3.9)
FWL
L M
QC
MQ R
P
B
H
B
h
b
B B
.
(c)
51
b.
15 4 A. Casagrande
B1 B2 (B1 B2)/2P R B1 B2 /2 PQ
Q k2 -3.3.13D X Y Y
Y Y0 X 0,Y0
q (3.3.8) Y0
kqY ············································································································································· (3.3.10)
YXYY ···························································································································· (3.3.11)
q
Q 2 k2/k1 10
q YesNo
q
OK
52
FWL
L M
QR
P
B
H
B
h
D
Y
XY0
B B
(7)
a. (a)
(Fs) 1.2
(b)
)
1.2 50 100 50
)
(c) .
( )
t
53
( ) t
sat ( )
t sat
t t
sat
t
sat
( )
t sat
.
(d)
Rsin O R
A C
w
O C
BB
A D
p wh
h a
sat
t
t
satB
h
a
O
A
p wh
w
b
t
sat
w
wsin
C
O
A
B
F
E
D t
sat w
(a) (b)
(c) (d)
ABEFDA
54
.
0.15 0.15 0.12
0.15 0.12 0.10 )
(1) (2) (3)
( ) ( )
(1) (3) (
)
( )
55
b.
2 1 3
c 1 3 U
c (a)
30 m 15 m
c
c c
c c
c CU CD
c UU CD
c
N c
56
c c 0
0
c c 0
0
Dunham
Peck N
Meyerhof
N
N N
N
N
N
Dunham
N N
c kN m
c Nc N
N N
Peck qu N
qu N
Dunham qu N
Peck qu NTerzaghi
N
q u q u
N c
57
(b)
15 4 p. -102 -111 c.
d.
9 10
(8)
58
(a)
(b) (c)
(b)
(c)
a.
3 1
b
59
C BA
A B
A B C
n n
n
n
n
(a) (b)
b.
BF
BF
F15 15 B85 85 B15 15
75 m 5
B
B BB
mm
(9)
B
B
60
1/2
FWL
H
H
61
15 4 57 5
( ) 9 10 ( ) 14 3
7 pp.51-65
62
FWL HWL
63
HWL
HWL
HWL
1.5
1.5
64
a b c
d e f
g
65
m s
V P
Hd
d
hv
HP
V m s
d
V
AdQ m s
A d L
d Hd Pg
V
V m sA md mQd m sL mHd mP mg m s
66
m
mm
B=d
d
HC
Q
B mQd m sC
° Hd B
Hd B
B
Hd m
Bdd
d
HCQ
B mQd m sCd m s
Cd
Hd m
67
Hd Hd
B
hv
HdHd
hv
B
68
YdH
X
Y mX mHd m
p
Xp Hd n
np n
Xp p X m
a Hd mb Hd mc Hd m
d Hd mr Hd mr Hd m
Hd m
hv
d
a
rr
b
n
p
Y
X
Hd
Yp
Xp
c
········································································································· (3.4.6)
69
Hd
d
d
Hdh
d
d
Hh
Hd m
hv
hd
P
Hd
d
Qd Cd B HdQd m s Cd m s B m Hd m P m
Cd
P Hd
Hd
P
HP d
70
Hd P
Cd PHd
C
d
d
HHa
HHa
H mHd mP mCCd H Hd
a a H Hd C Cd
Cd
Hd Hd
P
HWL HWL
T
P RT P
T
Hd Hd
R RR Hd HdR Hd
HWL Hd
71
B
A
R
T
R
T
R
T
A
Bt
Bc Bc
R
T
Hd
A
A A
A
B
A A
72
B B Ka Hd
Bt B Bc
B m B mKa
Hd mBt mBc m
d
d
Hdh
d
d
Hh
d
d
Hh
hd d Hd P
P Hd
C
P Hd R1
P/Hd 0.2 0.5 1 2 5
1.8 1.8 2 R1 Hd 0.5Hd 1.8 2
1/4 2.1 2.1 1.84 2.1 2 1.83
( ) 2.0 2.1 2.15 2.16 2.18
······································································································· (3.4.10)
73
b b
74
b b
Hd
P Levelh Vhv h
V
l l
hVA B C
V g
V g
V VgK hm
h V
P Hd h hv Z hg
V Z hhbg
dQ Z
P m Hd m h m hv m
Z m
V m sg m sQd m sb m
h l V l
rFhg
V
hh
rF
l h
Vhb
dQ
·········································································· (3.4.15)
75
Fr
h B ml mV B m s
BC
B hg
V hg
Vg
VVKhm
h C m
hbg
dQ
b C mV C m s
Vhb
dQ
Khm m
hm lII
IR
Vn IR
Vn
n I I R B mR C m
B CA B
C
76
b
VV g
V VgK hm
V g
A B
h V
b
h
L
B
dy
Hd
Hd
d
B
l
i i
X
y
B
d
77
m
s
iB d d B
Fr
DgVFr
m sg m s
D A T mA mT m
1/2.5
m q
m 0 q
Fr
dgV
Bdm
BdmBd
rFgQ ···························································································· (3.4.17)
m 0.7 m d / B 0.5
78
d 0.463rF
Q ( m s ) ··········································································································· (3.4.18)
0.44 0.5 d (0.643 0.61) Q2/5 (m s ) ································································································· (3.4.19)
A
A (B dm ) d (3.4.20)
X Bx (m) Zx (m)
Bx
LXB 11 ················································································································· (3.4.21)
Zx i1 X B (m)
B /B B /B 0.5 B X (m) L (m) B i1 1/13
l (m) l 4 d ························································································································· (3.4.22)
d (m) i2
i2 g n2 Fr 2d
Bd
···································································································· (3.4.23)
n
Bx B
a
Wt
b
Hd
Bx
B
d
R s
m
qd Qd Wt
qd Qd Wt
a b a a
b b
79
p
i
hQQQ
Q XVqVg
VV
h X mQ a m sQ a m sV a m sV a m sq m s m
V V V m sg m s
a a
d d
QQVV
X
h
80
hp
B L i
l
V g
V g
hm
A
B
d
d
V
Vhs
l
81
ms hg
Vdhg
Vd
d A mV m sd B mV m shs mhm m
m
mm R
lVnh
VVVm
RRRm
n R mR m l m
82
USBR III
m s mm s
USBR IV
d
Fdd
1
F
C
g
FF
FFF
dW
d md m
Fdg
V
V m s
83
W mC m s Cg m s
d
d
d L d
W
USBR III
m s m m s
dd1 F1
LIII 3 d2
84
d
d
d Lm
Lm
h
d
d hW h
S hS dh d
h h
W d
III
h h
h
F Vgd
d h
d h
III IV
85
USBR IVF
III d
LIV
W d
h d
Wd min
LIV IV
d LIV
F IV
m s m s
86
A
A
V
W tw
b
tw
tw cmtw
cm
a
cm
W
W
t p W
W
W
cm
A A
W W
W
b
t w
W
c
cm
W tb W
cm
cm
b
cmQ
m /s a b c tw tf tb tp
W Q
Q m sW
m
W
Yq q Q
H
Y
V
d
TW
q
b b
87
I III or IV
He
P
Y
Ld
df dd
VTW
hd
LI III or IVX
Ld
USBR III USBR IVLd D hd He Y
d d F D Yq
YdF
Yd
YgqD c
q m s mg m sY m
dcg
qm
Fdg
V
dVq
m
V m sd d F
USBR III IV F
FUSBR I
88
F USBR IVF USBR III
USBR I
F
D
hd
Lp
LB Lp dc
dc dc
dc
TW dc
He
P
He
P
Y
Ld LI III or IV
df dd TW
hd
Lp Y hd He
Lp Y hd HeLp Y hd He
Lp Y hd He
Lp Y hd He
F V g d
Ld Y hd He
Ld Y hd He
Ld Y hd He
Ld Y hd He
Ld Y hd He
dc Y
df Yd Y
d Y
V d F Xdc df
Y
V
X
89
m dc dc
q q gY hd
dc Lp Lp Dhd He Y
dc
He
P
Y
Lp
LB Lp+ dc
hd
dc
dc
dcTW dc
90
LGW
He
LB
TW He
eG
HgNWL Q m
Q m sW mN g m s
mm W
m He
m LG
USBR IVd d Q d Y Q
q
91
Fb dg
V
Fb m g m sV m s d m
Fb C V dFb mC V m s d m
m
Fb V dFb m V m sd m
m
m
HWL HWL
92
E N D
START
No
Yes
No
Yes
93
1) L L (3 5)H 2)
H
L
94
Westergaard
hbKP whew
hhew
Pew kNKh
w kN mh mb mhew m
hew
Pe wh
Westergaard V
·················································································· (3.4.33)
95
1) 2)
96
1) 2)
97
END
T
START
END
OK
NO
98
1) 2)
99
1) 2)
100
(N/mm2)
SD295 176 264
157 264
SD345 196 294
176 294
( ck 21N/mm2)
8 12
0.42 0.63
1.5 2.25
( ck 24N/mm2)
9 13.5
0.45 0.67
1.6 2.4
101
h m h m
h h
m m m
m
A
RHWLFWL
102
mmm m mm m
(mm) (mm)
200 150 230
200 300 200 250
300 400 230 300
400 300
cm
TT/2
T/2
T/2 T
T/2
103
(VP)
D13mm 16mm D16mm 20mm L 500mm
D16 19mm 19mm D19mm 25mm L 500mm
D22mm 25mm D25mm 30mm L 500mm
1) U.S.Bureau of Reclamation Design of Small Dams
D.R.Waldron Design of Labyrinth Weirs, MSc thesis, Utah State Univ.
D.S.Miller Discharge Characteristics, Balkena PublishersN.Hay,G.Taylor Performance and Design of Labyrinth Weirs, Jour. of HY,ASCE
T/2
T/2
T VP
500 m 500 m
104
105
106
HgCA Q
A mQ m sCg m sH m
Q Q C
C QQ
H
FWL
H
107
mm
mm
x x
x
a
b
D
x
mm
D
a
b
m s m smm
VA Q
A m Q m s V m s
108
0.15 0.20 m 0.60 m
H m
B m B
m
109
S USS US
mm
110
mmQp
Qp
111
Q e
AIRneQ
Q e m sn nR mIA m
rad
h D
R A h
cosDh
sinD
A
sinDR
h D A R
mm
h D m
A m
R m
R
112
m
H m
H m
m
m m
m
H
H
m m
H
H
113
aD
a
a D
D
m
114
F.W.L.
D
V P
mm mm
VP
D mm a m a m D mm a m a m
) mm
115
m
mm
IP
S
116
1m
m b
h
m
m
m
cm
117
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125
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iH i m
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148
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154
155
156
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157
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168
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173
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176
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180
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182
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183
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184
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186
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187
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188
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58
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189
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kN m OK
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190
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191
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P Fs H V fP Ph
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kN mkN m
192
mm
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mm
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Q
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193
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m
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mm
mm
195
Qmax
m s
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mm
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m
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196
3.272
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0.836
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197
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198
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205
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208
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210
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211
JIS A
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212
kg m
213
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cm
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m
215
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218
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223
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224
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227
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228
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l
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236
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239
p Frederick Lux Design and Application of Labyrinth Weirs, International Symposium on Design of Hydraulic Structures nd p
No
240
ts
241
242
mm
N mm
243
244
kN m
m
2
245
10m
m
m
Af Ar Ac
b
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A
246
247
248
249
250
251
252
, m
,
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253
Md
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dkm
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254
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km
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255
km
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256
N
Vol.9 No.3 443-455 URL https://www.jstage.jst.go.jp/article/jgs/9/3/9_443/_pdf
URL http://www.naro.affrc.go.jp/nkk/introduction/files/d_sendan.pdf
SBIFT 2009
URL http://www.web-gis.jp/e-Forum/2009/132.pdf
257
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