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蛇行河川の内部接続性に関する実験－
埋蔵されたチャンネルへの適用に向けて
EXPERIMENTAL STUDY OF CONNECTIVITY IN MEANDERING RIVERS:
IMPLICATIONS FOR STRATIGRAPHIC STRUCTURE OF BURIED CHANNELS
STRATODYNAMICS WORKSHOP
Nagasaki University, August 28, 2013
Matthew Czapiga and Gary Parker
Dept. of Civil & Environmental Engineering and Dept. of Geology
University of Illinois Urbana-Champaign, USA
1
実験を行ったのはMatthew Czapigaという、私の院生です。
My student Matt Czapiga performed the experiments
2
蛇行河川の内部接続性とは
How is internal connectivity defined for meandering rivers?
A
A点とB点を考える
Consider points A and B
そしてある属性を考える
And some attribute 
B
Wampool River, UK
3
蛇行河川の内部接続性とは
How is internal connectivity defined for meandering rivers?
たとえば、 ＝流速、または水深
For example,  = velocity or depth
A
ある水理条件において、２点をつ
なぐ、l <  < uという条件を満
たす、連続した経路が存在する
確立を求める。
B
At a given flow, we look for the
probability of a path between
two points for which the
condition l <  <  is satisfied.
4
層序学ー埋蔵されたチャンネルへ適用性
Stratigraphy - Applicability to buried channels
 ＝炭化水素の透性係数
 = hydraulic conductivity of hydrocarbon
吸い出せるかな
Can I suck it out?
http://sepwww.stanford.edu/oldsep/david/Thai/cube.gif
5
Abreu, Sullivan, Pirmez, Mohrig (2006)
事例として河川における、船の航行可能性を考える
As an example, we consider river navigability (traversability)
 = H = 水深 depth
船が座礁せずに航行するには水深がある最低値Hminを下回ってはいけない。ここ
に、H  Hminを満たす、距離Lの連続した経路の存在確率PT(HHmin, L)を求める。
A minimum depth Hmin is required in order for a ship to navigate without going
aground. What is the probability PT(HHmin, L) that a continuous path of length L
exists satisfying H  Hmin?
大丈夫
かな？
6
２０１２年、ミシシピ川流域の渇水
Mississippi River basin, drought of 2012
断面ではなくて区間平均の満杯水理幾何パラメータ
Hydraulic Geometry Parameters based on Reach Averaging rather than
Cross-section
bf
=
Hbf
=
Bbf
=
満杯状態における水面高
water surface elevation at bankfull flow
満杯水深
bankfull depth
満杯川幅
bankfull width
Wabash River, USA
8
満杯水理幾何のパラメータで無次元化する
Dimensionless Formulation using Parameters of Hydraulic Geometry

=
Hmin
=
L
=
Pc
=
（あるときの）水面高  ｂｆ
water surface elevation at a given time  bf
航行するに必要とする最低水深（喫水）
minimum depth required for navigation (draft)
縦断方向の航行経路距離（任意）
length of navigation path
L距離に渡って、連続した経路が存在する確立
Probability that H  Hmin over continuous path of length L
bf  

Hbf
We assume that
Hmin

Hbf
Pc  Pc (, ,)
Lmin

Bbf
と仮定する
9
無次元パラメータの意味
Meaning of Dimensionless Parameters
Hmin

Hbf
  喫水が増大する draft increases, Pc
bf  

Hbf
  水位が下がる
stage decreases, Pc
Lmin

Bbf
  航行距離が増大する
navigation path lengthens, Pc
10
固定河床近似
Frozen Bed Approximation
とをひとつのパラメータ =  + に組み込む
Roll  and  Into a Single Parameter  =  + 
喫水が増大することと水深が減少ことを同等であると考える
Assume that increased draft is equivalent to shallower flow
FR82 Cross Sections
Elevation AHD (m)
6
4
2
0
-2
-4
-6
-8
-10
-12
-14
PT (, ) ,     
0
100
6
200
300
Distance (m)
400
500
FR88 Cross Sections
Elevation AHD (m)
4
2
0
-2
-4
-6
-8
0
50
100
150
200
250
Distance (m)
300
350
400
450
Elevation AHD (m)
6
FR90 Cross Sections
この条件を正確に満たすには、川床形状は水位に対して不変でなければなない。
4
2
In order for this condition
to hold precisely, the bed shape must be invariant to
0
stage.
-2
-4
-6
従ってハイドログラフを伴う、局所洗掘と堆積を無視することになる。
So local scour and-8 0fill associated
hydrograph
is 350neglected.
50
100 with
150the flow
200
250
300
400
Distance (m)
11
実河川の計算例
Sample Calculation for a River
Pc  Pc (, )
1
0.8
data from V. Smith, D.
Mohrig
0.6
Success Rate
Trinity River USA
P0.4c
0.2

Delta
0.5
3.5
6.5
8
9.5
11
12.5
14
15.5
17
18.5
0.1 Hbf
0.4 Hbf
0.7 Hbf
1.0 Hbf
1.3 Hbf
1.6 Hbf
1.9 Hbf
20
5
2
0

Beta
 ~ 指数関数形
exponential function?
 ~ 正規分布形
Gaussian distribution?
12
固定河床近似の適用例
Example of Application of Frozen Bed Approximation
Vermillion River,
Minnesota, USA
Computed Bankfull
Connectivity,  = 0
Estimated Connectivity Assuming
 = 0.6
 = bf - 0.6 Hbf
「台地」
Pc=1
「山腹」
Pc
「盆地」
Pc=0

Path Width = 0.01*BBF

13
水位が下がると接続性が減少する
As stage falls, connectivity is reduced
Computed Bankfull
Connectivity,  = 0

Estimated Connectivity Assuming
 = 0.6

14
Previous
Work Approximation Realistic?
でもその近似はどうかな？
Is the Frozen-bed
Qw=6120 m3 s-1
Q = 6120 m3/s
Qw=34,300 m3 s-1
Q = 34,300 m3/s
Mississippi River
Cour. J. Nittrouer
では、実験で試してみよう
OK, Let’s test it experimentally
Kinoshita Flume, Ven Te Chow Hydrosystems Laboratory
16
河床材料－クルミ殻粉
Sediment - Walnut shells
D50=1.1mm
Flow:
Q= 3 L/s
H=3-4 cm
C.S.# 10
C.S.# 20
17
「満杯流量」における平衡状態に達してから流量を下げて間もな
く、局所再編成を調べる
After equilibrium is reached at “bankfull flow”, we lower the flow
and investigate bed reorganization shortly afterward
「満杯流量」
“Bankfull flow”
Q = 12.3 l/s
tEQ = 4 hrs
「流量を下げて５分後」
5 minutes after lowering discharge
Q = 10 l/s
tEQ = 0.33 hrs
18
クソッ! 流量を下げると接続性が増えた！
Aw Shit! Connectivity was higher at the lower flow!
Predicted low
flow, frozen-bed
Actual low flow,
frozen-bed



Probability of Connectivity Pc
Bankfull

Width = 0.01*BBF
More connected here!
19
水深の残差
Residual Difference in Depth
Bankfull is Deeper
Bedforms have migrated
in some places
Ripple section shows
more depth in QH,EQ->M
Low Flow is Deeper
20
流量が下がったのに、接続性が増えた原因は河床形態が再編成
し、波長も波高もさがったことにあるようである
Connectivity apparently increased at low flow due to reorganization
of bedforms: shorter wavelength and amplitude
「満杯流量」
“Bankfull flow”
「流量を下げて５分後」
Five minutes after lowering discharge
21
結論ー
実河川における、固定河床近似の妥当性を追及するには、
ハイドログラフのさまざまな時点での音波調査が必要である。
Conclusion:
In order to investigate the frozen-bed approximation in rivers,
sequential seismic bed surveys at different points of a hydrograph are
necessary.
Qw=6120 m3 s-1
Q = 6120 m3/s
Qw=34,300 m3 s-1
Q = 34,300 m3/s
Mississippi River
Cour. J. Nittrouer
22
ご清聴ありがとうございます
Thank you for your attention
23
ここから先は添削しなくても結構です！
24

How do depth fluctuations compare from QH,Eq to QH,EqM?
Root mean square fluctuations are normalized by the average channel depth within the reach. For
both cases, the fluctuations occur on the order of the average channel depth; this is significantly larger
than our accompanying analysis of river data.Q Bedforms
occurring in the Kinoshita flume are more
( = 0.55)
L,BF
2 similar to bars than dunes. This is likely caused by the large sediment size used (D 50 = 1 mm , S.G. =
1.3), which is very mobile, but too large to form dune features.
1
Overall trends
in fluctuations
are quite similar
between
these0.1experiments;
therefore,
the increase
in 0.5
-0.4
-0.3
-0.2
-0.1
0
0.2
0.3
0.4
connectivity is related to the local reorganization
bed material which opens up more or larger
Q
(of
= 0.73)
H,BF,1
2
connective paths.

0
-0.5
1
0
-0.5
Normalized Root Mean Square
-0.4
-0.3
-0.2
fluctuation
magnitude
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.1
0.2
0.3
0.4
0.5
0.1
0.2
0.3
0.4
0.5
Q ( = 0.78)
Q
H,BF,2H,EQ

2
1
0
-0.5
-0.4
-0.3
-0.2
-0.1
0
Q
2

Q
( = 0.75)
H,bBF
H,EQ->M
1
0
-0.5
-0.4
-0.3
-0.2
-0.1
0
^
2
Normalized
Width
25
解析の対象としている蛇行河川
Meandering Rivers being Analyzed
25 Km
Scaling
500 m
River Name
BBF (m)
HBF (m)
Mississippi River
~1200
30-50
Wabash River
290
5.5
Trinity River 1
120
5.10
Trinity River 2
190
5.25
Vermillion River
15
1
Kinoshita Flume
0.35
0 - .3
26
解析の対象としている蛇行河川
Meandering Rivers being Analyzed
Vermillion River, USA
Trinity River Downstream, USA
Trinity River Upstream, USA
Wabash River, USA
27
Mississippi River, USA
面積高度曲線
Hypsometric Curves
超過確率
1
Vermillion River
Trinity River 1
Trinity River 2
Wabash River
0.9
0.8
Percent Exceedance
0.7
尾根が流れ方向なのかそれと直角なのか
わからないから接続性の定量化に直接適
用できない。
Not directly adaptable to connectivity
because whether the high points extend
streamwise or lateral is not specified.
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.5
1
1.5
2
H/HH/Hbf
bf
2.5
3
3.5
4
4.5
28

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