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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 WORKSHOPNagasaki University, August 28, 2013

Matthew Czapiga and Gary Parker Dept. of Civil & Environmental Engineering and Dept. of Geology

University of Illinois Urbana-Champaign, USA

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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

3Wampool River, UK

蛇行河川の内部接続性とはHow is internal connectivity defined for meandering rivers?

A

B

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

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蛇行河川の内部接続性とはHow is internal connectivity defined for meandering rivers?

A

B

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。

At a given flow, we look for the probability of a path between

two points for which the condition l < < is satisfied.

たとえば、 ＝流速、または水深

For example, = velocity or depth

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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

Abreu, Sullivan, Pirmez, Mohrig (2006)http://sepwww.stanford.edu/oldsep/david/Thai/cube.gif

吸い出せるかなCan I suck it out?

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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(HHmin, 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(HHmin, L) that a continuous path of length L exists satisfying H Hmin? 大丈夫

かな？

２０１２年、ミシシピ川流域の渇水Mississippi River basin, drought of 2012

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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 = 満杯状態における水面高water surface elevation at bankfull flow

Hbf = 満杯水深bankfull depth

Bbf = 満杯川幅bankfull width

Wabash River, USA

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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

= （あるときの）水面高　　ｂｆ

water surface elevation at a given time bf

Hmin = 航行するに必要とする最低水深（喫水）minimum depth required for navigation (draft)

L = 縦断方向の航行経路距離（任意）length of navigation path

Pc = 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

bfH

min

bf

H

H min

bf

L

B

c cP P ( , , ) We assume that と仮定する

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無次元パラメータの意味Meaning of Dimensionless Parameters

min

bf

H

H

bf

bfH

min

bf

L

B

　　喫水が増大する　 draft increases, Pc

　　水位が下がる　 stage decreases, Pc

　　航行距離が増大する　 navigation path lengthens, Pc

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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

TP ( , ) ,

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。In order for this condition to hold precisely, the bed shape must be invariant to stage.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 fill associated with the flow hydrograph is neglected.

FR82 Cross Sections

-14-12-10-8-6-4-20246

0 100 200 300 400 500Distance (m)

Elevation A

HD

(m

)

FR88 Cross Sections

-8

-6

-4

-2

0

2

4

6

0 50 100 150 200 250 300 350 400 450Distance (m)

Elevation A

HD

(m

)

FR90 Cross Sections

-8

-6

-4

-2

0

2

4

6

0 50 100 150 200 250 300 350 400Distance (m)

Elevation A

HD

(m

)

FR92 Cross Sections

-8

-6

-4

-2

0

2

4

6

0 100 200 300 400 500Distance (m)

Elevation A

HD

(m

)

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c cP P ( , )

b ~ 指数関数形exponential function?

d ~ 正規分布形Gaussian distribution?

0

0.2

0.4

0.6

0.8

1

Delta

Succ

ess

Rate

Beta

Pc

実河川の計算例Sample Calculation for a River

Trinity River USA data from V. Smith, D. Mohrig

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固定河床近似の適用例Example of Application of Frozen Bed Approximation

Path Width = 0.01*BBF

Vermillion River, Minnesota, USA

Estimated Connectivity Assuming = 0.6

= bf - 0.6 Hbf

「台地」 Pc=1

「山腹」

「盆地」 Pc

=0

Pc

Computed Bankfull Connectivity, = 0

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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

Previous WorkQw=6120 m3 s-1 Qw=34,300 m3 s-1

でもその近似はどうかな？ Is the Frozen-bed Approximation Realistic?

Mississippi RiverCour. J. Nittrouer

Q = 6120 m3/s Q = 34,300 m3/s

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Kinoshita Flume, Ven Te Chow Hydrosystems Laboratory

では、実験で試してみようOK, Let’s test it experimentally

C.S.# 10 C.S.# 20

河床材料　－クルミ殻粉Sediment - Walnut shellsD50=1.1mm

Flow:Q= 3 L/sH=3-4 cm

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「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/stEQ = 4 hrs

「流量を下げて５分後」5 minutes after lowering dischargeQ = 10 l/stEQ = 0.33 hrs

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Bankfull

Width = 0.01*BBF

Prob

abili

ty o

f Con

necti

vity

Pc

More connected here!

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

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Bankfull is Deeper

Low Flow is Deeper

Bedforms have migrated in some places

Ripple section shows more depth in QH,EQ->M

水深の残差Residual Difference in Depth

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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

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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 Qw=34,300 m3 s-1

Mississippi RiverCour. J. Nittrouer

Q = 6120 m3/s Q = 34,300 m3/s

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ご清聴ありがとうございますThank you for your attention

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ここから先は添削しなくても結構です！

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How do depth fluctuations compare from QH,Eq to QH,EqM?

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.50

1

2

QL,BF

( = 0.55)

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.50

1

2

QH,BF,1

( = 0.73)

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.50

1

2

QH,BF,2

( = 0.78)

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.50

1

2

QH,bBF

( = 0.75)

2̂

QH,EQ

QH,EQ->M

Normalized Width

Normalized Root Mean Square fluctuation magnitude

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. Bedforms occurring in the Kinoshita flume are more similar to bars than dunes. This is likely caused by the large sediment size used (D50 = 1 mm , S.G. =

1.3), which is very mobile, but too large to form dune features.

Overall trends in fluctuations are quite similar between these experiments; therefore, the increase in connectivity is related to the local reorganization of bed material which opens up more or larger

connective paths.

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Sca

lin

g

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

500 m

25 Km

解析の対象としている蛇行河川Meandering Rivers being Analyzed

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解析の対象としている蛇行河川Meandering Rivers being Analyzed

Vermillion River, USA

Trinity River Upstream, USA

Trinity River Downstream, USA

Wabash River, USA Mississippi River, USA

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面積高度曲線Hypsometric Curves

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Vermillion RiverTrinity River 1Trinity River 2Wabash River

H/Hbf

Perc

ent E

xcee

danc

e

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.

H/Hbf

超過確率