CHAPTER 31: EROSIONAL NARROWING AND WIDENING OF A CHANNEL AFTER DAM REMOVAL

1

1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to

RIVERS AND TURBIDITY CURRENTS© Gary Parker November, 2004

CHAPTER 31:EROSIONAL NARROWING AND WIDENING OF A CHANNEL AFTER DAM

REMOVALThis chapter was written by Gary Parker, Alessandro Cantelli and Miguel Wong

View of a sediment control dam on the Amahata River, Japan. Image courtesy H. Ikeda.

2



CONSIDER THE CASE OF THE SUDDEN REMOVAL, BY DESIGN OR ACCIDENT, OF A DAM FILLED WITH SEDIMENT

Before removal

3



REMOVAL OF THE DAM CAUSES A CHANNEL TO INCISE INTO THE DEPOSIT

After removal

4



AS THE CHANNEL INCISES, IT ALSO REMOVES SIDEWALL MATERIAL

sidewall sediment eroded as channel incises

top of reservoir deposit

A first treatment of the morphodynamics of this process was given in Chapter 15.

5



EXNER EQUATION OF SEDIMENT CONTINUITY WITH SIDEWALL EROSIONThe formulation of Chapter 15 is reviewed here.

Bb = channel bottom width, here assumed constantb = bed elevationt = elevation of top of bankQb = volume bedload transport rateSs = sidewall slope (constant)p = porosity of the bed deposits = streamwise distancet = timeBs = width of sidewall zones = volume rate of input per unit length of sediment from sidewalls

ss

bt SB

sbb

b sQ

tB

tS2

tB2 b

s

btbss

Ss

Bb


ttb

Bs

t

b

s > 0 for a degrading channel, i.e. b/t < 0

6



EXNER EQUATION OF SEDIMENT CONTINUITY INCLUDING SIDEWALL EROSION contd.

sQ

tS2B bb

s

btb

Ss

Bb


ttb

Bs

t

b

In Chapter 15, the relations of the previous slide were reduced to obtain the relation:

or

sQ

S2B

1t

b

s

btb

b

That is, when sidewall erosion accompanies degradation, the sidewall erosion suppresses (but does not stop) degradation and augments the downstream rate of increase of bed material load.

7



ADAPTATION TO THE PROBLEM OF CHANNEL INCISION SUBSEQUENT TO DAM REMOVAL: THE DREAM MODELS

1200 ft

Dam

Saeltzer Dam, California before its removal in 2001.

Cui et al. (in press-a, in press-b) have adapted the formulation of the previous two slides to describe the morphodynamics of dam removal. These are embodied in the DREAM numerical models. These models have been used to simulate the morphodynamics subsequent to the removal of Saeltzer Dam, shown below.

8



THE DREAM MODELS

sQ

S2B

1t

b

s

btbm

b

Specify an initial top width Bbt and a minimum bottom width Bbm.

If Bb > Bbm, the channel degrades and narrows without eroding its banks.

If Bb = Bbm the channel degrades and erodes its sidewalls without further narrowing.

)(S2BBs

QB1

t

btsbtb

b

b

b

But Bbm must be user-specified.

Ss

Bb > Bbm

Bbt

Ss

Bb = Bbm


9



SUMMARY OF THE DREAM FORMULATION

Ss

increasing time

no narrowing and sidewall erosion when Bb = Bbm

trajectories of left and right bottom

bank position

top of depositnarrowing without sidewall erosion when Bb > Bbm

But how does the process really work? Some results from the experiments of Cantelli et al. (2004) follow.

10



EROSION PROCESS VIEWED FROM DOWNSTREAM

rte-bookdamremfrontview.mpg: to run without relinking, download to same folder as PowerPoint presentations.

Double-click on the image to see the video clip.

11



NOTE THE TRANSIENT PHENOMENON OFEROSIONAL NARROWING

12



EROSION PROCESS VIEWED FROM ABOVE Double-click on the image to see the video clip.

rte-bookdamremtopview.mpg: to run without relinking, download to same folder as PowerPoint presentations.

13



EVOLUTION OF CENTERLINE PROFILEUPSTREAM (x < 9 m) AND DOWNSTREAM (x > 9 m) OF THE DAM

Upstream degradation Downstream aggradation

Former dam location

14



CHANNEL WIDTH EVOLUTION UPSTREAM OF THE DAMThe dam is at x = 9 m downstream of sediment feed point.

Note the pattern of rapid channel narrowing and degradation, followed by slow channel widening and degradation. The pattern is strongest near the dam.

15



-6

-5

-4

-3

-2

-1

0

20 21 22 23 24 25

Water Surface Width (cm)

Wat

er S

urfa

ce E

leva

tion

(cm

)

Progress in time

Subsequent 16.0 minutes of run: period of erosional widening

First 4.3 minutes of run: period of erosional narrowing

REGIMES OF EROSIONAL NARROWING AND EROSIONAL WIDENING

The dam is at x = 9 m downstream of sediment feed point.

The cross-section is at x = 8.2 m downstream of the sediment feed point, or 0.8 m upstream of the dam.

16



SUMMARY OF THE PROCESS OF INCISION INTO A RESERVOIR DEPOSIT

rapid incision with

narrowing

Ss


bank position top of deposit

slow incision with

widening

incisional narrowing suppresses sidewall

erosion

incisional widening enhances sidewall

erosion

17



CAN WE DESCRIBE THE MORPHODYNAMICS OF RAPID EROSIONAL NARROWING, FOLLOWED BY SLOW EROSIONAL WIDENING?

18



The earthflow is caused by the dumping of large amounts of waste rock from the Porgera Gold Mine, Papua New Guinea.

PART OF THE ANSWER COMES FROM ANOTHER SEEMINGLY UNRELATED SOURCE: AN EARTHFLOW IN PAPUA NEW GUINEA

19



THE EARTHFLOW CONSTRICTS THE KAIYA RIVER AGAINST A VALLEY WALL

Kaiya River

earthflow

The Kaiya River must somehow “eat” all the sediment delivered to it by the earthflow.

20



THE DELTA OF THE UPSTREAM KAIYA RIVER IS DAMMED BY THE EARTHFLOW

earthflow

The delta captures all of the load from upstream, so downstream the Kaiya River eats only earthflow sediment

21



THE EARTHFLOW ELONGATES ALONG THE KAIYA RIVER, SO MAXIMIZING “DIGESTION” OF ITS SEDIMENT

A downstream constriction (temporarily?) limits the propagation of the earthflow.

22



THE VIEW FROM THE AIRKaiya River

The earthflow encroaches on the river, reducing width, increasing bed shear stress and increasing the ability of the river to eat sediment!

23



THE BASIS FOR THE SEDIMENT DIGESTER MODEL(Parker, 2004)

• The earthflow narrows the channel, so increasing the sidewall shear stress and the ability of the river flow to erode away the delivered material.• The earthflow elongates parallel to the channel until it is of sufficient length to be “digested” completely by the river.

This is a case of depositional narrowing!!!

River

Earthflow Sediment taken sideways into stream

Upstream dam created by earthflow

24



GEOMETRY

H = flow depthn = transverse coordinatenb = Bb = position of bank toeBw = width of wetted banknw = Bb + Bw = position of top

of wetted bankSs = slope of sidewall (const.)b = elevation of bed = volume sediment input per unit streamwise width from earthflow

• The river flow is into the page.• The channel cross-section is assumed to be trapezoidal.• H/Bb << 1.• Streamwise shear stress on the bed region = bsb = constant in n• Streamwise shear stress on the submerged bank region = bss = bsb = constant

in n, < 1.• The flow is approximated using the normal flow assumption.

sw SBH

Ss

inerodible valley wall

b

b+H

Hn

nb

Bb Bw

river

earthflownw

neq̂

neq̂

25



EXNER EQUATION OF SEDIMENT BALANCE ON THE BED REGIONLocal form of Exner:

where qbs and qbn are the streamwise and transverse volume bedload transport rates per unit width.

Integrate on bed region with qbs = qbss, qbn = 0;

nq

sq

t)1( bnbs

p

bbb n

0bn

n

0bs

n

0p dnn

qdns

qdnt

)1(

Ss


b

b+H

Hn

nb

Bb Bw

river

earthflownw

neq̂

bnbnbnsb

bnsbsbbp qq̂,

Bq̂

sq

t)1(

/t(sediment in bed region)

differential steamwise transport

transverse input from wetted bank region

26



EXNER EQUATION OF SEDIMENT BALANCE ON WETTED BANK REGION

Integrate local form of Exner on wetted bank region with region with:qbs = qbss for nb < n < nb + Bw

qbn = - at n = nt where q denotes the volume rate of supply of sedimentper unit length from the earthflow

Geometric relation:

Result:

w

n

w

b

w

b

n

nbn

n

nbs

n

np dnn

qdns

qdnt

)1(

bebnsb

bssbsss

bs

bwp q̂q̂

sBqHq

sS1

tBS

tB)1(

tBS

tt)Bn(S b

sb

bsb

Ss


b

b+H

Hn

nb

Bb Bw

river

earthflownw

neq̂

neq̂

/t(sediment in wetted bank region)

differential steamwise transport

transverse output to bed region

transverse input from earthflow

27



EQUATION FOR EVOLUTION OF BOTTOM WIDTH

Eliminate b/t between

Note that there are two evolution equations for two quantities, channel bottom elevation b and channel bottom width Bb. To close the relations we need to have forms for qbsb, qbss and . The parameter is specified by the motionof the earthflow.

bnsq̂

b

bnsbsbbp B

q̂s

qt

)1(

and

to obtain

bewbw

bwbns

b

w

bss

ws

bssbss

ws

bsbbsp q̂

B1

BBBBq̂

sB

Bq

sH

BSq

sq

BSH

sq

tBS)1(

bebnsb

bssbsss

bs

bwp q̂q̂

sBqHq

sS1

tBS

tB)1(

neq̂

Ss


b

b+H

Hn

nb

Bb Bw

river

earthflownw

neq̂

28



FLOW HYDRAULICSFlow momentum balance: where S = streamwise slope and Bw = H/Ss,

Flow mass balance

Manning-Strickler resistance relation

bsbb

bs

2ss

bbb BH

S21BgHSB

BH

SS1S

1B

bsbw B

HS211UHBQ

Dnk,kHC,UC ks

6/1

sr

2/1f

2fb

Here ks = roughness height, D = grain size, nk = o(1) constant. Reduce under the condition H/Bs << 1 to get:

10/3

2b

2r

2w

3/1s

SgBQkH

Ss


b

b+H

Hn

nb

Bb Bw

river

earthflownw

neq̂

29



BEDLOAD TRANSPORT CLOSURE RELATIONSShields number on bed region:

where R = (s/ - 1) 1.65. Shields number on bank region:

Streamwise volume bedload transport rate per unit width on bed and bank regions is qbsb and qbss, respectively: where s = 11.2 and c* denotes a critical Shields stress,

10/7

10/3

2b

2r

2w

3/1sbb

bb SgBQk

D1

RgD

R

10/710/3

2b

2r

2w

3/1s

bbbs

bs SgBQk

DRgD

R

5.4

bb

c5.1bbsbss

5.4

bb

c5.1bbsbsb 1DRgDq,1DRgDq

(Parker, 1979 fit to relation of Einstein, 1950). Transverse volume bedload transport rate per unit width on the sidewall region is qbns, where n is an order-one constant and from Parker and Andrews (1986),

sbb

cn

5.4

bb

c5.1bbss

bb

cnbssBbnbns S1DRgDSqqq̂

b

Ss


b

b+H

Hn

nb

Bb Bw

river

earthflownw

neq̂

30



SUMMARY OF THE SEDIMENT DIGESTER

10/710/3

2b

2r

2w

3/1s

bb SgBQk

D1

R bbbs

5.4

bb

c5.1bbsbss

5.4

bb

c5.1bbsbsb

1DRgDq

1DRgDq

sbb

cn

5.4

bb

c5.1bbsbns S1DRgDq̂

b

bnsbsbbp B

q̂s

qt

)1(

10/3

2b

2r

2w

3/1s

SgBQkH

Equation for evolution of bed elevation

Equation for evolution of bottom width

bewbw

bwbns

b

w

bss

ws

bssbss

ws

bsbbsp q̂

B1

BBBBq̂

sB

Bq

sH

BSq

sq

BSH

sq

tBS)1(

Hydraulic relations

Sediment transport relations As the channel narrows the Shields number increases

Higher local streamwise and transverse sediment transport rates counteract channel narrowing

A higher Shields number gives higher local streamwise and transverse sediment transport rates.

The earthflow encroaches on the channel

31



EQUILIBRIUM CHANNELEquilibrium channels that transport bedload without eroding their banks can be created in the laboratory (Parker, 1979). The image below shows such a channel (after the water has been turned off). The image is from experiments conducted by J. Pitlick and J. Marr at St. Anthony Falls Laboratoty, University of Minnesota.

32



EQUILIBRIUM CHANNEL SOLUTION

As long as < 1, the formulation allows for an equilibrium channel without widening or narrowing as a special case (without input from an earthflow).

cbbbsbb

c Choose bed shear stress so that bank shear stress = critical value

01DRgDq5.4

bb

c5.1bbsbss

Streamwise sediment transport on wetted bank

region = 0

0S1DRgDq̂ sbb

cn

5.4

bb

c5.1bbsbns

Transverse sediment transport on

wetted bank region = 0

b5.4

5.1

csb B1DRgDQ

Total bedload transport rate

10/710/3

2b

2r

2w

3/1sbsbc

bb SgBQk

D1

RgD

R

10/3

2b

2r

2w

3/1s

SgBQkH

Three equations; if any two of Qw, S, H, Qb and Bb are specified, the other three can be computed!!

33



ADAPTATION OF THE SEDIMENT DIGESTER FOR EROSIONAL NARROWING

• As the channel incises, it leaves exposed sidewalls below a top surface t.• Sidewall sediment is eroded freely into the channel, without the

external forcing of the sediment digester.• Bb now denotes channel bottom half-width• Bs denotes the sidewall width of one side from channel bottom to top

surface.• The channel is assumed to be symmetric, as illustrated below.

nt

Bb t

b

Ss

Hn

nb

Bs

river

ss

bt SB

34



INTEGRAL SEDIMENT BALANCE FOR THE BED AND SIDEWALL REGIONS

On the bed region, integrate Exner from n = 0 to n = nb = Bb to get

On the sidewall region, integrate Exner from n = nb to n = nt under the conditions that streamwise sediment transport vanishes over any region not covered with water, and transverse sediment transport vanishes at n = nt

nt

Bb t

b

Ss

Hn

nb

Bs

river

ss

bt SB

b

bnsbsbbp B

q̂s

qt

)1(

35



INTEGRATION FOR SIDEWALL REGION

Upon integration it is found that

or reducing with sediment balance for the bed region,

nt

Bb t

b

Ss

Hn

nb

Bs

river

ss

bt SB

bnsb

bssbsss

bs

bsp q̂

sBqHq

sS1

tBS

tB)1(

bs

bsbns

b

s

bss

ss

bssbss

ss

bsbbsp BB

BBq̂s

BBq

sH

BSq

sq

BSH

sq

tBS)1(

36



INTEGRAL SEDIMENT BALANCE: SIDEWALL REGION

For the minute neglect the indicated terms:

The equation can then be rewritten in the form:

As the channel degrades i.e. b/t < 0, sidewall material is delivered to the channel.

Erosional narrowing, i.e. Bb/t < 0 suppresses the delivery of sidewallmaterial to the channel.

bnsb

bssbsss

bs

bsp q̂

sBqHq

sS1

tBS

tB)1(

t

BSt

B)1(q̂ bs

bspbns

37



INTEGRAL SEDIMENT BALANCE: SIDEWALL REGION contd.

rapid incision with narrowing

Ss


bank position top of deposit

slow incision with

widening

incisional narrowing suppresses sidewall

erosion

incisional widening enhances sidewall

erosion

t

BSt

B)1(q̂ bs

bspbns

38



INTERPRETATION OF TERMS IN RELATION FOR EVOLUTION OF HALF-WIDTH

bs

bsbns

b

s

bss

ss

bssbss

ss

bsbbsp BB

BBq̂s

BBq

sH

BSq

sq

BSH

sq

tBS)1(

This term always causes widening whenever it is

nonzero.

Auxiliary streamwise termsThis term causes narrowing whenever sediment transport is increasing in the streamwise direction.

But this is exactly what we expect immediately upstream of a dam just after removal: downward concave long profile!

39



REDUCTION FOR CRITICAL CONDITION FOR INCEPTION OF EROSIONAL NARROWING

bs

bsbns

b

b

bsbB

bsbS

bsp BB

BBq̂s

BBqN

sS

SqN

tBS)1(

Narrows if slope increases downstream

WidensEither way

Where NS and NB are order-one parameters,

At point of width minimum Bb/s = 0

40



REDUCTION FOR CRITICAL CONDITION FOR INCEPTION OF EROSIONAL NARROWING contd.

bs

bsbns

b

b

bsbB

bsbS

bsp BB

BBq̂s

BBqN

sS

SqN

tBS)1(

Where Ns and Nb are order-one parameters,

After some reduction,

where M is another order-one parameter.

That is, erosional narrowing can be expected if the long profile of the river is sufficiently downward concave, precisely the condition to be expected immediately after dam removal!

sbb

c

s

sbb SB

BBMsS

SB

41



NUMERICAL MODELING OF THE MORPHODYNAMICS OF EROSIONAL NARROWING AND WIDENING

Wong et al. (2004) used the formulation given in this chapter to numerically model one of the experiments of Cantelli et al. (2004). The code will eventually be made available in this e-book. Meanwhile, some numerical results are given in the next two slides. The reasonable agreement was obtained with a minimum of parameter fitting.

42



0.27

0.29

0.31

0.33

0.35

0.37

0.39

0.41

2.20 3.20 4.20 5.20 6.20 7.20 8.20

Distance in the downstream direction (m)

Wat

er s

urfa

ce e

leva

tion

(m)

initial profilecalcmeas

COMPARISON OF NUMERICAL MODEL WITH EXP. 5 OF CANTELLI et al. (2004): EVOLUTION OF LONG PROFILE

Calculated and measured long profile 1200 seconds after commencement of experiment.

43



0.15

0.17

0.19

0.21

0.23

0.25

0.27

0.29

0 200 400 600 800 1000 1200

Time (seconds)

Cha

nnel

wid

th a

t wat

er s

urfa

ce e

leva

tion

(m)

calcmeas

COMPARISON OF NUMERICAL MODEL WITH EXP. 5 OF CANTELLI et al. (2004): EVOLUTION OF CHANNEL WIDTH

Calculated and measured water surface width 0.9 m upstream of original position of dam.

44



REFERENCES FOR CHAPTER 31Cantelli, C. Paola and G. Parker, 2004, Experiments on upstream-migrating erosional narrowing

and widening of an incisional channel caused by dam removal, Water Resources Research, 40(3), doi:10.1029/2003WR002940.

Cui, ,Y., Parker, G., Braudrick, C., Dietrich, W. E. and Cluer, B., in press-a, Dam Removal Express Assessment Models (DREAM). Part 1: Model development and validation, Journal of Hydraulic Research, preprint downloadable at: http://cee.uiuc.edu/people/parkerg/preprints.htm .

Cui, Y., Braudrick, C., Dietrich, W.E., Cluer, B., and Parker, G, in press-b, Dam Removal Express Assessment Models (DREAM). Part 2: Sample runs/sensitivity tests, Journal of Hydraulic Research, preprint downloadable at: http://cee.uiuc.edu/people/parkerg/preprints.htm .

Einstein, H. A., 1950, The Bed-load Function for Sediment Transportation in Open Channel Flows, Technical Bulletin 1026, U.S. Dept. of the Army, Soil Conservation Service.

Parker, G., 1979, Hydraulic geometry of active gravel rivers, Journal of Hydraulic Engineering, 105(9), 1185‑1201.Parker, G., 2004, The sediment digester, Internal Memorandum 117, St. Anthony Falls

Laboratory, University of Minnesota, 17 p, downloadable at: http://cee.uiuc.edu/people/parkerg/reports.htm .

Wong, M., Cantelli, A., Paola, C. and Parker, G., 2004, Erosional narrowing after dam removal: theory and numerical model, Proceedings, ASCE World Water and Environmental Resources 2004 Congress, Salt Lake City, June 27-July 1, 10 p., reprint available at: http://cee.uiuc.edu/people/parkerg/conference_reprints.htm .


RIVERS AND TURBIDITY CURRENTS

http://cee.uiuc.edu/people/parkerg/preprints.htm

http://cee.uiuc.edu/people/parkerg/preprints.htm

http://cee.uiuc.edu/people/parkerg/reports.htm

http://cee.uiuc.edu/people/parkerg/conference_reprints.htm

Documents

CHAPTER 31: EROSIONAL NARROWING AND WIDENING OF A CHANNEL AFTER DAM REMOVAL