Nov 4, 2014

2014 International Workshop on

Typhoon and Flood

River Embankment Failure due to Overtopping

- In Case of Non-cohesive Sediment -

Prof. Hajime NAKAGAWA

Prof. of Disaster Prevention Research Institute,

Kyoto University, Japan

Contents

１. About river embankment failure

２. An example of recent flood disasters

due to river embankment breach

3. Flood risk in Japan

4. Research on bank breach due to overtopping

5. Conclusions

3

1. About river embankment failure

Characteristics of river EMB

Principally made of sediments from the several viewpoints (economic,

easy to get the material, easy to repair, easy to stick to foundation

ground, easy to modify, good for environment, etc.）

Cause of river EMB failure

Phenomenon Cause of REB failure Form of failure

Overtopping ・Abnormal flood

・Water level rise due to

bridge pier, weir, etc.

・Short of river EMB height

Erosion at the top

and toe of the

slope

Sliding ・Seepage of rainwater into

river EMB body

・Seepage of river water due

to water level rise

Slope siding

Erosion ・Water collide portion

・Steep slope river

Erosion at the toe

of front and back

side slope

Leakage of

water

・Insufficient protection of

river EMB against seepage

・Existence of water channel

in the river EMB body

Piping failure

boiling

http://www.zina-studio.com/p489212137/

h1834C228#h1834c228

Illustration by Zina Deretsky/National Science

Foundation

Damaged form overtopping not

overtopping

total

Breach 183 62 245

Partial collapsed

(riverside)

26 184 210

Partially collapsed

(residential side)

19 37 56

Not damaged 78 0 78

total 306 283 589

Classification of failure form of REB

(Muramoto,1986)

(75%) (25%)

6

2. An example of recent flood disasters due to river embankment breach

EMB breach at the Maruyama River in 2004

Breach at Tachino, Maruyama River

River Bank Breach

Torii Bridge

11

8

3. Flood risk in Japan (Related to river EMB)

Cities are locating on low-lying area in Japan

Low lying

areas are

Protected

by REB

Landuse in Japan

Population Property

Low lying area

River & lakes

Out of low lying area

Forest

In Japan, 50% of population and 75% of property exist in the flood prone area

that is 10% of the Japan territory. Therefore, once big flood and bank breach

happen, damage becomes very severe. Low lying areas

are Protected by

REB

Teritory

(380,000km2)

Holland

(storm surge)

UK

(Thames R.)

USA

(Mississippi R. )

France

(Seine R. )

Japan

1/100

1/Return Period

1/500

1/1,000

1/10,000

Completed in 1985

Completed 89% in 2002

Completed in 1983

Completed in 1988

Completed 60%

in 2006

1/30-1/40 years (Big rivers)

1/5 – 1/10 (Small rivers)

(Current target)

Delay of river improvement works

No./

ye

ar

No./

year

1977 ~ 2004(year)

1977 ~ 2004(year)

1976 ~ 2004(year)

1987 ~ 1996 1997 ~ 2006

1987 ~ 1996

1997 ~ 2006

6. Extraordinary heavy rainfall

14

230

186

110

157

103

188

251

190

295

156

112

256

132159

95

178

331

275245

207

174182

360

196

243

194

254

169

209

275

0

50

100

150

200

250

300

350

400

57 58 59 60 61 62 63 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

1982-1991

187 events

16

10

5

8 9

15

29

15

11 12

6

11

6

10 10 10

28

31

10

22

11

16

24

8

23

14

18

12

16

21

0

5

10

15

20

25

30

35

57 58 59 60 61 62 63 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

2002-2011

16.3 events 1982-1991

13 events

1992-2001

14.4 events

1.2 times

1.3 times

Precipitation in one hour > 50mm (1,000 observatories)

Global warming effect, vulnerability of the society, rainfall prediction, runoff process, etc.

1992-2001

199 events

2002-2011

226 events

Precipitation in one hour > 80mm (1,000 observatories)

In such an environment and situation, basic

research on the mechanism of river embankment

and its countermeasures are essential.

Necessity of Research on River

Embankments

13

4. Research on bank breach due to overtopping 4.1 Objectives

Objectives

The main objective of this research is to develop a new

numerical model that can compute the river EMB erosion

process in accordance with the infiltration calculation at the

EMB surface.

River EMB Research：Approach from the

Hydroscience and Hydraulic Engg.

River EMB of the Jamuna River,

Bangladesh

This study focuses on

• erosion due to overtopping flow

• non-cohesive homogeneous

sediments

15

Embankment

dam body Seepage

Overtopping flow

Erosion

Water level raising

*Unsaturated soil

*steep slope

Deposition Slope failure

Embankment

dam body

The process of embankment breach by overtopping is very complex because it

involves mutually dependent interactions between fluvial hydraulics, sediment

transport and embankment stability.

16 Fig. Scheme of Unsaturated Soils

Bulk water

Meniscus water

r1

r2 ua

uw

T

Meniscus water

F F

Particle Particle

Surface tension and interface curvature give rise to a difference

between pore-water pressure (uw) and pore-air pressure (ua) that is

generally equated to matric suction (=ua – uw).

The internal stress is induced by the capillary tension of meniscus

water clinging to the contact point of soil particles and acts so as to

connect the soil particles tightly.

In some circumstances, the water in the soil will form menisci

between particles.

12

11

rrTuu wa

• Suction：ua-uw

au ： pore-air pressure

wu ： pore-water pressure

21, rr ： radius of curvature of meniscus

T ： surface tension of meniscus water

Unsaturated Soils

Resistance shear stress due to suction is …

Moisture characteristic curve

Suction

Appare

nt

sh

ear

str

ength

mH

2O

No.8(d=0.1mm)

No.7(d=0.174mm)

No.6(d=0.334mm)

Suction

W

ate

r conte

nt

In the unsaturated condition,

sediment of smaller sized

diameter is more difficult to be

eroded due to suction.

No.8(d=0.1mm)

No.7(d=0.174mm)

No.6(d=0.334mm)

Critical shear velocity of the

sediment particles（u*c ）

Density of sediment particle: 2.65

Kinematic viscosity of water: 0.01cm2/s

Sediment diameter : d（cm）

Iwagaki

Formula (cm/s)2

Shear stress is almost proportional to sediment diameter.

In the saturated condition, smaller the sediment diameter,

easier to move resulting in more erodible.

19

4.2 Numerical Model of

Embankment Failure

20

1. Seepage flow model • Richards’ equation

• van Genuchten equation(1980)

2. Flow model • Depth-averaged shallow water flow

equations (momentum and continuity

equations)

3. Erosion and Deposition Using framework of Non-Equilibrium

sediment transport model:

• pick-up rate equation (Erosion rate)

considering the effect of shear strength due to suction

• sediment movement is calculated using

motion of equation

• sediment deposition (probability density

function )

4. Slope failure Slope stability analysis:

• Simplified Janbu’s Method considering

the effect of shear strength due to suction

2-D (vertical slice)

2-D (vertical slice)

Horizontal 2-D

Numerical Model of Embankment Failure

21

Seepage analysis model (1/2)

tC

zK

zxK

xzx

1

Richards’ equation

: water pressure head,

zx KK , : hydraulic conductivity in the x and y directions,

C : specific moisture capacity, wC

w : volumetric water content of the soil

※continuity equation in the unsaturated EMB

Seepage analysis in the EMB

22

Flow model Depth averaged model

: depth averaged flow velocities

xyyyxx ,, : Reynolds stresses

vu,

g Gravitational acceleration H : water level

bybx , : bottom shear stresses

: density of water

Momentum equations

)()(

xyxxbx

yxhx

Hg

y

uv

x

uu

t

u

)()(

yyxyby

yxhy

Hg

y

vv

x

vu

t

v

x

v

y

u

y

v

x

u xyyyxx

,2,2

6*hu

31222 hvuugnbx

31222 hvuvgnby

0)()(

y

vh

x

uh

t

h

Continuity equation

h : flow depth

n : Manning’s roughness coefficient

Overtopping flow analysis

pm

succp

s

kGF

g

dp

*

0 11

sL

sL

k

kG

1

cos

s

sL

sL

bbs k

k

1

cos

cossincos*

Pick-up rate model（Nakagawa・Tsujimoto, 1985）+ introduction of effect of suction

c* : non-dimensional critical shear stress

,*G

: coefficients of pick up rate and non-dimensional critical shear stress considering the local slope and flow direction

sp ：pick-up rate

：non-dimensional shear stress

：specific weight of sediment particle (=2.65) ：angle with near bed flow direction and

direction of sediment particle motion

：angle with direction of sediment particle motion and max. slope of bed

: experimental coefficients

pS ：mesh area projected on the horizontal plane

rE ：erosion rate

6,4 32 AA

：ratio of drag force to lift force (=0.85) Lk

：friction coefficient of sediment(=0.7) s

pp mkF ,,0

: shape coefficients of sediment particle

32 , AA

suc* : increse of non-dimensional critical shear stress due to suction

In saturated condition,

0.0* suc

Effect of suction is considered as a increase of non-dimensional critical shear stress

psp SpA

dAV

2

3

pV ：sediment volume picked up in a unit time

pp

p

rS

VE

1

：porosity p

24

2

2

2

2dAuCR bDT

2

2

3

3 dAgfdAF suc

FRT

gdCCgd

u

D

suc

D

b

1

2tan

3

4

1

2

m

b

d

ad

u

u 2.30log75.5 10

*

210

2

10

2

**

19log75.51

2

19log75.5

1

3

4

1

mD

suc

mD

cc

ddgdC

ddCgd

u

210

*19log75.51

2

gdCD

sucsuc

ddm

succc ***

tantan

rs

r

rs

rwasuc guu

• Drag force • Friction force

Log low

63.0a

4.0,0.1tan DC cuu **

63 A

42 A

Shear strength due to suction, Vanapalli et al. (1996)

wa uu : matric suction

wa uu , : pore-air and pore-water pressure

: Water pressure head of surface mesh

w : moisture content : internal frictional angle

In order to take into account the role of shear strength due to suction, we consider

critical condition for sediment movement. (Egiazaroff, 1965) tanf

In the critical shear stress condition,

bu

By addition of the shear strength to friction force, Egiazaroff formula can be express by

following equation.

For a uniform sediment,

d : diameter of sediment

: flow velocity affects the sediment

25

Sediment transport analysis

（transportation and deposition)

2,1,,,

,3

3

jkjkjkj

kjsed

km FWDtd

uddAC

Motion of equation of sediment particle

Sediment transport process after detachment is calculated by the

following motion of equation,

※direction

：drag force kjD ,

：weight in the water kjW ,

：friction force kjF ,

：additional mass ksedm

3

3 kmksed dACm

：additional mass coefficient mC

：ratio of sediment particle

density to that of water (＝

2.65)

63 A

：velocity of sediment ksedu

tEDif rss

tEDif rss

Unsaturated soil

Saturated layer

Flow

26

infiltration rate:

Depth of saturated layer in one-step erosion

: Hydraulic conductivity in z

direction

: water pressure head

Erosion process of embankment surface

Erosion rate:

Unsaturated soil

Saturated layer

Flow

Unsaturated soil

Saturated layer

Flow

sD

stt

tUD ss :

zs KU zK

rE

tst

ut

tEtE rsr

urusr tEDtE

rsss EDt

0 usu tttt

Erosion within Saturated layer

27

Safety

factor

Slope stability analysis Flow

W

Δx

Ei

Ei+1

Xi Xi+1

Slip

surface

a

b

Ti Ni

As a slip surface calculation, simple

Junbu method is adopted.

n

i

ii

n

i

i

rs

rwiaiiiwii

s

W

luuluNlc

F

1

1

sin

tantan

sii

iirsrwiaiiw

s

i

iF

luuucF

W

N

tantan1cos

sintantan1

Safety factor considering the

effect of suction is

Modeling of local sliding

Dynamic programming method is used for the calculation of slip surface with minimum

safety factor

28

4.3 Numerical simulation for experiments (comparisons with experimental results)

500cm

Pump

Water supply 50cm

Drop

Water tank

Fixed bed

Video Camera

Experimental flume

Ujigawa Open Laboratory, DPRI, Kyoto Univ.

Experiments on river EMB erosion by over topping

EMB

Channel width = 30cm

Embankment Shape

30

Flow

Fixed bed

15cm

15cm

30cm 30cm 30cm 20cm 10cm 10cm

Dam body

Erodible bed

Flat bed (bottom of the flume)

Flow

40cm

80cm 35cm

Dam body

Flat bed (bottom of the flume)

Fig. – Side view of embankment shape

80cm

Type-B

Type-A

Fixed bed

31

Case Dam Type

Discharge (cm3/sec)

Sediment type

Initial water

content (%)

Porosity of dam body

1

A 7840

Sediment-No.6

13.0 0.51

2 Sediment

-No.7 11.5 0.51

3 Sediment

-No.8 12.0 0.55

4 B

1172 Sediment-No.7

6.79 0.55 5 -

Table – Experimental cases (Non cohesive sediment)

Experimental Conditions for Type-A, B

Parameters Sediment-

No.6 Sediment-

No.7 Sediment-

No.8

Ks(m/s) 2.15*10-4 8.75*10-5 1.56*10-5

dm(mm) 0.334 0.174 0.100

d50(mm) 0.285 0.146 0.078

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

100.0

10.00 100.00 1000.00

Per

cen

t fi

ner

by w

eigh

t, %

Diameter (μm)

Sediment-8

Sediment-7

Sediment-6

Grain-side distribution of EMB

No.6

No.7 No.8

Each sediment size (Type-A,B)

32

Simulated Results

(Sediment-No.7)

80s

60s

40s 20s

Failure of River embankment due to overtopping

Simulated failure process of embankment due to

overtopping with volumetric water content variation

Experimental results

(Video data)

Comparisons between simulated and

experimental results of failure process

(Sediment-No.7)

33

Simulated Results

(Sediment-No.7)

(Sediment-No.6)

(Sediment-No.8)

dm=0.334mm

dm=0.174mm

dm=0.100mm

80s

60s

40s

20s

40s 20s

10s 30s

80s

60s

40s 20s 100s

Embankment shape (Dam type-A)

Simulated and

experimental results of

embankment shape

Simulated Results

Embankment shape

(Sediment-No.8)

7.1* c※Trial calculation 60s

40s 20s

100s

dm=0.100mm

Shields Diagram

Simulated and experimental results of

embankment shape (Dam type-A)

Comparisons of simulated results with and without suction

Simulated Results

(Sediment-No.8)

Sensitivity of hydraulic conductivity (Case-3: sediment-No.8) (K1; Ks=7.8×10-6, K2; Ks=1.56×10-5, K3; Ks=3.12×10-5).

(Sediment-No.8) Sensitivity of hydraulic conductivity

K1= K2 * 0.5

K3= K2 * 2.0

40 sec. 100 sec.

Comparisons of with and without suction

with

suction

without

suction }}

big erosion

rate

K bigger

then

E faster

36 Fig. – Comparisons of simulated and experimental results of temporal moisture variations

inside the embankment

Simulated Results

Fig. – Positions of WCRs (m1 to m9) in Case-5 experiment

Seepage process inside the EMB (Type-B)

0

0.1

0.2

0.3

0.4

0.5

0 200 400 600 800

Volu

met

ric

Wat

er C

onte

nt

Time (sec)

Exp (m1)

Sim (m1)0

0.1

0.2

0.3

0.4

0.5

0 200 400 600 800

Volu

met

ric

Wat

er C

onte

nt

Time (sec)

Exp (m2)

Sim (m2)

0

0.1

0.2

0.3

0.4

0.5

0 200 400 600 800

Volu

met

ric

Wat

er C

onte

nt

Time (sec)

Exp (m4)Sim (m4)

0

0.1

0.2

0.3

0.4

0.5

0 200 400 600 800

Volu

met

ric

Wat

er C

onte

nt

Time (sec)

Exp (m5)Sim (m5)

0

0.1

0.2

0.3

0.4

0.5

1000 1200 1400 1600 1800 2000 2200

Volu

met

ric

Wat

er C

onte

nt

Time (sec)

Exp (m6)Sim (m6)

0

0.1

0.2

0.3

0.4

0.5

1000 1400 1800 2200V

olu

met

ric

Wat

er C

onte

nt

Time (sec)

Exp (m8)Sim (m8)

15cm

15cm

30cm 30cm 30cm 20cm 10cm 10cm

WCR

15cm 15cm 25cm 30cm 5cm

5cm

5cm

5cm

m1 m2

m3 m4

m5

m6

m7

m8

m9

5.0

10.0

15.0

20.0

25.0

30.0

35.0

390.0 410.0 430.0 450.0 470.0 490.0

Ele

vat

ion

(cm

)

Distance (cm)

Initial

sim-10s

sim-20s

sim-30s

sim-40s

exp-10s

exp-20s

exp-30s

exp-40s

37

Simulated Results

dm=0.174mm

Embankment shape

(Dam type-B)

Simulated and experimental results of

embankment shape (Dam type-B)

(Case-4: sediment-No.7)

38

5. Conclusions

5. Conclusions

39

• In this study, a new expression for resisting shear strength due to

suction was derived in pick-up formula to compute the erosion of

unsaturated river embankment by flow overtopping.

• The proposed model was tested for erosion of embankment under

different sediment sizes (Sediment No.6, 7, and 8) and embankment

shapes (Type-A and B).

An embankment erosion model is developed using combined depth

average flow, seepage flow, sediment transport model based on non-

equilibrium model, and slope stability model.

• Generally, the proposed numerical model well reproduced the

experimental results on processes of river embankment surface erosion

due to overtopping flow.

• We used pick-up formulas based on both saturated and unsaturated

conditions to simulate the erosion process of embankment surface that

occurs simultaneously with infiltration.

(1/2)

Conclusions

40

• In small-sized sediments condition, the great shear strength and the low

infiltration rate cause a lag of erosion and delay the failure time, and

these phenomena were able to be reproduced using the proposed

model.

• A numerical model that can reproduce the temporal change of

embankment shape during the erosion process due to overtopping flow

is important and useful to consider a countermeasure against

embankment failure.

(2/2)

• There remains many problems to be solved, such as effects of

cohesiveness, mixture of sediment size, applicability of the model to the

real river EMB, etc. The model refinement is necessary in very near

future.

Thank you very much for your kind attention!