micro and macro modeling of internal erosion and scouring ... · shore protection adjust to sea...

ICSE-6 2012 (Paris)

1

Kenichi MAEDA (Nagoya Institute of Technology, JAPAN)

David Muir WOOD (University of Dundee, UK)

Akihiko KONDO (Nagoya Institute of Technology, JAPAN)

Micro and Macro Modeling of Internal

Erosion and Scouring

with Fine Particle Dynamics

6th International Conference on Scour and Erosion

GeoScience & Geotechnics

ICSE-6 2012 (Paris)

2

Large Model Test for a reservoir dike with

heavy rain: occurrence of piping

Surface flow and then seepage into

slope , small piping

Sliding and cracking

Piping, erosion (loss of fine particle)

and Jamming-sealing

Conducted by

National

Agriculture and

Food Research

Organization, NARO

(Japan)

clean water -> loss of fine particle -> muddy water -> outflow of large particle with loud rumbling sound

Heavy rain 130-150 mm/h with water

storage of high water level

ICSE-6 2012 (Paris)

…..depression and sink hole

２ｍ

2008.8 2010.1

On water service tube that

becomes superannuated

shore protection adjust to sea

Fine particle movement Due to

undulation of water level in tidal river

3

in tidal river , collapse of bank and shore

protector

ICSE-6 2012 (Paris)

A purpose of this study to solve internal

erosion in multi-scale and multi-phase

4

log(scale)

phase

seepage

force

inter-particle

contact

To observe

removal (loss)

and jamming of

fine particle

narrowing grading soil-water-

air-structure

Discrete

Element (DEM)

Continuum

approximation

(constitutive model)

SPH or FEM numerical

scheme with constitutive

model

≪ (grain) (grain) (void) (soil element)

piping

(structure)

To reveal rules of local plastic

deformation or local failure

with changing grading

ICSE-6 2012 (Paris) 1D Seepage test (downward flow)

移動出来る間隙の存在

外力（浸透力）の作用

粒度分布の変化で表現

動水勾配の変化で表現

0 200 400 600 800 10000

2.0

4.0

6.0

8.0

10.0

Hyd

raul

ic g

radi

ent,

i

Elapsed time (min)

monotonic hydraulic loading test

0.05 0.10 0.50 1.00 5.000

20

40

60

80

100

Grain Diameter , D(mm)

W(%

)

直線下に凸上に凸

直線分布⇒全粒径が等しく配分

下の凸分布⇒細粒分と大きい粒径

上に凸分布⇒中間粒径が多い

移動出来る間隙の存在

外力（浸透力）の作用

粒度分布の変化で表現

動水勾配の変化で表現

0 200 400 600 800 10000

2.0

4.0

6.0

8.0

10.0

Hyd

raul

ic g

radi

ent,

i

Elapsed time (min)

monotonic hydraulic loading test

0.05 0.10 0.50 1.00 5.000

20

40

60

80

100

Grain Diameter , D(mm)

W(%

)

直線下に凸上に凸

直線分布⇒全粒径が等しく配分

下の凸分布⇒細粒分と大きい粒径

上に凸分布⇒中間粒径が多い

Sample: Glass beads

Relative density Dr=80%

To measure amount of leached particle (removal and jamming of particle)

monotonic increasing

Existence of movable void size

External force(Seepage force)

Change in hydraulic grad.

Different grading shapes

5 the bottom filter hole size = 0.3mm

Downward Hyd. Grad. From small to very large 10

ICSE-6 2012 (Paris)

Grain size distribution of samples

Satisfy H=F in all finer grain

Pay attention to range of 4D against to removable grain size

Straight（st）

Step grading（sp）

Coarse grading(cv）

Effect of Grading Shape

0.01 0.05 0.1 0.5 1 5 100

20

40

60

80

100

Grain size , D (mm)

Per

cen

t fi

ner

by w

eig

ht

(%)

cv3 cv2 cv1 st sp1 sp2 sp3

filter size =0.300

Satisfy H>F for all finer grain

Not contain enough filter particle(4D) for clogging (convex downward grading)

This series can be divided to 3 group

6

(convex upward grading)

ICSE-6 2012 (Paris)

0 50 100 150 200 250

0.0001

0.001

0.01

0.1

1

0

2

4

6

8

10

Duration time , t (min)Weig

ht

of

leached p

art

icle

s , W

(%

)

Hy

dra

uli

c g

rad

ien

t ,

i

sp3 sp2 sp1 st cv1 cv2 cv3

Leaching process with different grading shapes

Amount of Leached particle (internal erosion)：

convex downward ≫ convex upward ≧Straight

Grading Time history of Leaching (erosion)

0.01 0.05 0.1 0.5 1 5 100

20

40

60

80

100

Grain size , D (mm)

Per

cent

finer

by w

eig

ht

(%)

cv3 cv2 cv1 st sp1 sp2 sp3

filter size =0.300

Increase along with the distance from straight grading 7

convex downward

grading

Due to fine particle removal, the

soil with convex downward

grading becomes to have more

convex downward grading;

internal erosion induces

removal particle.

Straight grading

ICSE-6 2012 (Paris)

Effect of hydraulic undulation

0 200 400 600 800 10000

0.02

0.04

0.06

0.08

0

2.0

4.0

6.0

8.0

10.0

Mas

s p

erce

nt

of

G.B

. fl

ow

ing

ou

t, W

e (%

)

Elapsed time (min)

monotonic hydraulic loading testcyclic hydraulic loading test

Hydra

uli

c g

radie

nt,

i

0 1 2 3 4 5 6 7 8 9 100

0.2

0.4

0.6

0.8

0

0.1

0.2

0.3

0.4

Hydraulic gradient, i

Mas

s p

erce

nt

of

G.B

. fl

ow

ing

ou

t, W

e (%

)

Vel

oci

ty o

f fl

ow

, v

(cm

/s) monotonic hydraulic loading test

cyclic hydraulic loading test

An undulation of seepage force

Time history We - hydraulic grad.

0 200 400 600 800 10000

2.0

4.0

6.0

8.0

10.0H

ydra

uli

c g

radie

nt,

i

Elapsed time (min)

cyclic hydraulic loading test

Amount of internal erosion in cyclic loading is 1.5 times as that in monotonic loading

Cyclic Monotonic

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DEM simulation: particle and void size

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Kenney and Lau (1985) focused mass fractions of D and 4D

and suggested “stability of grading”…….

Therefore, the size of arching and its stability are important

to understand the mechanism of the removal and the

jamming of fine particle.

Particle mobility: DEM + CFD

biaxial mixture: Dmax and Dmin

Drag force depending on Re number is applied to particles

10

RD=Dmax/Dmin=3 RD=Dmax/Dmin=4 RD=Dmax/Dmin=5

ICSE-6 2012 (Paris)

To observe void size and its frequency

with different grading shapes

The number of void whose diameter is larger than Dmin, is largest in the case of convex downward and is less than 5% of total number voids.

0 0.5 1 1.5 20

10

20

30

Fre

quency,

(%)

Normalized controlling constriction size, Dvoid/Dmin

Movable void size

0.01 0.02 0.04 0.10

20

40

60

80

100

Grain size diameter[m]

W (

%)

Grading

void size

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ICSE-6 2012 (Paris)

0.01 0.02 0.04 0.10

20

40

60

80

100

Grain size diameter[m]

W (

%)

Continuity length of voids is about 1-4 times as small particle. Smaller particle just go around larger particle.

Grading

0 2 4 6 8 100

20

40

60

80

100

Normalized movable distance, X/Dmin

Fre

quency,

(%)

12

To observe continuity of void with different

grading shapes

X

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From DEM simulation to develop Continuum modelling

: soil element size

13

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14

？

yy

m

m

？

yy

m

m

.constm

.constm

1) monotonic loading test biaxial compression test:

shearing with constant σm

？

yy

m

m

.constm

2

yyxx

m

xx

yy

stress-strain-dilatancy: 2D DEM

2) removal (erosion) test the finest particle is forced to be

removed: and observation of

deformation behaviors under

constant stress

3) reloading test (shearing

after erosion) shearing sample subjected to

erosion

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stress chains

Deformation-failure of soil element removal

test of fine particle

in 2D DEM

specimen

1 2 4 100

20

40

60

80

100

Grain size , D (cm)

W (

%)

RD=2

RD=5

RD=10

RD=20

Before removal After removal

5%

The finest particle was forced to be removed repeat to simulate internal

erosion: Two criteria for terminating this repeated process of particle

removal: the normal strain exceeds 25%; the removed particle size is equal

to the 5% grain size (D5) of the original sample.

D5 D5 D5 D5

ICSE-6 2012 (Paris)

0 5 100

0.1

0.2

0.3

0.4

Normal Strain, yy (%)

Str

ess

Rat

io,

m /

m

Dense RD=10Removal test m=const

16

Dense Loose

0 5 100

0.1

0.2

0.3

0.4

Normal strain, yy (%)

Str

ess

Rat

io,

m/

m

Loose RD=10Removal test m=const

stress-strain due to fine particle

removal

The 5% grain size (D5) of the original sample can be removed under

isotropic compression and lower shear stress ratio but large strain

generated strain under high shear stress level even if about 1.5% grain

size of the original samples.

monotonic shearing

ICSE-6 2012 (Paris)

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Dense Loose

0 5 10

-3

-2

-1

0

1

2

Volu

met

ric

Str

ain,

v (

%)



0 5 10

-3

-2

-1

0

1

2

Normal srain, yy(%)

Loose RD=10Removal test m=const

Volu

met

ric

stra

in,

v(%

)

monotonic shearing

monotonic shearing

Volumetric change (dilatancy) due to

fine particle removal

Volumetric change due to particle removal shows contractive; negative

dilatancy. Particle removal induce compression in soil element, but

increase void ratio in dense sample.

ICSE-6 2012 (Paris)

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0 5 100

0.1

0.2

0.3

0.4


Str

ess

Rat

io,

m/

m

Dense RD=10Shear after Removal up to 5.0% grain size

0 5 100

0.1

0.2

0.3

0.4


Str

ess

Rat

io,

m/

m


the reduction of peak strength of soil element due to erosion (fine

particle removal)

reloading test (shearing after eroion

due to fine particle removal) the removed particle size is equal to

the 1.5% grain size

of the original grain size.

the removed particle size is equal to

the 5.0% grain size

of the original grain size.

ICSE-6 2012 (Paris)

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For express plasticity in internal erosion

critical state soil mechanics with changing grading

by shifting “critical state line”

D. M. Wood & K. Maeda: Acta Geotechnica (2007);

D. M. Wood, K. Maeda & E. Nukudani : Geotechnique, 60 (6) (2010)

1 2 4 100

20

40

60

80

100

Grain size , D (cm)

W(%

)

RD=2

RD=5RD=10

RD=20

before removal after removal

changing grading: internal erosion by

removal of fine particle

0 1.0 2.0 3.0

1.15

1.20

1.25

Mean normal stress, m (MPa)

Sp

ecif

ic v

olu

me,

v

RD=dmax/dminRD=2

5

10

20

well grading

poor grading

erosion

critical state lines with changing

grading (changing material)

ICSE-6 2012 (Paris)

Performance of proposed model

0 5 10 15 20 25 30-0.1

0

0.1

0.2

0.3

0.4 -4

-3

-2

-1

0

1

Volu

met

ric

Str

ain,

v (

%)

Shear Strain, d (%)

Str

ess

Rat

io,

m /

m

Cam-cray model (+ subloading surface)

0 5 10 15 20 25 30-0.2

0

0.2

0.4 -6

-4

-2

0

2 Volu

met

ric

Str

ain,

v (

%)

Shear Strain, d (%)

Str

ess

Rat

io,

m /

m

Cam-cray model (+ subloading surface)

Proposed continuum model Including erosion effect

DEM simulation results

0 5 10 15 20 25 30-0.1

0

0.1

0.2

0.3

0.4

Dense : 5% removal RD=10 m=const

Shear Strain, d (%)

Str

ess

Rati

o,

m /

m

0 5 10 15 20 25 30-0.2

0

0.2

0.4 -6

-4

-2

0

2

Dense : 5% removal RD=10 m=const

Volu

met

ric

Str

ain

, v (

%)

Shear Strain, d (%)

Str

ess

Rati

o, m

/

m

From previous 3 results, we made the continuum model.

20

ICSE-6 2012 (Paris)

IVBC problem involving continuum modelling with

erosion structural size

21

ICSE-6 2012 (Paris) Numerical simulation of problems with internal erosion

Layer of Solid

Air

Water

Porous material,

soil

sff

fsfLayer of Fluid

Total volume fraction: 1 = (Volume fraction: n) + (Volume fraction: 1-n)

Superposition

of fluid-solid

layers

Interaction body force

Tentatively Darcy’s law is kept.

)(2 fsfs f

k

gn vvf

n：Porosity

g：Acceleration of gracity

ρf：Density of fluid

k：Permeability

vs：Velocity of solid

vf：Velocity of fluid

Soil-fluid coupling

Seepage around sheet pile (K. Maeda, M. Sakai (2004))

Superposition of

smoothed physical values

Smoothed physical values

by using smoothed function for each particle

x

Limited zone of influence

x1

x2

o

Particle : i

Particle : j

rij

xi

xj

κhi hi

Smoothed Particle Hydrodynamics (SPH)

x'x'x'xx dfhWf )(),()(

The feature of the SPH method is as follows;

Mesh free

Lagrangian method

Initial modeling is easy.

22

ICSE-6 2012 (Paris)

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(m)

particle fixed regionupstream

downstream

(a) (b)

(c) (d)

ex.) dike failure and washed-out

under constant water level

ICSE-6 2012 (Paris)

upstream

5m initial state

collapse and flow

unit: 1/s

0.0 1.0 2.0 3.0 4.0 5.0

ex.) natural dam (landslide dam)

failure under constant water level

24

unit: 1/s

0.0 1.0 2.0 3.0 4.0 5.0

unit: 1/s

0.0 1.0 2.0 3.0 4.0 5.0

unit: 1/s

0.0 1.0 2.0 3.0 4.0 5.0

Even under constant water level,

localization of deformation and

failure occur.

ICSE-6 2012 (Paris)

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initial surface

seepage (a)

water

sandy soil

impermeable

sheet-pile

deformed surface

(b) seepage

ex.) seepage and erosion around sheet-pile

under constant difference in water height

The settlement in Fig. (b) with erosion is larger than that without

erosion in Fig.(a), and the deformation in Fig. (b) is localized.

(a) without internal erosion; (b) with internal erosion (fine

particle removal). Water level was kept constant where water

flowed from right to left and the erosion was controlled by

(changing rate in narrowing grading ) the value of δIG.

ICSE-6 2012 (Paris)

increasing

- local permeability

- local shearing or failure,

looseness, relaxation

role of local plastic deformation due to fine

particle dynamics on internal erosion

26

seepage force &

macro shearing

progressive failure:

piping

fine particle

removal

fine particle

jamming

(clogging) increment of local

hydraulic gradient

heterogeneity of void

(decreasing permeability)

local hydraulic

fracture

increment of local shear

plastic deformation and

compression

(vol. of local compression) ≨ (vol. of removed particle)

increasing void ratio

ICSE-6 2012 (Paris)

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ICSE-6 2012 (Paris)

28

seepage force

internal erosion

deformation ? or failure ?

Loss of finer particle & narrowing grading

According to the site investigations

was observed, and it called internal erosion.

How can we deal with this phenomenon?

“The internal erosion changes soil property itself progressively. “

ICSE-6 2012 (Paris)

Focus on particle moving（previous research）

Not constitute microstructure

Existence of movable void size

External force（Seepage force）

H＞F ２,

1, D＜ DFilter

Stable condition for internal erosion （Kenny et.al, 1985）

1 4

Removable size: D is 1/4 of filter min. size

Filter particle need to contain more than finer

Unstable

Stable

To consider the certain particle stability…

It’s necessary following three condition

29

ICSE-6 2012 (Paris)

30

isotropic

compression

constant

volume

圧縮膨張

-1.0 -0.5 0 0.5 1.0 1.5 2.01.0

1.5

2.0

2.5

Pri

nci

pal

str

ess

rati

o,

1 /

2

Pricipal strain increment ratio, - d2 /d1

Dense RD=10 Removal test m=const

removal process

monotonic shear process

start of removal

isotropic

compression

constant

volume

圧縮膨張

-1.0 -0.5 0 0.5 1.0 1.5 2.01.0

1.5

2.0

2.5Loose RD=10Removal test m=const

Principal strain increment ratio, -d2/d1

Pri

nci

pal

str

ess

rati

o,

1/

2

removal process

start of removal

monotonic shear process

Dense Loose comp. comp. dil. comp. dil.

stress-dilatancy due to fine particle

removal

ICSE-6 2012 (Paris)

Basically,

But, cyclic loading causes particle removal. It’s necessary to estimate stability against forcing fluctuation

Angle meter

down

?

nsc fftan

nf

sf

Rotate principal stress direction by sloping to express fluctuation ctan

θ

Arch microstructure As Clogging model

arch structure doesn’t break by seepage force …

Not influenced from arch shape and number of composing particles

Aluminum Laminated body

Try to simply estimate…

31

ICSE-6 2012 (Paris)

Arch microstructure As Clogging model

a/b

Num. 0.5 0.75 1 1.25 1.5 1.75

7 29.3° f A F K P

8 23.4° 34.7° B G 34.4° 26.2°

9 11.7° h C 33.0° 34.0° 29.4°

10 18.0° i D 33.4° 28.2° 32.6°

11 9.2° j E 32.3° 31.1° 24.0°

Circle

Angle in chart: breakage slope angle. if it blank, not break by sloping

Stable condition: Arch shape close to circle composed number of particle is few

Arching shape

Composing num.

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ICSE-6 2012 (Paris)

Stability of Clogging microstructure

Most stable shape is determined by current stress condition.

Removal amount increase by cyclic loading

0 200 400 600 800 10000

0.02

0.04

0.06

0.08

0

2.0

4.0

6.0

8.0

10.0

Mas

s p

erce

nt

of

G.B

. fl

ow

ing

ou

t, W

e (%

)

Elapsed time (min)

monotonic hydraulic loading testcyclic hydraulic loading test

Hydra

uli

c g

radie

nt,

i

b

a

b

a

a

ba

b

Resistible fluctuation range exists. if number of particle have a lot,

it goes unstable by a lot of num. of

breakable point.

Erosion concentrate just after i changed

It along with the amplitude of fluctuation even hydraulic grad. Just only decrease

According to simple experiment

As a reason…

33

ICSE-6 2012 (Paris)

34

to solve internal erosion in geotechnical problems

To simulate removal and jamming of fine particle -> model test & DEM

To fined a rule of plastic deformation and failure due to fine particle removal -> DEM

To suggest continuum modelling of internal erosion: changing grading :

To calculate of IVBC problem by Smoothed Particle Hydrodynamics (SPH)

ICSE-6 2012 (Paris)

35

under constant hydraulic gradient

0 1000 2000 3000 40000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

6

8

10

12

14

16

18

elapsed time (min.)

accu

mu

lati

on

mas

s p

erce

nt

of

g.b

. fl

ow

ing

ou

t, W

e (%

)

flu

x o

f w

ater

, Q (

cm3/s

)

flux of water, Q (cm3/s)

accumulation mass percent of g.b. flowing out, We (%)

mass percent of g.b. flowing out (%)

step grading

Even under constant hydraulic

gradient, some fine particles

were removed from the sample.

And the removal and the

jamming of fine particle

occurred alternatively.

Finally internal erosion stopped.

changing grading: grading became coarser

Removal of

fine particle

Jamming of

fine particle

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36

1 2 4 100

20

40

60

80

100

Grain size , D (cm)

W (

%)

RD=2

RD=5

RD=10RD=20

poor grading

sample use and DEM parameter

well grading

RD=Dmax/Dmin=2, 5, 10, 20

slider:

= tan

dash pot: n spring: kn

particle b

（mass: mb） non-tension

divider

a

b

b

a

spring: ks

dash pot: s

particle a

（mass: ma）

parameter sym.(unit) value

[ particle; contact model ]

Diameter

D min –

Dmax

(m)(RD)

0.5 - 0.10 (2)

0.02 – 0.10 (5)

0.01 – 0.10 (10)

0.005 – 0.10

(20)

particle density s （kg/m3） 2700

spring coeff. in normal

direc. kn (N/m) 1.0108

spring coeff. in shear direc. ks (N/m) 2.5107

viscous damping (normal) hn 1 (critical)

viscous damping (shear) hs 1 (critical)

interparticle friction coeff. tan 0.25

calculation time t (s) 1.010-6

[ assembly: referred value ]

density （kg/m3） 1800

P-wave velocity Vp (m/s) 266

S-wave velocity Vs (m/s) 133

parameter sym.(unit) value

[ particle; contact model ]

Diameter

D min –

Dmax

(m)(RD)

0.5 - 0.10 (2)

0.02 – 0.10 (5)

0.01 – 0.10 (10)

0.005 – 0.10

(20)

particle density s （kg/m3） 2700

spring coeff. in normal

direc. kn (N/m) 1.0108

spring coeff. in shear direc. ks (N/m) 2.5107

viscous damping (normal) hn 1 (critical)

viscous damping (shear) hs 1 (critical)

interparticle friction coeff. tan 0.25

calculation time t (s) 1.010-6

[ assembly: referred value ]

density （kg/m3） 1800

P-wave velocity Vp (m/s) 266

S-wave velocity Vs (m/s) 133

ICSE-6 2012 (Paris)

37 0 1.0 2.0 3.0

1.15

1.20

1.25

Mean effective stress, m (MPa)

circular particle (cl01)

Sp

ecif

ic v

olu

me,

v

C.S.L. for Dence C.S.L. for Loose

RD=Dmax/Dmin=20 I.C. Shear

I. C. ; isotropic compression processShear; shear process

origin of shearing critical state

0 5 10-0.1

0

0.1

0.2

0.3

0.4

0.5 -10

-8

-6

-4

-2

0

2

Shear testDense samples m=0.10(MPa)

Volu

met

ric

Str

ain,

v (

%)


Str

ess

Rat

io,

m /

m

RD=02 RD=05 RD=10 RD=20

0 5 10-0.1

0

0.1

0.2

0.3

0.4

0.5 -10

-8

-6

-4

-2

0

2

Shear testMedium samples m=0.10(MPa)

Volu

met

ric

Str

ain,

v (

%)

Normal Strain, yy (%)S

tres

s R

atio

, m

/

m

RD=02RD=05RD=10RD=20

0 5 10-0.1

0

0.1

0.2

0.3

0.4

0.5 -10

-8

-6

-4

-2

0

2

Shear testLoose samples m=0.10(MPa)

Volu

met

ric

Str

ain,

v (

%)


Str

ess

Rat

io,

m/

m

RD=02 RD=05 RD=10 RD=20

Dense Medium Loose

monotonic shearing

0.05 0.1 0.5 1 5

1.15

1.20

1.25


Speci

fic

volu

me, v

=1+

e

Critical State Lines

RD = 2 RD = 5 RD =10 RD =20 poor grading

well grading

ICSE-6 2012 (Paris)

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State parameter : y

y ＝v - vcs ＝（1+e）-（1+ecs）

0.05 0.1 0.5 1 5

1.15

1.20

1.25


Specif

ic v

olu

me, v

=1

+e

CSL y=0

y<0

y>0 Loose

Dense

ICSE-6 2012 (Paris)

39

The granular material subjected to erosion changed to be a different material with different grading. The state parameter is useful to the available strength not only for the material before erosion but also after erosion, independently of degree of erosion.

State parameter : y

ICSE-6 2012 (Paris)

40

Modelling mechanical erosion

soil mechanics with changing grading

D. M. Wood & K. Maeda: Acta Geotechnica (2007);

D. M. Wood, K. Maeda & E. Nukudani : Geotechnique, 60 (6) (2010)

1 2 4 100

20

40

60

80

100

Grain size , D (cm)

W(%

)

RD=2

RD=5RD=10

RD=20


changing grading: internal erosion by

removal of fine particle

0 1.0 2.0 3.0

1.15

1.20

1.25


Sp

ecif

ic v

olu

me,

v

RD=dmax/dminRD=2

5

10

20

well grading

poor grading

erosion

critical state lines with changing

grading (changing material)

ICSE-6 2012 (Paris)

0 5 100

0.1

0.2

0.3

0.4


Str

ess

Rat

io,

m /

m


monotonic shearing

Stress-Strain

Removal Test

1 2 4 100

20

40

60

80

100

Grain size , D (cm)

W(%

)

RD=10


0 5 10

-3

-2

-1

0

1

2

Volu

met

ric

Str

ain,

v (

%)



Dilatancy

Deformation due to

one particle removal

and reach to critical state by 5% finer removal & high stress ratio.

Even under the constant stress condition, sample have compression

Catch up the deformation by progressively removing finer under constant stress

41

ICSE-6 2012 (Paris)

0 5 100

0.1

0.2

0.3

0.4


Str

ess

Rat

io,

m/

m


0 5 100

0.1

0.2

0.3

0.4


Str

ess

Rat

io,

m/

m


Reduction of peak value due to removal can be observed

Reloading test (shearing after erosion)

1.5% grain size removed 5% grain size removed

Aims to evaluate the effects for potential of sample strength, it’s verified by the shearing after erosion test.

Shear behavior

42

ICSE-6 2012 (Paris)

0 5 100

0.1

0.2

0.3

0.4


Str

ess

Rat

io,

m/

m


Proportional relation between Potential of peak strength and State parameter

Potential of peak strength can be expected same as without one by state parameter(yn - ncv): relative density index for critical state.

Relative density index for critical state

without erosion

It’s well known for ordinary shear behave, proportional relation with State parameter.

It can put on same line by thought Removal behave as loose sample.

43

ICSE-6 2012 (Paris)

44

diameter: 2.4m

depth: 6.7m

WAC Bennett DAM

（1996.6）

Two large sink holes in a fill dam

44

micro and macro modeling of internal erosion and scouring ... · shore protection adjust to sea...

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