P.-Y. Hicher

Research Institute in Civil and Mechanical Engineering, UMR 6183 CNRS –

Ecole Centrale de Nantes – University of Nantes

Modelling the Behaviour of Soil

Subjected to Internal Erosion

ICSE6, Paris August 29 - 31

Outline

Micro-mechanical Model

Modeling of internal erosion

Behavior of eroded soils subjected to internal

and external input loads

Summary

Micromechanical Approach

[Chang CS & Hicher PY (2005), Int. J. Solids & Structures]

Macro scale

Micro scale

Global stress-strain relation

Inter-particle force-displacement relation

Localization &

Homogenization

(Static method)

Stress

Inter-particle

movement

Inter-particle

force

Strain

1

,

1

N

j i j kiku lA

j ij i kkAf n

i ij jf K

ij ijkl klC

Normal compression

(elastic behavior)

Shear sliding

[Coulomb-type]

Kinetic of extraction of the solid particles

p

Interparticle friction p depends on void ratio e (interlocking of particles)

Loading parameter: fe = mextracted

/ minitial

klijklij C

Strain response

change in e

homogenization

loading parameter

Induced mechanical responses

Triaxial compression pursued for intact samples after extraction

Increase of the porosity

Change from a dense/dilative behaviour to a loose/contractive behaviour

Scholtes, L, Hicher, P.-Y., Sibille, L. CRAS Mécanique (2010)

-2

-1

0

1

2

3

0 5 10 15 20

q=600 kPa e1q=600 kPa evq=500 kPa e1q=500 kPa evq=400 kPa e1q=400 kPa evq=250 kPa e1q=250 kPa ev

e1

, e

v (

%)

fe (%)

Dense samples e0 = 0.3

Induced deformations

under constant effective stresses

Influence of the deviatoric stress

Induced mechanical responses

Triaxial compression pursued for intact samples after extraction

Increase of the porosity

Change from a dense/dilative behaviour to a loose/contractive behaviour

Scholtes, L, Hicher, P.-Y., Sibille, L. CRAS Mécanique (2010)

Stress-strain relationships without

and with internal erosion under

different initial stress conditions:

(a) deviatoric stress versus axial

strain and

(b) volumetric strain versus axial

strain (final hydraulic gradient

=8.0).

Chang & Zhang, ASTM J., 2011

Experimental results

on silty sand

Instability due to internal erosion (1)

Internal erosion creates:

Increase in void ratio

Instability of the soil mass

due to an increase in pore

water pressure

Erosion due to water seepage

0

0.1

0.2

0.3

0.4

0.5

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

failure linecritical state linedrained triaxial pathconstant q=200kPaconstant q=300kPa

q (

MP

a)

p' (MPa)

-1.5

-1

-0.5

0

0.5

1

0.1 0.15 0.2 0.25 0.3 0.35 0.4

constant q testse1-q=200kPaev-q=200kPae1-q=300kPaev-q=300kPa

e1

, e

v (

%)

p' (MPa)

Influence of pore water pressure increase

Constant – q tests on intact samples

Failure is obtained when the

stress paths reach the plastic

limit

-0.5

0

0.5

1

1.5

2

2.5

0.1 0.15 0.2 0.25 0.3 0.35 0.4

constant q testse1-q=200kPaev-q=200kPae1-q=300kPaev-q=300kPa

e1

, e

v (

%)

p' (MPa)

Influence of pore water pressure increase - cont.

Constant –q tests on eroded samples

Failure is obtained before the

critical state line.

An instable state is reached

which corresponds to the

vanishing of the second order

work

0

0.1

0.2

0.3

0.4

0.5

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

instability linecritical state linedrained triaxial pathconstant q=200kPaconstant q=300kPa

q (

MP

a)

p' (MPa)

Impact of a fast external loading

such as shock, seismic loading…

Instability due to internal erosion (2)

0

50

100

150

200

0 20 40 60 80 100 120 140 160

CD testCU testCD + U test1CD + U test2CD + U test3

q (

kP

a)

p' (kPa)

0

50

100

150

200

250

300

0 1 2 3 4 5

CU testCD + U test1CD + U test2CD + U test3

q (

kP

a)

eps1 (%)

Dr = 60%

Unconditionally

stable behavior

Undrained triaxial tests

0

20

40

60

80

100

120

0 50 100 150 200 250

CU test P'0=100kPaCU test p'0=200kPaD+U test1D+U test2D+U test3Drained pathinstability line CU tests

q (

kP

a)

p' (kPa)

0

20

40

60

80

100

120

0 2 4 6 8 10

CU testCD + U test1CD + U test2CD + U test3

q (

kP

a)

eps1 (%)

Dr = 30%

Existence of an

unstable domain

Undrained triaxial tests

0

20

40

60

80

100

0 1 2 3 4 5

CU test

CD + U test 1

CD + U test 2

CD + U test 3

q (

kP

a)

eps1 (%)

0

20

40

60

80

100

120

0 100 200 300 400 500 600

CU test p'0=100kPaCD + U test 2CD + U test 3CD + U test 1CU test p'0=200kPaCU test p'0=400kPaCD testinstability line for undrained tests

q (

kP

a)

p' (kPa)

Dr = 0

Large domain of

instability

Undrained triaxial

tests

hydropower plant in

Dychow (Poland)

Sliding by instability of part

of the material constituting

the embankment dam

Failure of a hydraulic dam

The material responsible for the sliding is a silty sand subjected to internal erosion

during a period of 60 years, which put it in a relative density as small as 15 to 20%.

Summary

The microstructural model can capture with reasonable accuracy the

conditions of instability detected experimentally.

We focused here on the influence of the stress and strain paths,

demonstrating that the conditions of instability can be reached far below

the plastic limit.

The initial void ratio is an important parameter, which controls the

amplitude of the unstable domain. Instability condition linked to

internal erosion can occur due to the decrease of initial density during

suffusion

The numerical results appear to agree with observations made on

embankment dams which underwent internal erosion, and in particular

with the description of their modes of failure.

Thank you for your attention