Report Behaviour and Analysis of Reinforced Concrete Walls Subjected to Reversed Cyclic Loading
Modelling the Behaviour of Soil Subjected to Internal Erosion
Transcript of Modelling the Behaviour of Soil Subjected to Internal Erosion
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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
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Outline
Micro-mechanical Model
Modeling of internal erosion
Behavior of eroded soils subjected to internal
and external input loads
Summary
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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]
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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
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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)
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-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
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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)
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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
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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
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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
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-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)
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Impact of a fast external loading
such as shock, seismic loading…
Instability due to internal erosion (2)
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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
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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
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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
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hydropower plant in
Dychow (Poland)
Sliding by instability of part
of the material constituting
the embankment dam
Failure of a hydraulic dam
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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%.
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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.
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Thank you for your attention