Hydro-mechanical coupling and strain localization in saturated

Transcription

Laboratoire 3S Sols, Solides, Structures
Université de Grenoble - CNRS
Équipe GDR Géomatériaux, Déformation et Rupture
Géomécanique
Localization in Saturated
Porous Media with
Hydro-Mechanical Coupling
Jacques Desrues, Laboratoire 3S, Grenoble (France)
Frédéric Collin, Geomac department, ULG Liège (Belgium)
A work performed in collaboration during a stay
of J. Desrues in ULg.
17th ALERT School – Coupled multi-physics processes in Geomechanics
Aussois - October 13th-15th
Outline
a a brief introduction to the phenomenon:
experimental observations of strain
localization
a the undrained case : what is different
a HM coupled numerical analysis of drained,
undrained and partially drained biaxial tests
in sand
Laboratoire 3S Université de Grenoble - CNRS
Équipe GDR : Géomatériaux, Déformation et Rupture
Strain Localisation ?
What does it look like ?
Want to see more ?
a you can find this video
and a number of other documents on the
Web page :
http://l3sphnum.hmg.inpg.fr/hps1/etagere.html
including articles, thesis, reports, videos,
experimental data
a Or send me an email to get the address
Field observations
a evidence of a localized shear structure
at a 100 m scale (el centro earthquake, california)
Field observations
(earthquake, Turkey)
Conjugate shear bands in perlite (Melos island, Greece)
Photography I. Vardoulakis
Localized deformation in rocks
a localized decohesion
of the rock layers at
small scale, organized
in a band
(kink band)
Photo J Desrues, Barlock creek
near Baltimore (Ireland)
… another triaxial test
In this test,
a shorter specimen is
used, in conjunction
with careful lubrication
of the ends,
in order to improve the
homogeneity of the
deformation process:
Localization is still the
final deformation
mode.
100
mm
Localisation
is observed
in the field …
but also in
Laboratory
tests
axisymmetric triaxial
compression test on a
sand specimen
(Hostun RF sand)
200 mm
overall axial strain 15 %
evidence of a shear plane
Next …
… in clay specimens
Strain localization in a
2D granular material
Scheeneli’s
material
retaining wall (model)
Strain localization in a model
material
The shear plane
is in fact a
shear band
Deformation at
failure is localized:
evidence of
a « shear plane »
Next…
noir
P
Experimental Setup :
Biaxial Apparatus
Biaxial
Apparatus
3S Lab
Grenoble
France
Desrues J., Viggiani G. (2004) Strain localization in sand: an overview of the experimental results obtained in Grenoble using stereophotogrammetry, Int. J. Num. Anal.
Meth. Geom. vol.28 No 4, pp 279-321
Desrues J.Laboratoire
(1984) La localisation
de la déformation
dans les milieux
granulaires, Thèse DE (Docteur
d'état),
Université
de Grenoble (USMG-INPG)
(in french)
3S Université
de Grenoble
- CNRS
Équipe
GDR
: Géomatériaux,
Déformation
et Rupture
Localisation in
Biaxial test on Sand
:
Observation :
- Multiple SB
- Non zero thickness
- Large strain
in the SB
- « reflexion » on
the top platten
Localisation and Stress peak
Localization
and stress peak
1-2
2-3
3-4
4-5
5-6
Localized volumetric strain
Undrained Biaxial Test
Mokni M., Desrues J. (1999) Strain localisation measurements in undrained plane-strain biaxial tests on Hostun RF sand,
Mechanics of cohesive-frictional materials vol.4 , pp. 419-41
Roger V., Desrues J., Viggiani G. (1998) Experiments on strain Localisation in dense sand under isochoric conditions, in:
Localisation and Bifurcation Theory for Soils and Rocks, Oka F. Ed., Balkema, pp. 239-248
Questions :
a
a
a
a
Does localisation exist in undrained tests ?
Is it different from drained tests ?
(What is different ?)
What are the governing parameters ?
Questions :
a
a
a
a
Does localisation exist in undrained tests ?
Is it different from drained tests ?
(What is different ?)
What are the governing parameters ?
Localization in an undrained test dilatant specimen
Localization in an undrained test contractant specimen
Results
a Does localisation exist in undrained tests ?
Yes, in both dilatant and contractant specimens
a Is it different from drained tests ?
a (What is different ?)
a What are the governing parameters ?
Results
a (What is different ?)
drained vs undrained localization
s'1
--s'3
8
shfnd02 - Undrained BiaxialTest
shf40 - Drained Biaxial Test
sig'3 ini = 100kPa
7
900
U (kPa)
pore
pressure
700
S'3
effective
confining
pressure
6
500
5
4
300
3
100
2
-100
1
0
0
0,02
0,04
0,06
0,08
0,1
0,12
-300
0,14
epsa
Results
Yes !
a What is different ?
Results
Yes !
Results
Yes !
first evidence: it may be delayed considerably in terms of
critical strain
cavitation in the pore fluid
U (kPa)
R
Cavitation pressure
at 20°C
εaxiale (%)
εaxiale (%)
U0=100, 300, 600, 900 kPa ; σ ’ 3 = 100 kPa
Outline
a a brief introduction to the phenomenon:
experimental observations of strain
localization
a the undrained case : what is different
a HM coupled numerical analysis of drained,
undrained and partially drained biaxial tests
in sand
Objectives :
to study the response of the Localization criterion
in the context of hydromechanical coupling :
Localisation criterion : constitutive models can provide a prediction of
the onset of strain localisation using a theoretical approach socalled shear band analysis which leads to a bifurcation criterion,
solely based on the local behaviour of the material
`Comparison with experimental finding that in
undrained dilating material, localization can be
precluded by pore pressure depletion;
`Comparison between the bifurcation prediction (local
criterion) and the “spontaneous” response of the
numerical model;
Studied case :
Modeling biaxial tests on saturated
Hostun RF S28 sand, with or
without geometrical
imperfections, with a special
attention to Strain Localisation
Different cases :
a Drained – Undrained,
a Rate effect – permeability effect
a Special tests : injection
Theoretical &Numerical
tools used :
aLarge strain, fully coupled, Finite Element
formulation implemented in LAGAMINE
FEM Code ( Geomac, ULg)
aHypoplastic Constitutive model CLoE
aNon Linear Shear Band analysis for
hypoplastic models : bifurcation criterion
CLoE : a Hypoplastic Model developped with
special attention to localisation studies
C consistance
LoE Localisation Explicite
∇
limit surface
general
stress state
axisymmetric
stress state
Out-of-axis shear moduli
Explicit Bifurcation Criterion for CLoE
Shear Band Equations :
G G
1
0
F = F + g⊗n
G
G
n .σ 1 = n .σ 0
σ = f ( F )
• Incrementally Linear (ized) case :
G G
det( n . L. n ) = 0
• General case :
G
G G
G
0
n . f ( F + g ⊗ n ) = n . f ( F 0 )
• CLoE :
C = Pil−1blk nk n j + Pjl−1blk nk ni − 2 = 0
Drained vs Undrained behavior
of porous media
a Drained behavior means that no pore pressure is generated in
the medium due to the deformation process, because the pore
fluid
is able to flow with respect to the skeleton. Volumetric strain
is possible. Permeable boundaries, and slow process are
necessary.
a Undrained behavior means that pore pressure is generated
because the pore fluid cannot flow with respect to the
skeleton to accommodate the deformation process. The
deformation is isochoric (no volume change). This can result
from different situations :
` impermeable boundaries of the domain (e.g. laboratory test
specimen)
` very rapid loading process (e.g. earthquakes)
` very low permeability (clays, argiliceous rocks)
of porous media
In Undrained situations, one can distinguish between
Globally undrained and Locally undrained
In GU situations, relative drainage can appear between zones of the domain…
for example, between shear bands and blocks in our case;
(Vardoulakis, 1991)
of porous media
In Undrained situations, one can distinguish between
Globally undrained and Locally undrained
In GU situations, relative drainage can appear between zones of the domain…
for example, between shear bands and blocks in our case;
In LU situations, no relative drainage can take place, volumetric strain is zero
in every point in the domain.
Pore pressure field will become heterogeneous if shear banding tends to start.
Local reinforcement/weakening can be expected. But this may be vanishing
with time, due to delayed relative drainage (diffusion). This process can be
unsafe.
Biaxial test modeling :
Perfect / Imperfect
Next…
HM Coupling & Localization
9Comparison Meca Only – HM drained
9Comparison Open Drainage
Slow – Fast – Very Fast
9Close Drainage Slow – Fast
9Delayed Drainage
9Injection
9Delayed Drainage
9Injection
2,185
2,37
2,5
2.0
2.5
Numerical tests :
Calcul MécaPur compression, imparfait, pesant (c1)
Meca Only ( = dry) versus HM saturated
+ Open Drainage + Slow
(with / without geometrical imperfections)
CLoE law, dense RF-S28 sand (all computations)
Bifurcation : Starts first in a few elements, in the
vicinity of the notches
…then extends to almost all the elements at axial
strain about 2,5 in both MO and HM case;
Numerical “spontaneous” localization develops in
the same way in both tests;
In the HM case, on can see the flow of the fluid
toward the (dilating) shear bands .
Calcul couplé, compression, imparfait,
Non pesant, drainage ouvert, lent (c7)
Comparison axial Load- Strain
Bifurcation MO & HM DO slow, both perfect
MO & HM DO slow, both perfect : loc everywhere at [2.23;2.3];
consistent with local integration : bif. at 2.24
Comparison Meca Only – HM drained
Hydro Mechanical coupling ok in the drained limit
Localization criterion in effective stress ok
9Delayed Drainage
9Injection
aComparison Meca Only – HM drained
aComparison Open Drainage
Slow : 1,2 mm/min …
Fast : x 1000
Very Fast : x 1000 000
0,012 min-1
12 min-1
12 000 min-1
(soit 1,2 km/min !)
1,5
2.0
1,65
1,7
2,5
2.5
rapide
lent
Calcul couplé, compression, imparfait, Non pesant, drainage ouvert, rapide (c8)
OD slow vs OD fast :
•
bifurcation : more or less the same, starts
somewhat later in the fast but generalizes at 2.5 in
both cases
•
no numerical « spontaneous » localization in the
fast test, contrary to in the slow test
•
Fluid flow is
organized
differentlyDéformation
in the two
tests;
Équipe
GDR : Géomatériaux,
et Rupture
Calcul couplé, compression, imparfait,
Non pesant, drainage ouvert, lent (c7)
Comparison axial Load- Strain
Bifurcation OD, fast
Bifurcation OD, slow & MO
a Comparison Meca Only – HM drained
a Comparison Open Drainage
Slow : 1,2 mm/min …
Fast : x 1000
Very Fast : x 1000 000
(i.e.1,2 km/min !)
0,012 min-1
12 min-1
12 000 min-1
¾ results : numerical « spontaneous » localization does not develop (already
the case for “fast” test),
¾ bifurcation is detected in a few elements in the corners of the specimen,
¾ load-strain curve shows that
¾ i) first, it departs completely from the drained tests …
¾ ii) then, the axial load starts increasing very fast …
¾ iii) but it coincides with the undrained test response (Closed Drainage)
Next…
Drainage & Rate effect
Hydro Mechanical coupling ok in the undrained limit :
indeed, open drainage with very high rate is equivalent
to closed drainage.
Localization criterion in effective stress ok in the
undrained limit : the experimental observation that
localization will NOT take place in an undrained
test is properly predicted by the theoretical &
numerical tools implemented.
9Closed Drainage Slow – Fast
9Delayed Drainage
9Injection
1.7
3.0
Closed Drainage :
Slow vs fast CD, perfect vs
imperfect geometry : no
bifurcation predicted, no
numerical localisation observed…
Fast Closed Drainage :
some perturbations can
Calcul couplé, compression, imparfait, Non pesant,
be
observed,
drainage
fermé, lent (c9) but not
Pas de bifurcation détectée.
localized. Example :
fluid flow in the
specimen (idem slow
case)
Fast case
9Delayed Drainage
9Injection
9Conclusion
9Delayed Drainage
9Injection
Very Fast OD (no
imperfections) followed by
relaxation with drainage.
Loading phase :
NO numerical “spontaneous”
localisation ; theoretical
bifurcation limited to corners
Drainage phase:
No much evolution toward
localization : deformation
remains limited and constrained
everywhere; Stresses decreases,
strain heterogeneities tend to
smooth out.
0.0004
0.00042
0.0005
0.0008
0.002
0.01
Pi : [-140,+100 kPa]
Pi : [+70,+100 kPa]
Pi: [-600,+100 kPa]
Pi: [-600,+100 kPa]
Pi: [-590,+100 kPa]
Pi : [-530,+100 kPa]
Pi : [-390,+100 kPa]
Sig moyenne effective sig’m [-1600, -300 kPa]
Q barre [0.8 , 1]
Epsdev [0.05 , 0.1]
Sig moyenne effective sig’m [auto]
C16 bis : DO rapide + relaxation avec drainage (relaxation)
Conclusions
aHM coupled analysis in LAGAMINE with
CLoE is ok
aShear band bifurcation analysis with CLoE
in LAGAMINE …. ok
aThese tools are effective in predicting
experimental observation in both drained,
undrained and partially drained situations.
Thank You !
Geometrical imperfections :
Comparison axial Load- Strain : fast
Open Dr fast & Closed Dr :
… identical

Hydro-mechanical coupling and strain localization in saturated

Transcription

Documents pareils

La climatisation - Greta de Grenoble

Bac pro PSPA - parcoursemploi

Charles ROBBEZ-MASSON - Faculté de droit de Grenoble

bureaux ifts a grenoble (38)

fiche technique top fun.pub

Acheter appartement 4 pièces GRENOBLE 74m²

MODIFICATION DE L`ENSEIGNE

Les resto`U partenaires du festival de la BD

Obtenir un CDD ou un CDI de pilote projet ou d

Acheter commerces et bureaux GRENOBLE