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7.3
Titrate:
WTNV122 - Triaxial Essai not drained with law CAM_CLAY
Date:
27/09/04
Author (S):
G. DEBRUYNE, J. EL GHARIB Key
:
V7.31.122-A Page:
1/10
Organization (S): EDF-R & D/AMA
Handbook of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of structures
voluminal
Document: V7.31.122
WTNV122 - Triaxial Essai not drained with the law
CAM_CLAY
Summary:
This test makes it possible to validate the mechanical law elastoplastic Cam_Clay specific to the grounds normally
consolidated. This law integrates an elastoplastic hydrostatic mechanism (of which the elastic part is
non-linear and the threshold of flow corresponds to the pressure of consolidation) coupled to a mechanism
deviatoric elastoplastic the elastic part is linear. The behavior is hardening or
softening according to the combination of the two mechanisms.
Three different modelings are carried out in 3D. In each modeling, the test is carried out in
hydro-mechanical coupling and it include/understand two ways of loading:
Modeling A is characterized by:
·
a hydrostatic way of compression in condition drained until the pressure of consolidation,
·
a way not-drained by maintaining the pressures lateral confining on the sample and by imposing one
vertical displacement of compression which induces a triaxial state of stresses, and a plastic mode
contractor.
Modeling B is characterized by:
·
a hydrostatic way of compression in condition drained until the critical pressure, equalizes with
half of the pressure of consolidation,
·
a way not-drained by maintaining the pressures lateral confining on the sample and by imposing one
vertical displacement of compression which induces a triaxial state of stresses up to the critical point.
Modeling C is characterized by:
·
a hydrostatic way of compression in condition drained until a pressure lower than
critical pressure,
·
a way not-drained by maintaining the pressures lateral confining on the sample and by imposing one
vertical displacement of compression which induces a plastic state of stresses triaxial dilating.
Handbook of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HT-66/04/005/A
Code_Aster ®
Version
7.3
Titrate:
WTNV122 - Triaxial Essai not drained with law CAM_CLAY
Date:
27/09/04
Author (S):
G. DEBRUYNE, J. EL GHARIB Key
:
V7.31.122-A Page:
2/10
1
Problem of reference
1.1 Geometry
Z
E
H
y
X
L
height: H = 1m
width: L = 1 m
thickness: E = 1 m
1.2
Properties of material
E = 22.4E6 Pa
= 0.3
= 1.E - 5
Parameters specific to CAM_CLAY:
PORO = 0.14, = 0.25, = 0.05, M = 0.9, CLOSE _ CRIT =.
3e5 Pa, Pa = 1.E5 Pa
1.3
Boundary conditions and loadings
The first way of loading is carried out with a state of hydrostatic stresses:
= = = P. One makes a first elastic design to P = Pa (to establish an initial state
xx
yy
zz
plastically acceptable). One increases then P to P, the pressure of water is maintained
sup
null
1
PRE = 0 (drained condition). For the second way, one maintains the pressure P on the faces
side and one imposes then a vertical displacement imposed in compression to model one
triaxial compression test, calculation is now not drained, which corresponds to a hydrostatic flow no one on
all faces.
For modeling a: P
= P
=.
6e5Pa = 2P (final state contracting)
sup
ion
consolidat
Cr
For modeling b: P
= P (final state criticizes with null voluminal variation)
sup
Cr
For modeling C: P
=.
2e5Pa < P (final state dilating)
sup
Cr
1.4 Conditions
initial
The plastic condition of compatibility requires that in an initial state the hydrostatic constraint be
strictly higher than zero. To initialize this constraint, one chose to carry out at the beginning a calculation
purely elastic while making evolve/move pressure of 0. with 1.E5 Pa. One only extracts from this calculation
the stress field at the points of gauss. This stress field resulting from the elastic design is
regarded as the initial state of the hydrostatic constraint necessary to the law Cam_Clay of calculation
according to.
Handbook of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HT-66/04/005/A
Code_Aster ®
Version
7.3
Titrate:
WTNV122 - Triaxial Essai not drained with law CAM_CLAY
Date:
27/09/04
Author (S):
G. DEBRUYNE, J. EL GHARIB Key
:
V7.31.122-A Page:
3/10
2
Reference solution
An exact solution exists as much as the loading is hydrostatic (cf SSNV160). For the second
triaxial way, an analytical solution is not obvious to find. In the same way, one does not have
data and of triaxial experimental test results allowing to compare with calculations.
This test is a test of not-regression.
Handbook of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HT-66/04/005/A
Code_Aster ®
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Titrate:
WTNV122 - Triaxial Essai not drained with law CAM_CLAY
Date:
27/09/04
Author (S):
G. DEBRUYNE, J. EL GHARIB Key
:
V7.31.122-A Page:
4/10
3 Modeling
With
Modeling A is characterized by:
·
a hydrostatic way of compression in condition drained until the pressure of
consolidation,
·
a way not-drained by maintaining the pressures lateral confining on the sample and while imposing
a vertical displacement of compression which induces a triaxial state of stresses, and a mode
contracting plastic.
3.1
Characteristics of modeling
Modeling 3D
Z
NO3
NO5
NO8
NO2
NO7
y
NO1
NO4
NO6
NO12
NO10
NO9
NO11
X
NO15
NO17
NO20
NO14
NO19
NO13
NO18
NO16
3.2
Characteristics of the grid
A number of nodes:
20
A number of meshs:
1 of type HEXA 20
6 of type QUAD 8
The following meshs are defined:
DROITE
NO3 NO5 NO8 NO10 NO12 NO15 NO17 NO20
GAUCHE
NO1 NO4 NO6 NO9 NO11 NO13 NO16 NO18
DEVANT
NO6 NO7 NO8 NO11 NO12 NO18 NO19 NO20
DERRIERE
NO1 NO2 NO3 NO9 NO10 NO13 NO14 NO15
BAS
NO13 NO14 NO15 NO16 NO17 NO18 NO19 NO20
HAUT
NO1 NO2 NO3 NO4 NO5 NO6 NO7 NO8
To represent the 1/8th structure, the boundary conditions in displacement imposed are:
On face BAS: DZ = 0
On face GAUCHE: DY = 0
On face DERRIERE: DX = 0
The loading is consisted of the same pressure divided into compression on the 3 meshs: `HAUT,
“DROITE” and “DEVANT” to simulate a hydrostatic test, and of a null water pressure to simulate
the condition of drainage (
1
PRE = 0). Then, the pressure distributed is maintained constant on
side faces “DROITE” and “DEVANT”, a displacement DZ is imposed on variable face “HAUT”
with time, and one changes the hydraulic loading (null flow) to simulate the condition not
drained.
Handbook of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HT-66/04/005/A
Code_Aster ®
Version
7.3
Titrate:
WTNV122 - Triaxial Essai not drained with law CAM_CLAY
Date:
27/09/04
Author (S):
G. DEBRUYNE, J. EL GHARIB Key
:
V7.31.122-A Page:
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3.3 Functionalities
tested
Commands
DEFI_MATERIAU CAM_CLAY
STAT_NON_LINE COMP_INCR
RELATION= `KIT_HM'
`RELATION_KIT'=
“CAM_CLAY”
“LIQU_SATU”
“HYDR_UTIL”
NEWTON
STAMP = “TANGENT”
3.4
Sizes tested and results
The components, and of the constraint are tested at moments 3., 6., 15. and 20. and
xx
yy
zz
value of the pressure of water PRE1 at moment 20 with node NO8. The values of reference are
values of not-regression.
Values of and:
xx
yy
Moment
Reference
Aster
1st loading
3. 3.000000+05
3.000000+05
1st loading
6. 6.000000+05
6.000000+05
2nd loading
15. 2.590356+05
2.590355371917+05
2nd loading
20. 2.495777+05
2.495776491115+05
Values of:
zz
Moment
Reference
Aster
1st loading
3. 3.000000+05
3.000000+05
1st loading
6. 6.000000+05
6.000000+05
2nd loading
15. 5.650431+05
5.650429335188+05
2nd loading
20. 5.578873+05
5.578813428168+05
Values of PRE1:
Moment
Reference
Aster
2emechargement
20. 3.50422+05
3.50422350888+05
Handbook of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HT-66/04/005/A
Code_Aster ®
Version
7.3
Titrate:
WTNV122 - Triaxial Essai not drained with law CAM_CLAY
Date:
27/09/04
Author (S):
G. DEBRUYNE, J. EL GHARIB Key
:
V7.31.122-A Page:
6/10
4 Modeling
B
Modeling B is characterized by:
·
a hydrostatic way of compression in condition drained until the critical pressure,
equalize with half of the pressure of consolidation,
·
a way not-drained by maintaining the pressures lateral confining on the sample and while imposing
a vertical displacement of compression which induces a triaxial state of stresses until
not criticizes.
4.1
Characteristics of modeling
Idem modeling A
4.2
Characteristics of the grid
Idem modeling A
4.3 Functionalities
tested
Idem modeling A
4.4
Sizes tested and results
The components, and of the constraint are tested at moments 3., 6., 15. and 20. and
xx
yy
zz
value of the pressure of water PRE1 at moment 20 with node NO8. The values of reference are
values of not-regression.
Values of and:
xx
yy
Moment
Reference
Aster
1st loading
3. 2.000000+05
2.000000+05
1st loading
6. 3.000000+05
3.000000+05
2nd loading
15.
2.100000+05
2.099999 +05
2nd loading
20.
2.100000+05
2.100000+05
Values of:
zz
Moment
Reference
Aster
1st loading
3. 2.000000+05
2.000000+05
1st loading
6. 3.000000+05
3.000000+05
2nd loading
15. 4.800000+05
4.799999+05
2nd loading
20. 4.800000+05
4.800000
+05
Values of PRE1:
Moment
Reference
Aster
2emechargement
20. 9.00000+E4
9.00000+E4
Handbook of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HT-66/04/005/A
Code_Aster ®
Version
7.3
Titrate:
WTNV122 - Triaxial Essai not drained with law CAM_CLAY
Date:
27/09/04
Author (S):
G. DEBRUYNE, J. EL GHARIB Key
:
V7.31.122-A Page:
7/10
5 Modeling
C
Modeling C is characterized by:
·
a hydrostatic way of compression in condition drained until a pressure lower than
critical pressure,
·
a way not-drained by maintaining the pressures lateral confining on the sample and while imposing
a vertical displacement of compression which induces a triaxial state of stresses dilating
plastic.
5.1
Characteristics of modeling
Idem modeling A
5.2
Characteristics of the grid
Idem modeling A
5.3 Functionalities
tested
Idem modeling A
5.4
Sizes tested and results
The components, and of the constraint are tested at moments 3., 6., 15. and 20. and
xx
yy
zz
value of the pressure of water PRE1 at moment 20 with node NO8. The values of reference are
values of not-regression.
Values of and:
xx
yy
Moment
Reference
Aster
1st loading
3. 2.000000+05
2.000000+05
1st loading
6. 2.200000+05
2.200000+05
2nd loading
15.
1.560470+05
1.560470100963+05
2nd loading
20.
1.815567+05
1.815567285399+05
Values of:
zz
Moment
Reference
Aster
1st loading
3. 2.000000+05
2.000000+05
1st loading
6. 2.200000+05
2.200000+05
2nd loading
15. 4.156324+05
4.156324653437+05
2nd loading
20. 4.382215+05
4.382215080457+05
Values of PRE1:
Moment
Reference
Aster
2emechargement
20. 3.844327+E4
3.844327146008+E4
Handbook of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HT-66/04/005/A
Code_Aster ®
Version
7.3
Titrate:
WTNV122 - Triaxial Essai not drained with law CAM_CLAY
Date:
27/09/04
Author (S):
G. DEBRUYNE, J. EL GHARIB Key
:
V7.31.122-A Page:
8/10
6
Summary of the results
tr ()
By interpreting the diagram, (P, Q), P = -
and Q = - (-) for three modelings of
3
3
1
this case test, one notes well that in modeling A [Figure 6-a], the loading remains
hydrostatic up to a value of 6.E5Pa. Once vertical displacement is imposed and
vary with time, the pressures on the side faces being maintained constant, a diverter
constraints is induced and increases with time with a positive work hardening. When one
bring closer the point Q = MP, one tends towards perfect plasticity with plastic flow without
work hardening and without variation of constraints (see [§6] Doc. [R7.01.14]).
MP
Q =
Appear 6-a: Q according to P (modeling A)
In modeling B [Figure 6-b], after a hydrostatic loading which reaches the critical pressure
with 3.E5Pa, the second loading is only deviatoric with a hydrostatic pressure
maintained with 3.E5Pa. When one reaches the point criticizes, one touches the critical slope, where plasticity is
perfect with plastic flow without work hardening and variation of constraints.
Handbook of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HT-66/04/005/A
Code_Aster ®
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Titrate:
WTNV122 - Triaxial Essai not drained with law CAM_CLAY
Date:
27/09/04
Author (S):
G. DEBRUYNE, J. EL GHARIB Key
:
V7.31.122-A Page:
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Appear 6-b: Q according to P (modeling B)
In modeling C [Figure 6-c], vertical displacement is imposed before the loading
hydrostatic reached the critical pressure. The diverter of the constraints varies with time, during
that the pressures on the side faces are maintained constant. Like the criterion of plasticity
is reached in the field of dilatancy, work hardening is negative and the diverter of the constraints
decrease with time.
Appear 6-c: Q according to P (modeling C)
Handbook of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HT-66/04/005/A
Code_Aster ®
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Titrate:
WTNV122 - Triaxial Essai not drained with law CAM_CLAY
Date:
27/09/04
Author (S):
G. DEBRUYNE, J. EL GHARIB Key
:
V7.31.122-A Page:
10/10
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