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®
Version
7.3
Titrate:
WTNV124 Essai of désaturation-consolidation: model of BARCELONA
Date:
27/09/04
Author (S):
G. DEBRUYNE, J. EL GHARIB
Key
:
V7.31.124-A
Page:
1/8
Manual of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HT-66/04/005/A
Organization (S):
EDF-R & D/AMA
Manual of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of structures
voluminal
Document: V7.31.124
WTNV124 - Test of désaturation-consolidation
with the model of Barcelona
Summary:
This test makes it possible to validate the model of Barcelona, which integrates an elastoplastic mechanical law coupled to
hydraulics (and possibly with thermics) in condition of nonsaturation of the liquid phase. This law
integrate an elastoplastic hydrostatic mechanism (of which the elastic part is non-linear and the threshold
of flow corresponds to a pressure of variable consolidation with suction) coupled to a mechanism
deviatoric elastoplastic. The characteristics of these mechanisms depend on suction (i.e.
difference between gas pressure and pressure of fluid). There are in particular two mechanisms
of work hardening in completely coupled pressure and suction. The surface of load of the model of Barcelona
present (in the diagram pressure hydrostatic-diverter and for a given suction) in the form
of an ellipse cutting the hydrostatic axis in two points: the value of the pressure of consolidation and
cohesion of material proportional to suction. In condition of complete saturation, this criterion is reduced to
that of the Cam_Clay model specific to the saturated normally consolidated grounds.
This test carried out in hydro-mechanical coupling (modeling HHM) includes/understands two ways of
loading:
1) a way of desaturation while making increase the capillary pressure beyond the threshold of plasticity
hydrous.
2) a hydrostatic way of compression on the désaturé sample.
Modeling is carried out in 3D.
Code_Aster
®
Version
7.3
Titrate:
WTNV124 Essai of désaturation-consolidation: model of BARCELONA
Date:
27/09/04
Author (S):
G. DEBRUYNE, J. EL GHARIB
Key
:
V7.31.124-A
Page:
2/8
Manual of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HT-66/04/005/A
1
Problem of reference
1.1 Geometry
Z
X
y
L
H
E
height: H = 1m
width: L = 1 m
thickness: E = 1 m
1.2
Properties of material
Elastic thermo properties:
7
4
.
22 E
E
=
AP
3
.
0
=
3
/
2500
m
kg
=
Parameters specific to the model of CAM_CLAY:
·
Initial porosity
14
.
0
=
PORO
·
Modulate plastic compressibility with of saturated
25
.
0
=
,
·
Modulate elastic compressibility
05
.
0
=
,
·
Critical line slope
9
.
0
=
M
,
·
Critical pressure equalizes with half of the pressure of consolidation to saturation
AP
E
CRIT
NEAR
7
.
3
_
=
,
·
Pressure of reference
5
.
1 E
AP
=
AP
Additional parameters specific to BARCELONA:
·
Parameters allowing to calculate the module of compressibility according to suction
[
]
6
5
.
12
,
75
.
0
,
)
exp (
)
1
(
)
0
(
)
(
-
=
=
+
-
-
=
E
R
R
p
R
p
C
C
·
Slope of cohesion
6
.
0
=
C
K
·
Initial threshold of suction PC0_INIT
7
6
)
0
(
0
E
p
C
=
·
Modulate elastic compressibility of suction
01
.
0
=
S
·
Modulate plastic compressibility of suction
05
.
0
=
S
Code_Aster
®
Version
7.3
Titrate:
WTNV124 Essai of désaturation-consolidation: model of BARCELONA
Date:
27/09/04
Author (S):
G. DEBRUYNE, J. EL GHARIB
Key
:
V7.31.124-A
Page:
3/8
Manual of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HT-66/04/005/A
Hydraulic properties: the hydraulic properties of material which are independent of the model
from Barcelona but nevertheless necessary to carry out coupled calculation are presented in
table below:
Liquid water
Density (kg.m
- 3
)
Heat with constant pressure (J.K
- 1
)
Opposite of the coefficient of compressibility (AP
- 1
)
Intrinsic permeability (m
2
)
viscosity
1.10
3
4180
0.510
- 9
1.10
- 18
1.10
- 3
Initial State
Porosity
Temperature
Capillary pressure
Gas pressure
Initial saturation in fluid
0,14
293°K
1.51 10
7
1.51 10
5
0,99
Constants
Constant of perfect gases
8,315
Coefficients
homogenized
Homogenized density
Capillary curve
Coefficient of Biot
2400
()
(
)
C
C
p
P
S
9
10
6
1
99
.
0
-
-
=
1
1.3
Boundary conditions and loadings
The first way of loading consists in carrying out a desaturation, with a pressure
hydrostatic constant
AP
E
P
7
.
1
=
(the gas pressure is maintained constant
with
AP
E
PRE
5
.
1
2
=
during all the test). The capillary pressure varies from zero until
AP
E
PRE
7
.
7
1
=
, beyond the threshold of plasticization equal initially to
AP
E
PRE
7
.
6
1
=
.
Work hardening due to the increase in suction causes an increase in the threshold of consolidation,
since two work hardenings hydrous and mechanical are coupled in the model of Barcelona. One
checks while following the second way consisting in exerting a hydrostatic pressure exceeding it
initial threshold (
AP
E
P
idiot
7
.
6
=
) without causing plasticization.
1.4 Conditions
initial
The initial stress (forced effective of Bishop) is selected in such way that the stress used
in the behavior (
D
gz
T
p 1
+
=
) is inside the surface of load.
Code_Aster
®
Version
7.3
Titrate:
WTNV124 Essai of désaturation-consolidation: model of BARCELONA
Date:
27/09/04
Author (S):
G. DEBRUYNE, J. EL GHARIB
Key
:
V7.31.124-A
Page:
4/8
Manual of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HT-66/04/005/A
2
Reference solution
In the absence of loading deviatoric, an exact solution is available for the deformations and
thresholds of work hardening at all the stages of the loading:
Reversible voluminal deformation in mechanical loading
0
0
1
P
P
Ln
E
v
+
=
Reversible voluminal deformation in hydrous loading
atm
atm
C
S
v
p
p
p
Ln
E
+
+
=
0
1
Total voluminal deformation in hydrous loading, after crossing of the threshold
:
0
if
0
)
1
(
C
p
C
p
atm
C
atm
C
S
v
p
p
p
p
Ln
E
>
-
+
+
+
+
=
Total voluminal deformation in mechanical loading, after crossing of the threshold of
consolidation:
P
dP
E
p
D
C
v
0
1
)
(
+
=
Coupling of the thresholds:
Cr
Cr
S
S
atm
C
C
P
dP
p
p
dp
-
-
=
+
0
0
Code_Aster
®
Version
7.3
Titrate:
WTNV124 Essai of désaturation-consolidation: model of BARCELONA
Date:
27/09/04
Author (S):
G. DEBRUYNE, J. EL GHARIB
Key
:
V7.31.124-A
Page:
5/8
Manual of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HT-66/04/005/A
3 Modeling
With
3.1
Characteristics of modeling
Modeling 3D
Z
X
y
NO12
NO2
NO3
NO10
NO9
NO13
NO15
NO14
NO11
NO20
NO19
NO18
NO1
NO7
NO6
NO8
NO16
NO4
NO5
NO17
3.2
Characteristics of the mesh
A number of nodes:
20
A number of meshs:
1 of type HEXA 20
6 of type QUAD 8
The following meshs are defined:
STRAIGHT LINE
NO3 NO5 NO8 NO10 NO12 NO15 NO17 NO20
LEFT
NO1 NO4 NO6 NO9 NO11 NO13 NO16 NO18
IN FRONT OF
NO6 NO7 NO8 NO11 NO12 NO18 NO19 NO20
BEHIND
NO1 NO2 NO3 NO9 NO10 NO13 NO14 NO15
LOW
NO13 NO14 NO15 NO16 NO17 NO18 NO19 NO20
HIGH
NO1 NO2 NO3 NO4 NO5 NO6 NO7 NO8
To account for the 1/8
ème
structure, the boundary conditions in displacement imposed are:
On the LOW face: DZ = 0
On the LEFT face: DY = 0
On the face BEHIND: DX = 0
The loading is consisted of the same pressure divided into compression on the 3 meshs: `HIGH,
“RIGHT” and “IN FRONT” to simulate a hydrostatic test. All the nodes are compelled with one
constant pressure of gas and with a suction varying from 0 to 7.10
7
AP
Code_Aster
®
Version
7.3
Titrate:
WTNV124 Essai of désaturation-consolidation: model of BARCELONA
Date:
27/09/04
Author (S):
G. DEBRUYNE, J. EL GHARIB
Key
:
V7.31.124-A
Page:
6/8
Manual of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HT-66/04/005/A
3.3 Functionalities
tested
Controls
DEFI_MATERIAU BARCELONA
STAT_NON_LINE COMP_INCR
NEWTON
RELATION= `KIT_HHM'
`RELATION_KIT'=
“BARCELONA”
“LIQU_SATU”
“HYDR_UTIL”
STAMP = “TANGENT”
3.4
Sizes tested and results
It is about a homogeneous test, the place of observation of the fields is indifferent. It will be tested
displacement
Z
U
with node 8 at moment 1 (end of the hydrostatic way), at moment 6.0 (crossing of
hydrous threshold) as well as the variables intern of indicator of plasticity and pressure criticizes with same
node. One tests then same the fields at moment 10 (loading purely hydrostatic in
crossing the old threshold thus without plasticization) and finally at the moment 20 where the new one is crossed
mechanical threshold (plasticization).
P
2
C
L
1
C
L
0
C
p
1
C
p
C
p
0
C
L
20
20
10
10
6
6
1
1
Values of
Z
U
:
Moment
Reference
Aster
1
Er
loading
1. - 5.607E-02
- 5.593E-02
2nd loading
6.0 - 7.565E-02
- 7.647E-02
3rd loading
10.0 - 1.3097E-01
- 1.3097E-01
4th loading
20. - 2.11952E-01
- 2.11951E-01
Plastic indicator (mechanical threshold):
Moment
Reference
Aster
1
Er
loading
1. 0
0
2nd loading
6.0 0
0
3rd loading
10.0 0
0
4th loading
20. 1
1
Hydrous indicator of irreversibility:
Moment
Reference
Aster
1
Er
loading
1. 0
0
2nd loading
6.0 1
1
3rd loading
10.0 0
0
4th loading
20. 0
0
Code_Aster
®
Version
7.3
Titrate:
WTNV124 Essai of désaturation-consolidation: model of BARCELONA
Date:
27/09/04
Author (S):
G. DEBRUYNE, J. EL GHARIB
Key
:
V7.31.124-A
Page:
7/8
Manual of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HT-66/04/005/A
Value of the hydrous threshold:
Moment
Reference
Aster
1
Er
loading
1. 6e+07
6e+07
2nd loading
6.0 7e+07
7e+07
3rd loading
10.0 7e+07
7e+07
4th loading
20. 1.108E+10
1.108E+10
Value of the mechanical threshold:
Moment
Reference
Aster
1
Er
loading
1. 3e+07
3e+07
2nd loading
6.0 5.6661E+08
5.7459E+08
3rd loading
10.0 5.74596E+08
5.74596E+08
4th loading
20. 25.0631E+08
25.0630E+08
Code_Aster
®
Version
7.3
Titrate:
WTNV124 Essai of désaturation-consolidation: model of BARCELONA
Date:
27/09/04
Author (S):
G. DEBRUYNE, J. EL GHARIB
Key
:
V7.31.124-A
Page:
8/8
Manual of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HT-66/04/005/A
4
Summary of the results
One obtains results on displacements which present a variation compared to the solution
analytical of about 0.2% in the reversible field and of 1% in the plastic range.
even official report can be made on the values of the thresholds of consolidation.