Code_Aster
®
Version
7.2
Titrate:
WTNV123 - Triaxial compression test with fixed suction: model of BARCELONA
Date:
26/10/04
Author (S):
G. DEBRUYNE, J. EL GHARIB
Key
:
V7.31.123-A
Page:
1/8
Manual of Validation
V7.31 booklet: Thermo hydro-mechanical in saturated porous environment
HT-66/04/005/A
Organization (S):
EDF-R & D/AMA
Manual of Validation
V7.31 booklet: Thermo hydro-mechanical in saturated porous environment
Document: V7.31.123
WTNV123 - Triaxial compression test with suction fixed with
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) is declined in three modelings:
Modeling A includes/understands two ways of mechanical loading, suction being fixed at a value
agent with a degree of saturation of 90%:
1) a hydrostatic way of compression
2) a way maintaining the pressures lateral confining on the sample and imposing a vertical pressure
additional which induces a triaxial state of stresses, until reaching the surface of load and
to generate plastic deformations in the contracting field.
Modeling B takes again modeling A but with a criterion of convergence of balance on each
generalized stress.
Modeling C continues modeling B by a deviatoric discharge then hydrostatic conclusive by
a deviatoric refill plasticizing in the dilating field.
All these modelings are carried out in 3D on a hexahedral element.
Code_Aster
®
Version
7.2
Titrate:
WTNV123 - Triaxial compression test with fixed suction: model of BARCELONA
Date:
26/10/04
Author (S):
G. DEBRUYNE, J. EL GHARIB
Key
:
V7.31.123-A
Page:
2/8
Manual of Validation
V7.31 booklet: Thermo hydro-mechanical in saturated porous environment
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
10
4
.
22
=
E
AP
3
.
0
=
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
CRIT
NEAR
7
10
.
3
_
=
,
·
Pressure of reference
5
10
=
AP
AP
Parameters specific to BARCELONA:
·
Parameters allowing to calculate the module of compressibility according to suction
[
]
6
10
5
.
12
,
75
.
0
,
)
exp (
)
1
(
)
0
(
)
(
-
=
=
+
-
-
=
R
R
p
R
p
C
C
·
Slope of cohesion
6
.
0
=
C
K
·
Initial threshold of suction PC0_INIT
7
0
10
882
.
4
)
0
(
=
C
p
Code_Aster
®
Version
7.2
Titrate:
WTNV123 - Triaxial compression test with fixed suction: model of BARCELONA
Date:
26/10/04
Author (S):
G. DEBRUYNE, J. EL GHARIB
Key
:
V7.31.123-A
Page:
3/8
Manual of Validation
V7.31 booklet: Thermo hydro-mechanical in saturated porous environment
HT-66/04/005/A
·
Modulate elastic compressibility of suction
01
.
0
=
S
·
Modulate plastic compressibility of suction
05
.
0
=
S
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
)
thermal expansion factor of the fluid (K
- 1
)
1.10
3
4180
10
- 4
Skeleton
Heat-storage capacity with constant stress
800
Initial State
Porosity
Temperature
Capillary pressure
Gas pressure
Initial saturation in fluid
0,14
293°K
1.51 10
7
10
5
0,9
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
For all modelings, one starts with a hydrostatic way of loading, with one
constant capillary pressure
AP
PRE
7
10
51
.
1
1
=
starting from a hydrostatic initial state until one
total hydrostatic pressure of
AP
T
7
10
4
=
. The gas pressure is maintained constant
AP
PRE
5
10
2
=
. Then, the pressure is maintained
P
on the side faces and one increases
vertical pressure until
AP
T
7
10
7
11
=
in compression in order to obtain a state of stress
biaxial of revolution. The capillary pressure and the gas pressure are maintained constant. One
the plastic threshold in the contracting field crosses then.
For modeling C, one continues the loading by carrying out a discharge of the stress
deviatoric (of
AP
7
10
7
with
AP
7
10
4
), then a hydrostatic discharge (of
AP
7
10
4
with
AP
7
10
75
.
1
) and finally a deviatoric refill in order to plasticize in the dilating field.
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
+
=
) the criterion does not violate. Initial capillary pressure,
agent with a degree of saturation of 0.9, is equal to 15.1 MPa.
Code_Aster
®
Version
7.2
Titrate:
WTNV123 - Triaxial compression test with fixed suction: model of BARCELONA
Date:
26/10/04
Author (S):
G. DEBRUYNE, J. EL GHARIB
Key
:
V7.31.123-A
Page:
4/8
Manual of Validation
V7.31 booklet: Thermo hydro-mechanical in saturated porous environment
HT-66/04/005/A
2
Reference solution
An exact solution for displacement exists as much as the loading is hydrostatic. For
second way the analytical solution is not available.
Code_Aster
®
Version
7.2
Titrate:
WTNV123 - Triaxial compression test with fixed suction: model of BARCELONA
Date:
26/10/04
Author (S):
G. DEBRUYNE, J. EL GHARIB
Key
:
V7.31.123-A
Page:
5/8
Manual of Validation
V7.31 booklet: Thermo hydro-mechanical in saturated porous environment
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 imposed in displacement 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. Then, the pressure distributed is
maintained constant on the side faces “STRAIGHT LINE” and “IN FRONT OF”, the vertical pressure increases on
the face “HIGH”.
Code_Aster
®
Version
7.2
Titrate:
WTNV123 - Triaxial compression test with fixed suction: model of BARCELONA
Date:
26/10/04
Author (S):
G. DEBRUYNE, J. EL GHARIB
Key
:
V7.31.123-A
Page:
6/8
Manual of Validation
V7.31 booklet: Thermo hydro-mechanical in saturated porous environment
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 6 (end of the hydrostatic way) like at moment 20 (end of
the test) as well as the variables intern of indicator of plasticity and critical pressure to the same node.
Values of
Z
U
:
Moment
Reference Aster
Difference (%)
1
Er
loading
6. 7.031-02 7.03158-02 5.25
10
5
2nd loading
20. X 2.06016-01
Plastic indicator (mechanical threshold, hydrous threshold):
Moment
Reference Aster Difference
(%)
1
Er
loading
6. 0
0
0
2nd loading
20. 1
1
0
Pressure criticizes in condition of saturation:
Moment
Reference Aster Difference
(%)
1
Er
loading
6. 3.+07
3+07
7.45
10
14
2nd loading
20. X
3.4371+07
Value of the hydrous threshold:
Moment
Reference Aster Difference
(%)
1
Er
loading
6. 4.882+07
4.882+07 4.58
10
14
2nd loading
20. X
7.79806+07
4 Modeling
B
It acts exactly of the same modeling as previously but with a test of convergence
on each generalized stress. The results are appreciably the same ones.
Code_Aster
®
Version
7.2
Titrate:
WTNV123 - Triaxial compression test with fixed suction: model of BARCELONA
Date:
26/10/04
Author (S):
G. DEBRUYNE, J. EL GHARIB
Key
:
V7.31.123-A
Page:
7/8
Manual of Validation
V7.31 booklet: Thermo hydro-mechanical in saturated porous environment
HT-66/04/005/A
5 Modeling
C
5.1
Characteristics of modeling
It always acts of the same modeling but with a prolongation of the loading until
plasticization in the dilating field.
5.2 Functionalities
tested
Controls
DEFI_MATERIAU BARCELONA
STAT_NON_LINE COMP_INCR
NEWTON
RELATION= `KIT_HHM'
`RELATION_KIT'=
“BARCELONA”
“LIQU_SATU”
“HYDR_UTIL”
STAMP = TANGENT
5.3
Sizes tested and results
Displacement is tested
Z
U
with node 8 at moment 34 (deviatoric discharge), at moment 46
(hydrostatic discharge) and finally at moment 60 as well as the variables intern of indicator of
plasticity and critical pressure and hydrous threshold with the same node and the same moments.
Values of
Z
U
:
Moment
Reference Aster
Difference (%)
1
Er
loading
6. 7.031-02 7.03158-02
3.41
10
5
2nd loading
20. X 2.06016-01
3rd loading
34. X 8.67365-02
4th loading
46 X 7.48391-02
5th loading
60 X 3.73485-01
Plastic indicator (mechanical threshold):
Moment
Reference Aster
Difference (%)
1
Er
loading
6. 0
0
0
2nd loading
20. 1
1
0
3rd loading
34. 0
0
0
4th loading
46 0
0
0
5th loading
60 1
1
0
Pressure criticizes in condition of saturation:
Moment
Reference Aster
Difference (%)
1
Er
loading
6. 3.+07 3.+07
7.45
10
14
2nd loading
20. X
3.4371+07
3rd loading
34. X
3.4371+07
4th loading
46 X 3.4371+07
5th loading
60 X 3.34488+07
Value of the hydrous threshold:
Moment
Reference Aster
Difference (%)
1
Er
loading
6. 4.882+07 4.882+07
4.58
10
4
2nd loading
20. X
7.79804+07
3rd loading
34. X
7.79804+07
4th loading
46 X
7.79804+07
5th loading
60 X
7.1012+07
Code_Aster
®
Version
7.2
Titrate:
WTNV123 - Triaxial compression test with fixed suction: model of BARCELONA
Date:
26/10/04
Author (S):
G. DEBRUYNE, J. EL GHARIB
Key
:
V7.31.123-A
Page:
8/8
Manual of Validation
V7.31 booklet: Thermo hydro-mechanical in saturated porous environment
HT-66/04/005/A
6
Summary of the results
The only results of reference relate to the first hydrostatic loading, in this case them
displacements and the thresholds in pressure and suction are calculated with a precision higher than 1%.