Code_Aster ®
Version
7.2
Titrate:
WTNV123 - Triaxial Essai 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

Organization (S): EDF-R & D/AMA

Handbook of Validation
V7.31 booklet: Thermo hydro-mechanical in saturated porous environment
Document: V7.31.123

WTNV123 - Triaxial Essai 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 liquid). 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
correspondent 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 constraint.

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.
Handbook of Validation
V7.31 booklet: Thermo hydro-mechanical in saturated porous environment
HT-66/04/005/A

Code_Aster ®
Version
7.2
Titrate:
WTNV123 - Triaxial Essai 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

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

Elastic thermo properties:

7
E =
4
.
22 10 Pa
= 0.3

Parameters specific to the model of CAM_CLAY:

·
Initial porosity PORO = 0.14
·
Modulate plastic compressibility with of saturated = 0.25,
·
Modulate elastic compressibility = 0.05,
·
Slope of the straight line criticizes M = 0.9,
·
Critical pressure equalizes with half of the pressure of consolidation to saturation
CLOSE _ CRIT
7
=.
3 10 Pa,
·
Pressure of reference
5
Pa = 10 Pa

Parameters specific to BARCELONA:

·
Parameters allowing to calculate the module of compressibility according to suction
(p) = (
C
[)
0 1
(- R) exp (- p) + R,
C
]
- 6
R =
,
75
.
0
=
5
.
12 10
·
Slope of cohesion K =
6
.
0
C

·
Initial threshold of suction PC0_INIT
7
p ()
0 = 882
.
4
10
c0
Handbook of Validation
V7.31 booklet: Thermo hydro-mechanical in saturated porous environment
HT-66/04/005/A

Code_Aster ®
Version
7.2
Titrate:
WTNV123 - Triaxial Essai 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

·
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)
1.103
Heat with constant pressure (J.K-1)
4180
thermal dilation coefficient of the liquid (K-1)
10-4
Skeleton
Heat-storage capacity with constant constraint
800
Initial State
Porosity
0,14
Temperature
293°K
Capillary pressure
1.51 107


Gas pressure
105


Initial saturation in liquid
0,9
Constants
Constant of perfect gases
8,315
Coefficients
Homogenized density
2400
homogenized capillary Courbe
S (
9
-
C
P) = 0 99
. (1 -.
6 10
PC)
Coefficient of Biot
1

1.3
Boundary conditions and loadings

For all modelings, one starts with a hydrostatic way of loading, with one
capillary pressure constant PRE
7
1 = 51
.
1
10 Pa starting from a hydrostatic initial state until one
total hydrostatic pressure of
7
= 4 10 Pa. The gas pressure is maintained constant
T
PRE
5
2 = 10 Pa. Then, one maintains the pressure P on the side faces and one increases
vertical pressure until
7
= 7 10 Pa in compression in order to obtain a state of stress
T11
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 constraint
deviatoric (of
7
7 10 Pa with
7
4 10 Pa), then a hydrostatic discharge (of
7
4 10 Pa with
7
75
.
1
10 Pa) and finally a deviatoric refill in order to plasticize in the dilating field.

1.4 Conditions
initial

The initial constraint (forced effective of Bishop) is selected in such way that the constraint used
in the behavior (
D
= T + pgz1) does not violate the criterion. Initial capillary pressure,
correspondent with a degree of saturation of 0.9, is equal to 15.1 MPa.
Handbook of Validation
V7.31 booklet: Thermo hydro-mechanical in saturated porous environment
HT-66/04/005/A

Code_Aster ®
Version
7.2
Titrate:
WTNV123 - Triaxial Essai 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

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.
Handbook of Validation
V7.31 booklet: Thermo hydro-mechanical in saturated porous environment
HT-66/04/005/A

Code_Aster ®
Version
7.2
Titrate:
WTNV123 - Triaxial Essai 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

3 Modeling
With

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 imposed in displacement 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. Then, the pressure distributed is
maintained constant on side faces “DROITE” and “DEVANT”, the vertical pressure increases on
face “HAUT”.
Handbook of Validation
V7.31 booklet: Thermo hydro-mechanical in saturated porous environment
HT-66/04/005/A

Code_Aster ®
Version
7.2
Titrate:
WTNV123 - Triaxial Essai 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

3.3 Functionalities
tested

Commands



DEFI_MATERIAU BARCELONA


STAT_NON_LINE COMP_INCR
RELATION= `KIT_HHM'


`RELATION_KIT'=

“BARCELONA”

“LIQU_SATU”

“HYDR_UTIL”
NEWTON
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
uz displacement 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 uz:

Moment
Reference Aster
Difference (%)
1st loading
6. ­ 7.031-02 ­ 7.03158-02 5.25
10­5
2nd loading
20. X ­ 2.06016-01

Plastic indicator (mechanical threshold, hydrous threshold):

Moment
Reference Aster Difference
(%)
1st loading
6. 0
0
0
2nd loading
20. 1
1
0

Pressure criticizes in condition of saturation:

Moment
Reference Aster Difference
(%)
1st loading
6. 3.+07
3+07
­ 7.45
10­14
2nd loading
20. X
3.4371+07


Value of the hydrous threshold:

Moment
Reference Aster Difference
(%)
1st loading
6. 4.882+07
4.882+07 ­ 4.58
10­14
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 constraint. The results are appreciably the same ones.

Handbook of Validation
V7.31 booklet: Thermo hydro-mechanical in saturated porous environment
HT-66/04/005/A

Code_Aster ®
Version
7.2
Titrate:
WTNV123 - Triaxial Essai 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

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

Commands



DEFI_MATERIAU BARCELONA


STAT_NON_LINE COMP_INCR
RELATION= `KIT_HHM'


`RELATION_KIT'=

“BARCELONA”

“LIQU_SATU”

“HYDR_UTIL”
NEWTON
STAMP = TANGENT

5.3
Sizes tested and results

One tests uz displacement 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 uz:

Moment
Reference Aster
Difference (%)
1st loading
6. ­ 7.031-02 ­ 7.03158-02
3.41
10­5
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 (%)
1st 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 (%)
1st loading
6. 3.+07 3.+07
­ 7.45
10­14
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 (%)
1st loading
6. 4.882+07 4.882+07
­ 4.58
10­4
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

Handbook of Validation
V7.31 booklet: Thermo hydro-mechanical in saturated porous environment
HT-66/04/005/A

Code_Aster ®
Version
7.2
Titrate:
WTNV123 - Triaxial Essai 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

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%.
Handbook of Validation
V7.31 booklet: Thermo hydro-mechanical in saturated porous environment
HT-66/04/005/A

Outline document