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Code_Aster
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Version
7.4
Titrate:
WTNV100 - Triaxial compression test not drained with model CJS (level 1)
Date:
05/07/05
Author (S):
C. CHAVANT, pH. AUBERT
Key
:
V7.31.100-B
Page:
1/14
Manual of Validation
V7.31 booklet: Mechanical hydro Thermo in porous environment of voluminal structures
HT-66/05/005/A
Organization (S):
EDF-R & D/AMA, CNEPE















Manual of Validation
V7.31 booklet: Mechanical hydro Thermo in porous environment of voluminal structures
Document: V7.31.100



WTNV100 - Triaxial compression test not drained with the model
CJS (level 1)



Summary

This test makes it possible to validate level 1 of model CJS. It is about a triaxial compression test in not drained condition.
In the first two modelings, calculations are carried out only on the solid part of the ground,
the aspect not drained being modelized by a null voluminal deformation of the skeleton, they are modelings
3D which differs one from the other only by the mesh.
In the third modeling, the hydraulic coupling is taken into account, the sample is completely saturated,
the skeleton and the fluid are supposed to be incompressible.
By reason of symmetry, one is interested only in the eighth of a sample subjected to a triaxial compression test.
The level of containment is of 100 kPa.
The results obtained with model CJS1 are compared with an analytical solution.
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Code_Aster
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Version
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Titrate:
WTNV100 - Triaxial compression test not drained with model CJS (level 1)
Date:
05/07/05
Author (S):
C. CHAVANT, pH. AUBERT
Key
:
V7.31.100-B
Page:
2/14
Manual of Validation
V7.31 booklet: Mechanical hydro Thermo in porous environment of voluminal structures
HT-66/05/005/A
1
Problem of reference
1.1 Geometry
Z
X
y
E
L
H
C
With
B
height:
H = 1 m
width:
L = 1 m
thickness: E = 1 m
Co-ordinates of the points (in meters):
With
B
C
X 0. 0.
0.5
y 0. 1.
0.5
Z 0. 0.
0.5
1.2
Material property
E = 22,4 10
3
kPa
= 0,3
Coefficient of biot b: 1
Water is supposed to be incompressible: UN_SUR_K = 0
Parameters CJS1:
= - 0,03
= 0,82
R
m
= 0,289
P
has
= - 100 kPa
1.3
Initial conditions, boundary conditions, and loading
1.3.1 Pure mechanical modeling
Phase 1:
One brings the sample in a homogeneous state:
xx
yy
zz
0
0
0
=
=
, by imposing the pressure of
containment corresponding on the front, side straight line and higher faces. Displacements are
locked on the faces postpones (
U
X
=
0
), side left (
U
y
=
0
) and lower (
U
Z
=
0
).
Phase 2:
One maintains displacements locked on the faces postpones (
U
X
=
0
), side left (
U
y
=
0
) and
lower (
U
Z
=
0
). One applies a displacement imposed to the higher face:
()
U T
Z
, in order to
to obtain a deformation
zz
= -
20%
(counted starting from the beginning of phase 2). On the front faces
and side straight line, one imposes displacements respectively
()
U T
X
and
()
U T
y
, in order to have one
null voluminal deformation for the sample, i.e. finally that one imposes
xx
yy
zz
=
= -
2
. It is the manner of reproducing the behavior of the solid phase during a test
triaxial not drained.
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Code_Aster
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Version
7.4
Titrate:
WTNV100 - Triaxial compression test not drained with model CJS (level 1)
Date:
05/07/05
Author (S):
C. CHAVANT, pH. AUBERT
Key
:
V7.31.100-B
Page:
3/14
Manual of Validation
V7.31 booklet: Mechanical hydro Thermo in porous environment of voluminal structures
HT-66/05/005/A
1.3.2 Modeling coupled with hydraulics
Phase 1:
One brings the sample in a homogeneous state of effective stresses:
xx
yy
zz
0
0
0
=
=
, while imposing
corresponding total pressure on the front, side straight line and higher faces and while imposing
everywhere null water pressures. Displacements are locked on the faces postpones (
U
X
=
0
),
side left (
U
y
=
0
) and lower (
U
Z
=
0
).
Phase 2:
One maintains displacements locked on the faces postpones (
U
X
=
0
), side left (
U
y
=
0
) and
lower (
U
Z
=
0
).
On all the faces, hydraulic flows are null.
One applies a displacement forced to the higher face in order to obtain a deformation
zz
= -
20%
(counted starting from the beginning of phase 2). On the front faces and side straight line, one
impose boundary conditions in total stress:
.
(
)
N
kPa
=
=
0
100
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Code_Aster
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Titrate:
WTNV100 - Triaxial compression test not drained with model CJS (level 1)
Date:
05/07/05
Author (S):
C. CHAVANT, pH. AUBERT
Key
:
V7.31.100-B
Page:
4/14
Manual of Validation
V7.31 booklet: Mechanical hydro Thermo in porous environment of voluminal structures
HT-66/05/005/A
2
Reference solution
2.1
Reference solution for the water pressure into linear
0
,
0
p
0
indicating the stresses, deformations and pressures of water obtained in the phase one a:
(
)
(
) (
)
(
)
µ
-
=
-
+
-
-
-
= -
+
-
0
0
0
0
0
0
2
tr
B p p
m
p p
M
btr
fl
In this writing,
M
indicate the module of biot and
NR
M
=
1
.
The boundary conditions of null flow and the conservation of the water mass give
m
=
0
Boundary conditions on the side walls and the fact that the state of stress is homogeneous
give:
xx
xx
-
=
0
0
One has thus finally to solve the two equations:
(
)
(
)
µ
2
2
2
xx
zz
xx
xx
zz
LP
B
p
M
Np
+
+
=
+
= -
= -



And one obtains:
(
)
(
)
µ
µ
µ
xx
zz
zz
B
NR
B
NR
p
B
B
NR
= -
+
+
+
= -
+
+


2
2
2
2
In our case,
µ
xx
zz
zz
p
= -
= -
2
;
2.2
Development of analytical solution CJS
One has permanently:
for the deformations:
xx
yy
zz
=
= -
2
for the stresses:
xx
yy
=
Elastic phase:
While writing the elastic law simply, it comes:
µ
xx
xx
zz
=
-
0
µ
zz
zz
zz
=
+
0
2
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Code_Aster
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Titrate:
WTNV100 - Triaxial compression test not drained with model CJS (level 1)
Date:
05/07/05
Author (S):
C. CHAVANT, pH. AUBERT
Key
:
V7.31.100-B
Page:
5/14
Manual of Validation
V7.31 booklet: Mechanical hydro Thermo in porous environment of voluminal structures
HT-66/05/005/A
In addition, one also knows that during this phase
I
1
(= trace (
)) remain constant bus
v
=
0
. One in
deduced for the components from the diverter:
S
I
I
xx
xx
xx
zz
zz
=
-
=
-
-
= -
µ
µ
1
0
10
3
3
and
S
I
I
zz
zz
zz
zz
zz
=
-
=
-
+
=
µ
µ
1
0
10
3
3
2
2
that is to say:
S
II
zz
= -
6
µ
and
()
det S
zz
=
2
3
3
µ
Consequently:
()
()
H
S
= -
1
1 6
/
Thus when the criterion is reached
F
D
=
0
, one a:
(
)
(
)
S
R I
R I
II
m
zz
m
1
6
1
0
1 6
10
1 6
10
-
+
= -
-
+
=
µ
/
/
I.e. the transition enters the states rubber band and perfectly plastic is done for one
axial deformation equalizes with:
(
)
µ
zz
trans
m
R I
=
-
10
1 6
6
1
/
The corresponding state of stresses is noted:
(
)
µ
µ
xx
trans
xx
m
R I
=
-
-
0
10
1 6
6
1
/
and
(
)
µ
µ
zz
trans
zz
m
R I
=
+
-
0
10
1 6
2
6
1
/
Plastic phase:
One notes
S
D
-
the diverter of the reverse of the tensor S
Generally, there are the following sizes:
(
)
S
S
xx
zz
xx
yy
= -
-
=
1
3
S
xx
zz
xx
-
=
-
-
1
3
(
)
S
xxd
zz
xx
-
=
-
-
3
2
(
)
S
zz
zz
xx
=
-
2
3
(
)
S
zz
zz
xx
-
=
-
1
3
2
S
zzd
zz
xx
-
=
-
3
that is to say:
(
)
S
II
zz
xx
= -
-
2
3
and
()
(
)
det S
zz
xx
=
-
2
3
3
3
Consequently:
()
(
)
H
S
= -
1
1 6
/
One deduces some:
()
Q
xx
=
-
1
6 1
1 6
/
and
()
Q
zz
= -
-
2
3 1
1 6
/
moreover:
(
)
F
R
D
xx
m
=
-
+
1
6 1
1 6
/
and
(
)

F
R
D
zz
m
= -
-
+
2
3 1
1 6
/
Like one a:
()
=
-




=
-




=
sign S
S
S
R
R
ij
ij
II
II
C
m
C
&
1
1
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Code_Aster
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Titrate:
WTNV100 - Triaxial compression test not drained with model CJS (level 1)
Date:
05/07/05
Author (S):
C. CHAVANT, pH. AUBERT
Key
:
V7.31.100-B
Page:
6/14
Manual of Validation
V7.31 booklet: Mechanical hydro Thermo in porous environment of voluminal structures
HT-66/05/005/A
then the tensor
N
is written:
N
xx
=
+
+




1
3
1
6
1
2
and
N
zz
=
+
-
+




1
3
2
3
1
2
It comes then for
G
D
:
()
()
G
R
R
xx
D
m
m
=
-
+
-
-
+
+
+




1
6 1
1
3
3
1
6
1
1 6
1 6
2
/
/
()
()
G
R
R
zz
D
m
m
= -
-
+
-
-
+
+
-
+




2
3 1
1
3
3
2
3
1
1 6
1 6
2
/
/
One also has according to the elastic law:
xx
xx
trans
xx
=
+
and
zz
zz
trans
zz
=
+
where:
(
)
()
(
)
(
)
µ
µ
µ
xx
xx
D
xx
D
v
D
D
zz
D
xx
D
D
xx
D
zz
D
G
tr G
G
G
G
=
-
+
-
= -
-
-
+
2
2
2
(
)
()
(
)
(
)
µ
µ
µ
zz
zz
D
zz
D
v
D
D
zz
D
zz
D
D
xx
D
zz
D
G
tr G
G
G
G
=
-
+
-
=
-
-
+
2
2
2
2
and with:
xx
xx
xx
trans
=
-
and
zz
zz
zz
trans
=
-
maybe, according to what precedes, one has for
S
II
:
(
)
(
)
(
)
[
]
(
)
(
)
[
]
S
G
G
S
G
G
II
zz
trans
xx
trans
zz
zz
trans
D
zz
D
xx
D
II
trans
zz
zz
trans
D
zz
D
xx
D
= -
-
+
-
-
-
=
-
-
-
-
2
3
3
2
2
3 3
2
µ
µ
µ
µ
and for
I
1
:
(
)
(
)
I
I
G
G
trans
D
xx
D
zz
D
1
1
3
2
2
=
-
+
+
µ
One deduces from it that the function of load déviatoire is written:
(
)
(
)
(
)
[
]
(
)
(
)
(
)
F
S
G
G
R I
R
G
G
D
II
trans
zz
zz
trans
D
zz
D
xx
D
m
trans
m
D
xx
D
zz
D
=
-
-
-
-
-
-
+
-
+
+
1
2
3 3
2
1
3
2
2
1 6
1 6
1
µ
µ
µ
/
/
By taking account of the fact that
()
F
D
trans
=
0
, one finds then for the plastic multiplier:
(
)
(
)
(
)
(
) (
)
µ
µ
µ
D
zz
D
xx
D
m
xx
D
zz
D
zz
zz
trans
G
G
R
G
G
=
-
-
-
+
+
-
3
1
2
3
2
3
2
2
1 6
/
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Code_Aster
®
Version
7.4
Titrate:
WTNV100 - Triaxial compression test not drained with model CJS (level 1)
Date:
05/07/05
Author (S):
C. CHAVANT, pH. AUBERT
Key
:
V7.31.100-B
Page:
7/14
Manual of Validation
V7.31 booklet: Mechanical hydro Thermo in porous environment of voluminal structures
HT-66/05/005/A
what gives with the formulas of
G
xx
D
and
G
zz
D
the preceding ones:
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
µ
µ
µ
D
m
m
zz
zz
trans
R
R
=
-
+
- -
-
-
+
-
2
3
1
3
1
2
1
3
2
1 6
2
1 6
1 6
/
/
/
One concludes from it finally the analytical expression from the stresses:
While posing:
()
(
)
has
B
= -
=
+
1
3
1 6
2
/
;
One a:
(
)
(
)
(
)
(
)
(
)
µ
µ
µ
µ
µ
xx
xx
trans
m
m
m
m
m
zz
zz
trans
B has
R has
has
R
B
R
has
B
R
has
has
R
-
=
-
+
+
-
+
+








+
-




-
-
+








-
2
3
2
1
6
3
1
6
1
3
2
3
2
(
)
(
)
(
)
(
)
(
)
µ
µ
µ
µ
µ
zz
zz
trans
m
m
m
m
m
zz
zz
trans
B has
R has
has
R
B
R
has
B
R
has
has
R
-
=
-
-
+
-
+
-
+










+
-




-
-
+










-
2
2
3
2
2
3
3
2
3
1
3
2
3
2

2.3
Results of reference
Stresses
xx
,
yy
and
zz
at points A, B and C.

2.4
Uncertainty on the solution
Exact analytical solution for CJS1.
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Code_Aster
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Version
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Titrate:
WTNV100 - Triaxial compression test not drained with model CJS (level 1)
Date:
05/07/05
Author (S):
C. CHAVANT, pH. AUBERT
Key
:
V7.31.100-B
Page:
8/14
Manual of Validation
V7.31 booklet: Mechanical hydro Thermo in porous environment of voluminal structures
HT-66/05/005/A
3 Modeling
With
3.1
Characteristics of modeling
3D:
Z
X
y
B
Cutting: 1 in height, in width and thickness.
Loading of phase 1:
Confining pressure:
xx
yy
zz
0
0
0
=
=
: ­ 100 kPa.
Level 1 of model CJS

3.2
Characteristic of the mesh
A number of nodes: 8
A number of meshs and types: 1
HEXA8
and 6
QUA4

3.3 Functionalities
tested
Controls
DEFI_MATERIAU CJS
STAT_NON_LINE COMP_INCR
RELATION
“CJS”
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Code_Aster
®
Version
7.4
Titrate:
WTNV100 - Triaxial compression test not drained with model CJS (level 1)
Date:
05/07/05
Author (S):
C. CHAVANT, pH. AUBERT
Key
:
V7.31.100-B
Page:
9/14
Manual of Validation
V7.31 booklet: Mechanical hydro Thermo in porous environment of voluminal structures
HT-66/05/005/A
4
Results of modeling A
4.1 Values
tested
Localization Number
of command
Deformation
axial
zz
(%)
Stress
(kPa)
Reference
Aster %
difference
Not A and B
1
­ 0.25
xx
­ 78.461538 ­ 78.461538 <
10­5
2
­ 0.50
xx
­ 56.923077 ­ 56.923077 <
10­5
3
­ 0.75
xx
­ 53.606 ­ 53.606 <
10
­ 5
4
­ 1.0
xx
­ 54.480 ­ 54.480 <
10
­ 5
8
­ 5.0
xx
­ 68.467 ­ 68.467 <
10
­ 5
23
­ 20.0
xx
­ 120.918 ­ 120.918
<
10
­ 5
1
­ 0.25
yy
­ 78.461538 ­ 78.461538 <
10
­ 5
2
­ 0.50
yy
­ 56.923077 ­ 56.923077 <
10
­ 5
3
­ 0.75
yy
­ 53.606 ­ 53.606 <
10
­ 5
4
­ 1.0
yy
­ 54.480 ­ 54.480 <
10
­ 5
8
­ 5.0
yy
­ 68.467 ­ 68.467 <
10
­ 5
23
­ 20.0
yy
­ 120.918 ­ 120.918
<
10
­ 5
1
­ 0.25
zz
­ 143,07692 ­ 143,07692
<
10
­ 5
2
­ 0.50
zz
­ 186.153846 ­ 186.153846
<
10
­ 5
3
­ 0.75
zz
­ 196.818 ­ 196.818
<
10
­ 5
4
­ 1.0
zz
­ 200.028 ­ 200.028
<
10
­ 5
8
­ 5.0
zz
­ 251.383 ­ 251.383
<
10
­ 5
23
­ 20.0
zz
­ 443.961 ­ 443.961
<
10
­ 5


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Code_Aster
®
Version
7.4
Titrate:
WTNV100 - Triaxial compression test not drained with model CJS (level 1)
Date:
05/07/05
Author (S):
C. CHAVANT, pH. AUBERT
Key
:
V7.31.100-B
Page:
10/14
Manual of Validation
V7.31 booklet: Mechanical hydro Thermo in porous environment of voluminal structures
HT-66/05/005/A
5 Modeling
B
5.1
Characteristics of modeling
This modeling differs from the preceding one by the smoothness of the mesh
3D:
Z
X
y
B
Cutting: 2 in height, in width and thickness.
Loading of phase 1:
Confining pressure:
xx
yy
zz
0
0
0
=
=
: ­ 100 kPa.
Level 1 of model CJS

5.2
Characteristic of the mesh
A number of nodes: 27
A number of meshs and types: 8
HEXA8
and 24
QUA4

5.3 Functionalities
tested
Controls
DEFI_MATERIAU CJS
STAT_NON_LINE COMP_INCR
RELATION
“CJS”
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Code_Aster
®
Version
7.4
Titrate:
WTNV100 - Triaxial compression test not drained with model CJS (level 1)
Date:
05/07/05
Author (S):
C. CHAVANT, pH. AUBERT
Key
:
V7.31.100-B
Page:
11/14
Manual of Validation
V7.31 booklet: Mechanical hydro Thermo in porous environment of voluminal structures
HT-66/05/005/A
6
Results of modeling B
6.1 Values
tested
Localization Number
of command
Deformation
axial
zz
(%)
Stress
(kPa)
Reference
Aster %
difference
Not A, B and C 5
­ 0.2
xx
­ 82.76923 ­ 82.76923 <
10
­ 5
10
­ 0.4
xx
­ 65.53846 ­ 65.53846 <
10
­ 5
20
­ 0.8
xx
­ 53.78079 ­ 53.78079 <
10
­ 5
40
­ 1.6
xx
­ 56.578176 ­ 56.578176 <
10
­ 5
60
­ 5.6
xx
­ 70.565109 ­ 70.565109 <
10
­ 5
100
­ 20.0
xx
­ 120.918065 ­ 120.918065
<
10
­ 5
5
­ 0.2
yy
­ 82.76923 ­ 82.76923 <
10
­ 5
10
­ 0.4
yy
­ 65.53846 ­ 65.53846 <
10
­ 5
20
­ 0.8
yy
­ 53.78079 ­ 53.78079 <
10
­ 5
40
­ 1.6
yy
­ 56.578176 ­ 56.578176 <
10
­ 5
60
­ 5.6
yy
­ 70.565109 ­ 70.565109 <
10
­ 5
100
­ 20.0
yy
­ 120.918065 ­ 120.918065
<
10
­ 5
5
­ 0.2
zz
­ 134.46154 ­ 134.46154
<
10
­ 5
10
­ 0.4
zz
­ 168.92308 ­ 168.92308
<
10
­ 5
20
­ 0.8
zz
­ 197.460849 ­ 197.460849
<
10
­ 5
40
­ 1.6
zz
­ 207.731697 ­ 207.731697
<
10
­ 5
60
­ 5.6
zz
­ 259.085935 ­ 259.085935
<
10
­ 5
100
­ 20.0
zz
­ 443.961194 ­ 443.961194
<
10
­ 5


background image
Code_Aster
®
Version
7.4
Titrate:
WTNV100 - Triaxial compression test not drained with model CJS (level 1)
Date:
05/07/05
Author (S):
C. CHAVANT, pH. AUBERT
Key
:
V7.31.100-B
Page:
12/14
Manual of Validation
V7.31 booklet: Mechanical hydro Thermo in porous environment of voluminal structures
HT-66/05/005/A
7 Modeling
C
7.1
Characteristics of modeling
3d_HM:
Z
X
y
B
Cutting: 1 in height, in width and thickness.
Loading of phase 1:
Confining pressure:
xx
yy
zz
0
0
0
=
=
: ­ 100 kPa.
Level 1 of model CJS
Coefficient of biot: 1
UN_SUR_K of water: 0

7.2
Characteristic of the mesh
A number of nodes: 20
A number of meshs and types: 1
HEXA20
and 6
QUA8

7.3 Functionalities
tested
Controls
DEFI_MATERIAU CJS
STAT_NON_LINE COMP_INCR RELATION “KIT_HM”
“RELATION_KIT”:
“CJS” “LIQU_SATU” “HYDR_UTIL”
background image
Code_Aster
®
Version
7.4
Titrate:
WTNV100 - Triaxial compression test not drained with model CJS (level 1)
Date:
05/07/05
Author (S):
C. CHAVANT, pH. AUBERT
Key
:
V7.31.100-B
Page:
13/14
Manual of Validation
V7.31 booklet: Mechanical hydro Thermo in porous environment of voluminal structures
HT-66/05/005/A
8
Results of modeling C
8.1 Values
tested
Localization Number
of command
Deformation
axial
zz
(%)
Stress
(kPa)
Reference
Aster %
difference
Not A and B
1
­ 0.25
xx
­ 78.461538 ­ 7,8462E+01
<
10
­ 5
2
­ 0.50
xx
­ 56.923077 ­ 5,6923E+01
<
10
­ 5
3
­ 0.75
xx
­ 53.606 ­ 5,3606E+01 <
10
­ 5
4
­ 1.0
xx
­ 54.480 ­ 5,4480E+01 <
10
­ 5
8
­ 5.0
xx
­ 68.467 ­ 6,8467E+01 <
10
­ 5
23
­ 20.0
xx
­ 120.918 ­ 1,2092E+02 <
10
­ 5
1
­ 0.25
yy
­ 78.461538 ­ 7,8462E+01
<
10
­ 5
2
­ 0.50
yy
­ 56.923077 ­ 5,6923E+01
<
10
­ 5
3
­ 0.75
yy
­ 53.606 ­ 5,3606E+01 <
10
­ 5
4
­ 1.0
yy
­ 54.480 ­ 5,4480E+01 <
10
­ 5
8
­ 5.0
yy
­ 68.467 ­ 6,8467E+01 <
10
­ 5
23
­ 20.0
yy
­ 120.918 ­ 1,2092E+02 <
10
­ 5
1
­ 0.25
zz
­ 143,07692 ­ 1,4308E+02
<
10
­ 5
2
­ 0.50
zz
­ 186.153846 ­ 1,8615E+02
<
10
­ 5
3
­ 0.75
zz
­ 196.818 ­ 1,9682E+02 <
10
­ 5
4
­ 1.0
zz
­ 200.028 ­ 2,0003E+02 <
10
­ 5
8
­ 5.0
zz
­ 251.383 ­ 2,5138E+02 <
10
­ 5
23
­ 20.0
zz
­ 443.961 ­ 4,4396E+02 <
10
­ 5
1
­ 0.25
pressure water 2,1538E+04
2.15385E+04
< 10
­ 5
2
­ 0.50
pressure water 4,3077E+04
4.30769E+04
< 10
­ 5

For the water pressure, one with the reference as long as the behavior is elastic linear

background image
Code_Aster
®
Version
7.4
Titrate:
WTNV100 - Triaxial compression test not drained with model CJS (level 1)
Date:
05/07/05
Author (S):
C. CHAVANT, pH. AUBERT
Key
:
V7.31.100-B
Page:
14/14
Manual of Validation
V7.31 booklet: Mechanical hydro Thermo in porous environment of voluminal structures
HT-66/05/005/A
9
Summary of the results
The values of Code_Aster are in perfect agreement with the values of reference. Concerning
coupling with hydraulics, this test proves that by means of computer, coupling CJS/THM functions and
that the equations of hydraulics are at least able to give again the null variation of volume
when water is incompressible.