Code_Aster ®
Version
5.0
Titrate:
SSNV135 triaxial Essai drained with model CJS (level 1)
Date:
05/02/02
Author (S):
C. CHAVANT, pH. Key AUBERT
:
V6.04.135-A Page:
1/8

Organization (S): EDF/AMA, CNEPE/GC
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
Document: V6.04.135
SSNV135 - Triaxial Essai drained with 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 drained condition. Three
levels of containment are simulated: 100, 200, then 400 kPa.

By reason of symmetry, one is interested only in the eighth of a sample subjected to a triaxial compression test.

The results obtained with model CJS1 are compared with the analytical solution.

Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
SSNV135 triaxial Essai drained with model CJS (level 1)
Date:
05/02/02
Author (S):
C. CHAVANT, pH. Key AUBERT
:
V6.04.135-A Page:
2/8


1
Problem of reference

1.1 Geometry

Z
E
height:
H = 1 m
width:
L = 1 m
thickness: E = 1 m
C
H
With
y
B
X
L


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 = 22,4 103 kPa
= 0,3

Parameters CJS1: = ­ 0,03
= 0,82
Rm = 0,289
Pa = ­ 100 kPa

1.3
Initial conditions, boundary conditions, and loading

Phase 1:
One brings the sample in a homogeneous state: 0 = 0 = 0
xx
yy
zz, by imposing the pressure of
containment corresponding on the front, side straight line and higher faces. Displacements are
blocked on the faces postpones (ux = 0), side left (uy = 0) and lower (uz = 0).

Phase 2:
One maintains displacements blocked on the faces postpones (ux = 0), side left (uy = 0) and
lower (uz = 0), as well as the confining pressure on the front faces and side straight line. One
apply a displacement imposed to the higher face: U (T)
Z
, in order to obtain a deformation
zz = - 20% (counted starting from the beginning of phase 2).
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
SSNV135 triaxial Essai drained with model CJS (level 1)
Date:
05/02/02
Author (S):
C. CHAVANT, pH. Key AUBERT
:
V6.04.135-A Page:
3/8


2
Reference solution

2.1
Development of the analytical solution for CJS1

One has permanently:
= = 0
xx
yy
xx

where 0
you
xx = C represents the confining pressure.

Remain to determine zz.

Elastic phase:

By writing the elastic law simply, one a:

0 = 0 + + (+ 2 µ) +
xx
xx
zz
xx
xx
= 0 + (+ 2 µ) + 2
zz
zz
zz
xx

where here and µ is the coefficients of Lamé.

By eliminating xx between these two equations, one finds:

µ (3 + 2 µ)
= 0 +
(

zz
zz

+ µ)
zz
Plastic phase:

One a:

I
0
0
you
1 = zz + 2 xx where xx = C represents the confining pressure.

One deduces some for the components from the diverter S:

1
0
1
S = 2
I
zz
- xx


and S
= 0 - I
3 1


xx
xx
1
3

1
3
0

1
0
that is to say: S
= 6 - I
II
xx


and det (S) = 2
I -

3 1
xx

3 1



1/6
Consequently: (
H S) = (1 -)

In addition, when one reaches the criterion of the mechanism déviatoire: S
(H) + R I
II
S
m
=
1
0
from where the relation:
0
6
I
xx
1 =

2
Rm
-
3
(1 -) 1/6
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
SSNV135 triaxial Essai drained with model CJS (level 1)
Date:
05/02/02
Author (S):
C. CHAVANT, pH. Key AUBERT
:
V6.04.135-A Page:
4/8


and finally, one has for the vertical constraint:

6 0

xx
=
- 2 0
zz
xx
2
Rm
-
3 (1 -) 1/6

Moreover, one can calculate that the transition enters the states rubber band and perfectly plastic is done
for an axial deformation equalizes with:





µ (3 + 2 µ)
6 0


xx
=
0
(

- 2
zz

+ µ)
xx
2
R

m
-

3
1/6


(1 -)


2.2
Results of reference

Constraints xx, yy and zz at points A, B and C.

2.3
Uncertainty on the solution

Analytical solution for CJS1.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
SSNV135 triaxial Essai drained with model CJS (level 1)
Date:
05/02/02
Author (S):
C. CHAVANT, pH. Key AUBERT
:
V6.04.135-A Page:
5/8


3 Modeling
With

3.1
Characteristics of modeling

3D:

Z
B
y
X


Cutting: 2 in height, in width and thickness.

Loading of phase 1:
Confining pressure: 0 = 0 = 0
xx
yy
zz: successively ­ 100 kPa, ­ 200 kPa and ­ 400 kPa.
Level 1 of model CJS

3.2
Characteristic of the grid

A number of nodes: 27
A number of meshs and types: 8 HEXA8 and 24 QUA4

3.3 Functionalities
tested

Commands




DEFI_MATERIAU CJS



STAT_NON_LINE COMP_INCR
RELATION
“CJS”


Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
SSNV135 triaxial Essai drained with model CJS (level 1)
Date:
05/02/02
Author (S):
C. CHAVANT, pH. Key AUBERT
:
V6.04.135-A Page:
6/8


4
Results of modeling A

4.1 Values
tested

For 0 = 0 = 0
xx
yy
zz: ­ 100 kPa

Localization Numéro deformation
constraint
Reference
Aster %
difference
of command axial
(kPa)
zz (%)
Not A, B and C
10 ­ 0.8
% xx
­ 100.0 ­ 100.0
<
10­5
100
­ 20.0
%
xx
­ 100.0 ­ 100.0
< 10­5

10 ­ 0.8
% yy
­ 100.0 ­ 100.0
< 10­5
100
­ 20.0
%
yy
­ 100.0 ­ 100.0
< 10­5

10 ­ 0.8
% zz
­ 279.2
­ 279.2 <
10­5
20
­ 1.6
%
zz
­ 367.159
­ 367.1587 <
10­5
40
­ 3.2
%
zz
­ 367.159
­ 367.1587 <
10­5
60
­ 7.2
%
zz
­ 367.159
­ 367.1587 <
10­5
100
­ 20.0
%
zz
­ 367.159
­ 367.1587 <
10­5

For 0 = 0 = 0
xx
yy
zz: ­ 200 kPa

Localization Numéro deformation
Référence constraint
Aster %
difference
of command
axial
(kPa)
zz (%)
Not A, B and C
10
­ 0.8%
xx
­ 200.0 ­ 200.0
<
10­5
100
­ 20.0
%
xx
­ 200.0 ­ 200.0
< 10­5

10 ­ 0.8
% yy
­ 200.0 ­ 200.0
< 10­5
100
­ 20.0
%
yy
­ 200.0 ­ 200.0
< 10­5

10 ­ 0.8
% zz
­ 379.2
­ 379.2 <
10­5
20
­ 1.6
%
zz
­ 558.4
­ 558.4 <
10­5
40
­ 3.2
%
zz
­ 734.317
­ 734.3174 <
10­5
60
­ 7.2
%
zz
­ 734.317
­ 734.3174 <
10­5
100
­ 20.0
%
zz
­ 734.317
­ 734.3174 <
10­5

For 0 = 0 = 0
xx
yy
zz: ­ 400 kPa

Localization Numéro deformation
Référence constraint
Aster %
difference
of command
axial
(kPa)
zz (%)
Not A, B and C
10
­ 0.8%
xx
­ 400.0 ­ 400.0
<
10­5
100
­ 20.0
%
xx
­ 400.0 ­ 400.0
< 10­5

10 ­ 0.8
% yy
­ 400.0 ­ 400.0
< 10­5
100
­ 20.0
%
yy
­ 400.0 ­ 400.0
< 10­5

10 ­ 0.8
%
zz
­ 579.2
­ 579.2 <
10­5
20
­ 1.6
%
zz
­ 758.4
­ 758.4 <
10­5
40
­ 3.2
%
zz
­ 1116.8
­ 1116.8 <
10­5
60
­ 7.2
%
zz
­ 1458.6348
­ 1468.6348 <
10­5
100
­ 20.0
%
zz
­ 1458.6348
­ 1468.6348 <
10­5

4.2 Parameters
of execution

Version: 5.03.08



Machine: SGI - ORIGIN 2000 - R12000
System: IRIX 64

Obstruction memory: 16 Mo
Time CPU To use: 120 S
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
SSNV135 triaxial Essai drained with model CJS (level 1)
Date:
05/02/02
Author (S):
C. CHAVANT, pH. Key AUBERT
:
V6.04.135-A Page:
7/8


5
Summary of the results

The values of Code_Aster are in triad with the values of the analytical solution of
reference.

Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
SSNV135 triaxial Essai drained with model CJS (level 1)
Date:
05/02/02
Author (S):
C. CHAVANT, pH. Key AUBERT
:
V6.04.135-A Page:
8/8

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Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A

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