Code_Aster ®
Version
6.4
Titrate:
SSNV160 - Hydrostatic Essai with law CAM_CLAY

Date:
02/06/03
Author (S):
J. EL GHARIB, G. DEBRUYNE Key
:
V6.04.160-B Page:
1/8

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

Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
Document: V6.04.160

SSNV160 - Hydrostatic Essai with the law
CAM_CLAY

Summary:

This test makes it possible to validate the mechanical law elastoplastic Cam_Clay specific to the grounds normally
consolidated the elastic part is non-linear and the plastic part is hardening or lenitive. It
test is a hydrostatic test of compression. These results are compared with an analytical solution for
two modelings 3D and axisymmetric. Modelings has and B which called upon linear search
are reabsorbed, this is why only modelings C and D are written.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/03/008/A

Code_Aster ®
Version
6.4
Titrate:
SSNV160 - Hydrostatic Essai with law CAM_CLAY

Date:
02/06/03
Author (S):
J. EL GHARIB, G. DEBRUYNE Key
:
V6.04.160-B 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

E = 4.2E7 Pa
= 0.285
=.
0
Parameters specific to CAM_CLAY:

PORO = 0.14, = 0.25, = 0.05, M = 0.9, CLOSE _ CRIT =.
3e5 Pa, Pa = 1.E5 Pa

1.3
Boundary conditions and loadings

The hydrostatic test is carried out with a state of homogeneous stresses:
= = = P. One
xx
yy
zz
fact a first elastic design to P = Pa. One increases then P to P while carrying out
sup
a loading with Cam_Clay followed by a discharge to Pa.

1.4 Conditions
initial

In CAM_CLAY, the elastic law requires a hydrostatic constraint in an initial state (the deformation being
null).

To initialize this constraint, one chose to carry out at the beginning a purely elastic calculation in
making evolve/move pressure of 0. with 1.E5 Pa. One extracts from this calculation only the field of
constraints at the points of gauss. This stress field resulting from the elastic design is considered
like the initial state of the hydrostatic constraint necessary to the law Cam_Clay of following calculation.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/03/008/A

Code_Aster ®
Version
6.4
Titrate:
SSNV160 - Hydrostatic Essai with law CAM_CLAY

Date:
02/06/03
Author (S):
J. EL GHARIB, G. DEBRUYNE Key
:
V6.04.160-B Page:
3/8

2
Reference solution

2.1
Method of calculation
tr ()
In a hydrostatic test:
= = and the hydrostatic constraint is P = -

xx
yy
zz
3
(convention of the soil mechanics).

For the calculation of the total voluminal deformation, one distinguishes the two cases:

1st case: Case of non-linear elasticity, the hydrostatic pressure is lower than the pressure of
consolidation:

P < P < 2P

0 = P
atm
Cr
ion
consolidat
1
P
P = P exp (
E
K) or E
=
Ln

atm
0 v
v
K
P
0
atm

in this case the total deflection is equal to the elastic strain:
E
=
v
v

2nd case: Case of plasticity, the hydrostatic pressure exceeded the pressure of consolidation, there is
thus hardening:

P > 2P = P
, P = 2P after plasticization.
Cr
ion
consolidat
Cr

and the critical pressure evolves/moves as follows

P = P exp (p
K)
Cr
cr0
v
P
p
1
1
P
and voluminal deformation:
Cr
= Ln
= Ln

v
K
P
K
2P
cr0
cr0

In this case, it is necessary to take into account the plastic deformation in the calculation of the total deflection
E
p
1
P
1
P
: = + =
Ln
+ Ln

v
v
v
K
P
K
2P
0
atm
cr0

2.2
Sizes and results of reference

The test is homogeneous. One tests the voluminal deformation in an unspecified node where
components are equal: =
=
xx
yy
zz

2.3
Uncertainties on the solution

None. Exact analytical result.

2.4 Reference
bibliographical

[1]
Charlez pH. A. (Total Report/ratio): example of model poroplastic: the model of Cam_Clay
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/03/008/A

Code_Aster ®
Version
6.4
Titrate:
SSNV160 - Hydrostatic Essai with law CAM_CLAY

Date:
02/06/03
Author (S):
J. EL GHARIB, G. DEBRUYNE Key
:
V6.04.160-B Page:
4/8

3 Modeling
C

3.1
Characteristics of modeling

Modeling 3D
Z
NO7
NO5
NO8
NO6
NO1
NO3
y
NO4
NO2
X


3.2
Characteristics of the grid

A number of nodes:
8
A number of meshs:
1 of type HEXA 8

6 of type QUAD 4

The following meshs are defined:

ARRIERE
NO1 NO3 NO7 NO5
AVANT
NO2 NO6 NO8 NO4
DROITE
NO1 NO5 NO6 NO2
GAUCHE
NO3 NO4 NO8 NO7
BAS
NO1 NO2 NO4 NO3
HAUT
NO5 NO7 NO8 NO6

To represent the 1/8th structure, the boundary conditions in displacement imposed are:

On nodes NO1, NO2, NO4 and NO3: DZ = 0
On nodes NO3, NO4, NO8 and NO7: DY = 0
On nodes NO2, NO6, NO8 and NO4: DX = 0

The loading is consisted of the same pressure divided into compression on the 3 meshs: `HAUT,
“DROITE” and “ARRIERE” to simulate a hydrostatic test.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/03/008/A

Code_Aster ®
Version
6.4
Titrate:
SSNV160 - Hydrostatic Essai with law CAM_CLAY

Date:
02/06/03
Author (S):
J. EL GHARIB, G. DEBRUYNE Key
:
V6.04.160-B Page:
5/8

3.3 Functionalities
tested

Commands



DEFI_MATERIAU CAM_CLAY


STAT_NON_LINE COMP_INCR
RELATION= `CAM_CLAY'
NEWTON
STAMP = TANGENT

REAC_ITER

3.4
Sizes tested and results

The component with node NO6 was tested, in this case =
=
xx
xx
yy
zz

Moment Reference
Aster
Difference
(%)
5000.
­ 2.30686 ­ 02
­ 2.3068616551409 ­ 02
7.17­05
6000.
­ 2.56819 ­ 02
­ 2.5681930900741 ­ 02
1.20­04
6500.
­ 3.14183 ­ 02
­ 3.1418280283251 ­ 02
­ 6.28­05
7000.
­ 3.67294 ­ 02
­ 3.6729351192775 ­ 02
­ 1.33­04
7500.
­ 4.16738 ­ 02
­ 4.1673840301798 ­ 02
9.67­05
8000.
­ 4.62991 ­ 02
­ 4.6299103361551 ­ 02
7.26­06
9000.
­ 4.21757 ­ 02
­ 4.2175660318354 ­ 02
­ 9.41­05
10000.
­ 1.64938 ­ 02
­ 1.6493780906496 ­ 02
­ 1.16­04

Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/03/008/A

Code_Aster ®
Version
6.4
Titrate:
SSNV160 - Hydrostatic Essai with law CAM_CLAY

Date:
02/06/03
Author (S):
J. EL GHARIB, G. DEBRUYNE Key
:
V6.04.160-B Page:
6/8

4 Modeling
D

4.1
Characteristics of modeling

Axisymmetric modeling

y
N4
N7
N3
D
C
N8
N6
With
B
N1
N5
N2
X


4.2
Characteristics of the grid

A number of nodes:
8
A number of meshs:
1 of type QUAD 8

4 of type SEG3

The following meshs are defined: AB, BC, CD and DA
To represent ¼ structure, one puts the boundary conditions following:
On AB: DY = 0
On AD: DX = 0
One imposes an equal pressure on the meshs BC and CD to simulate a hydrostatic test.

4.3 Functionalities
tested

Commands
Key word


DEFI_MATERIAU CAM_CLAY


STAT_NON_LINE COMP_INCR
RELATION= `CAM_CLAY'
NEWTON
STAMP = TANGENT

Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/03/008/A

Code_Aster ®
Version
6.4
Titrate:
SSNV160 - Hydrostatic Essai with law CAM_CLAY

Date:
02/06/03
Author (S):
J. EL GHARIB, G. DEBRUYNE Key
:
V6.04.160-B Page:
7/8

4.4
Sizes tested and results

The component with the C.a. node tested, in this case =
=
xx
xx
yy
zz

Moment Reference
Aster
Difference
(%)
5000.
­ 2.30686 ­ 02
­ 2.3068616551409 ­ 02
7.17­05
6000.
­ 2.56819 ­ 02
­ 2.5681930900741 ­ 02
1.20­04
6500.
­ 3.14183 ­ 02
­ 3.1418280283251 ­ 02
­ 6.28­05
7000.
­ 3.67294 ­ 02
­ 3.6729351192775 ­ 02
­ 1.33­04
7500.
­ 4.16738 ­ 02
­ 4.1673840301798 ­ 02
9.67­05
8000.
­ 4.62991 ­ 02
­ 4.6299103361551 ­ 02
7.26­06
9000.
­ 4.21757 ­ 02
­ 4.2175660318354 ­ 02
­ 9.41­05
10000.
­ 1.64938 ­ 02
­ 1.6493780906496 ­ 02
­ 1.16­04

Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/03/008/A

Code_Aster ®
Version
6.4
Titrate:
SSNV160 - Hydrostatic Essai with law CAM_CLAY

Date:
02/06/03
Author (S):
J. EL GHARIB, G. DEBRUYNE Key
:
V6.04.160-B Page:
8/8

5
Summary of the results

The values obtained with Code_Aster are in agreement with the values of the analytical solution of
reference.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/03/008/A

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