Code_Aster
®
Version
6.4
Titrate:
SSNV160 -
Hydrostatic test with the law
CAM_CLAY
Date:
02/06/03
Author (S):
J. EL GHARIB, G. DEBRUYNE
Key
:
V6.04.160-B
Page:
1/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/03/008/A
Organization (S):
EDF-R & D/AMA
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
Document: V6.04.160
SSNV160 - Hydrostatic test 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.
Code_Aster
®
Version
6.4
Titrate:
SSNV160 -
Hydrostatic test with the law
CAM_CLAY
Date:
02/06/03
Author (S):
J. EL GHARIB, G. DEBRUYNE
Key
:
V6.04.160-B
Page:
2/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/03/008/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
7
2
.
4th
E
=
AP
285
.
0
=
.
0
=
Parameters specific to CAM_CLAY:
14
.
0
=
PORO
,
25
.
0
=
,
05
.
0
=
,
9
.
0
=
M
,
5
.
3
_
E
CRIT
NEAR
=
AP,
5
.
1 E
AP
=
AP
1.3
Boundary conditions and loadings
The hydrostatic test is carried out with a state of homogeneous stresses:
P
zz
yy
xx
=
=
=
. One
fact a first elastic design until
AP
P
=
. One increases then
P
until
sup
P
while carrying out
a loading with Cam_Clay followed by a discharge until
AP
.
1.4 Conditions
initial
In
CAM_CLAY
, the elastic law requires a hydrostatic stress in an initial state (the deformation being
null).
To initialize this stress, one chose to carry out at the beginning a purely elastic calculation in
making evolve/move pressure of 0. with 1.E5 AP. One extracts from this calculation only the field of
stresses at the points of gauss. This stress field resulting from the elastic design is considered
like the initial state of the hydrostatic stress necessary to the law Cam_Clay of following calculation.
Code_Aster
®
Version
6.4
Titrate:
SSNV160 -
Hydrostatic test with the law
CAM_CLAY
Date:
02/06/03
Author (S):
J. EL GHARIB, G. DEBRUYNE
Key
:
V6.04.160-B
Page:
3/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/03/008/A
2
Reference solution
2.1
Method of calculation
In a hydrostatic test:
zz
yy
xx
=
=
and the hydrostatic stress is
()
3
tr
P
-
=
(convention of the soil mechanics).
For the calculation of the total voluminal deformation, one distinguishes the two cases:
1
Er
case: Case of non-linear elasticity, the hydrostatic pressure is lower than the pressure of
consolidation:
ion
consolidat
Cr
atm
P
P
P
P
=
<
<
0
2
)
exp (
0
E
v
atm
K
P
P
=
or
atm
E
v
P
P
Ln
K
0
1
=
in this case the total deflection is equal to the elastic strain:
E
v
v
=
2
ème
case: Case of plasticity, the hydrostatic pressure exceeded the pressure of consolidation, there is
thus hardening:
ion
consolidat
Cr
P
P
P
=
>
2
,
Cr
P
P 2
=
after plasticization.
and the critical pressure evolves/moves as follows
)
exp (
0
p
v
Cr
Cr
K
P
P
=
and voluminal deformation:
0
0
2
1
1
Cr
Cr
Cr
p
v
P
P
Ln
K
P
P
Ln
K
=
=
In this case, it is necessary to take into account the plastic deformation in the calculation of the total deflection
:
0
0
2
1
1
Cr
atm
p
v
E
v
v
P
P
Ln
K
P
P
Ln
K
+
=
+
=
2.2
Sizes and results of reference
The test is homogeneous. One tests the voluminal deformation in an unspecified node where
components are equal:
zz
yy
xx
=
=
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
Code_Aster
®
Version
6.4
Titrate:
SSNV160 -
Hydrostatic test with the law
CAM_CLAY
Date:
02/06/03
Author (S):
J. EL GHARIB, G. DEBRUYNE
Key
:
V6.04.160-B
Page:
4/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/03/008/A
3 Modeling
C
3.1
Characteristics of modeling
Modeling 3D
Z
X
y
NO1
NO2
NO3
NO4
NO8
NO7
NO6
NO5
3.2
Characteristics of the mesh
A number of nodes:
8
A number of meshs:
1 of type HEXA 8
6 of type QUAD 4
The following meshs are defined:
REAR
NO1 NO3 NO7 NO5
FRONT
NO2 NO6 NO8 NO4
STRAIGHT LINE
NO1 NO5 NO6 NO2
LEFT
NO3 NO4 NO8 NO7
LOW
NO1 NO2 NO4 NO3
HIGH
NO5 NO7 NO8 NO6
To account for the 1/8
ème
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: `HIGH,
“RIGHT” and “REAR” to simulate a hydrostatic test.
Code_Aster
®
Version
6.4
Titrate:
SSNV160 -
Hydrostatic test with the law
CAM_CLAY
Date:
02/06/03
Author (S):
J. EL GHARIB, G. DEBRUYNE
Key
:
V6.04.160-B
Page:
5/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/03/008/A
3.3 Functionalities
tested
Controls
DEFI_MATERIAU CAM_CLAY
STAT_NON_LINE COMP_INCR
NEWTON
RELATION= `CAM_CLAY'
STAMP = TANGENT
REAC_ITER
3.4
Sizes tested and results
The component
xx
with node NO6 was tested, in this case
zz
yy
xx
=
=
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
Code_Aster
®
Version
6.4
Titrate:
SSNV160 -
Hydrostatic test with the law
CAM_CLAY
Date:
02/06/03
Author (S):
J. EL GHARIB, G. DEBRUYNE
Key
:
V6.04.160-B
Page:
6/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/03/008/A
4 Modeling
D
4.1
Characteristics of modeling
Axisymmetric modeling
X
y
With
B
C
N1
N2
N3
N4
N5
N6
N7
N8
D
4.2
Characteristics of the mesh
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
Controls
Key word
DEFI_MATERIAU CAM_CLAY
STAT_NON_LINE COMP_INCR
NEWTON
RELATION= `CAM_CLAY'
STAMP = TANGENT
Code_Aster
®
Version
6.4
Titrate:
SSNV160 -
Hydrostatic test with the law
CAM_CLAY
Date:
02/06/03
Author (S):
J. EL GHARIB, G. DEBRUYNE
Key
:
V6.04.160-B
Page:
7/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/03/008/A
4.4
Sizes tested and results
The component
xx
with the node a.c. tested, in this case
zz
yy
xx
=
=
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
Code_Aster
®
Version
6.4
Titrate:
SSNV160 -
Hydrostatic test with the law
CAM_CLAY
Date:
02/06/03
Author (S):
J. EL GHARIB, G. DEBRUYNE
Key
:
V6.04.160-B
Page:
8/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/03/008/A
5
Summary of the results
The values obtained with Code_Aster are in agreement with the values of the analytical solution of
reference.