Code_Aster
®
Version
7.4
Titrate:
Taking into account of thermal dilation and the creep of desiccation
Date:
03/01/05
Author (S):
Y. The POPE
Key
:
V6.04.180-A
Page:
1/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
Organization (S):
EDF-R & D/MMC
Manual of Validation
V6.04 booklet: Non-linear statics of the voluminal structures
Document: V6.04.180
SSNV180 - Taking into account of dilation
thermics and of the creep of desiccation in
model
BETON_UMLV_FP
Summary:
This test makes it possible to validate the taking into account of thermal dilation and the creep of desiccation in the law
of behavior
BETON_UMLV_FP
. The results of this test are compared with a numerical solution
obtained with Scilab 2.7.2 in the case of a modeling 3D.
Code_Aster
®
Version
7.4
Titrate:
Taking into account of thermal dilation and the creep of desiccation
Date:
03/01/05
Author (S):
Y. The POPE
Key
:
V6.04.180-A
Page:
2/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
1
Problem of reference
1.1 Geometry
Z
X
y
L
H
E
Height:
H = 1,00 [m]
Width:
L = 1,00 [m]
Thickness: E = 1,00 [m]
1.2
Properties of material
31
=
E
[GPa]
modulus of elasticity
2
,
0
=
Poisson's ratio
60
=
Re
K
[µm/m]
endogenous coefficient of withdrawal
10
=
rd
K
[µm/Mr. m
3
/L]
coefficient of withdrawal of desiccation
10
=
[µm/m/°C]
thermal expansion factor
Here one informs also the curve sorption-desorption which connects the water content
C
with the hygroscopy
H
.
In this case one supposed that the two quantities were connected by the following linear relation:
C
[L/m
3
] =
H
[%].
Parameters specific to clean creep:
5
20
,
1
+
=
E
K
Sr
[MPa]
spherical part: rigidity connects associated with the skeleton formed by
blocks of hydrates on a mesoscopic scale
4
22
,
6
+
=
E
K
if
[MPa]
spherical part: rigidity connects intrinsically associated with
hydrates on a microscopic scale
4
86
,
3
+
=
E
K
D
R
[MPa]
deviatoric part: rigidity associated with the capacity with water adsorbed with
to transmit loads (load bearing toilets)
10
21
,
2
+
=
E
Sr
[MPa.s]
spherical part:viscosity connects associated with the mechanism with
dissemination within capillary porosity
10
16
,
4
+
=
E
if
[MPa.s]
spherical part: viscosity connects associated with the mechanism with
dissemination interlamellaire
10
19
,
6
+
=
E
D
R
[MPa.s]
deviatoric part:viscosity associated with the water adsorbed by
layers of hydrates
12
64
,
1
+
=
E
D
I
[MPa.s]
deviatoric part: viscosity of interstitial water.
Parameters specific to the creep of desiccation:
4
30
.
5
+
=
E
fd
[MPa.s]
Code_Aster
®
Version
7.4
Titrate:
Taking into account of thermal dilation and the creep of desiccation
Date:
03/01/05
Author (S):
Y. The POPE
Key
:
V6.04.180-A
Page:
3/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
1.3
Boundary conditions and loadings
In this test, one creates a homogeneous field of drying in the structure varying linearly on
one 750 days duration, initial moisture is worth 100% (condition of a sealed test-tube) and decrease
gradually up to 50% to the 750
ème
day.
The degree of hydration varies linearly from 0 to 1 between the initial moment and the 28
ème
day.
The temperature of reference is worth 20°C. The thermal loading corresponds to a front elevation in
temperature varying of 20 °C and 40°C between the initial moment and the final moment.
The mechanical loading corresponds to an one-way compression according to the direction
vertical (Z in 3D); its intensity is 12 [MPa]. The load is applied in 1s and is maintained
constant during 100 days.
1.4 Conditions
initial
The beginning of calculation is supposed the moment 1. At this moment there is neither field of drying, nor forced
mechanics.
At moment 0, one applies a field of drying corresponding to 100% of hygroscopy, a field
of hydration corresponding to a null advance and a thermal field to the temperature of
reference.
Code_Aster
®
Version
7.4
Titrate:
Taking into account of thermal dilation and the creep of desiccation
Date:
03/01/05
Author (S):
Y. The POPE
Key
:
V6.04.180-A
Page:
4/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
2
Reference solution
2.1
Method of calculation
One did not develop the analytical solution for this hydro-mechanical loading. Also, the solution
from reference is obtained numerically by using the software Scilab 2.7.2. Each component of
deformation is calculated separately:
·
the deformations of endogenous withdrawal are given starting from the relation:
-
.
Re
Re
K
=
where
indicate the degree of hydration of material
·
the deformations of withdrawal of desiccation are given starting from the relation:
-
C
K
rd
rd
&
&
.
=
where
C
indicate the water content of material
·
the deformations of thermal dilation are given starting from the relation:
-
(
)
ref.
HT
T
T
-
=
where
T
and
ref.
T
indicate the temperature at the moment respectively
running and the temperature of reference of material
·
the deformations of clean creep are calculated numerically by using one
discretization identical to that established in Code_Aster.
·
the deformations of creep of desiccation are calculated analytically from
relation:
-
H
fd
fd
&
&
1
=
where
)
(
C
F
H
=
indicate the moisture of material
The results of calculation with Scilab are presented in the figure below.
Code_Aster
®
Version
7.4
Titrate:
Taking into account of thermal dilation and the creep of desiccation
Date:
03/01/05
Author (S):
Y. The POPE
Key
:
V6.04.180-A
Page:
5/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
2.2
Sizes and results of reference
The test is homogeneous. One tests the deformation in an unspecified node.
2.3
Uncertainties on the solution
Numerical result obtained with Scilab 2.7.2.
2.4 References
bibliographical
[1]
POPE Y.: Relation of behavior UMLV for the clean creep of the concrete,
Reference material of Code_Aster, [R7.01.06] 16 p (2002).
Code_Aster
®
Version
7.4
Titrate:
Taking into account of thermal dilation and the creep of desiccation
Date:
03/01/05
Author (S):
Y. The POPE
Key
:
V6.04.180-A
Page:
6/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
3 Modeling
With
3.1
Characteristics of modeling
Modeling 3D
Z
X
y
NO2
NO1
NO3
NO4
NO8
NO7
NO5
NO6
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:
S_ARR
NO3 NO7 NO8 NO4
S_AVT
NO1 NO2 NO6 NO5
S_DRT
NO1 NO5 NO8 NO4
S_GCH
NO3 NO2 NO6 NO7
S_INF
NO1 NO2 NO3 NO4
S_SUP
NO5 NO6 NO7 NO8
The boundary conditions in displacement imposed are:
On nodes NO1, NO2, NO3 and NO4: DZ = 0
On nodes NO3, NO7, NO8 and NO4: DY = 0
On nodes NO2, NO6, NO7 and NO8: DX = 0
The loading is consisted of the same field of drying and the same nodal force 1/4 applied
on the four nodes of S_SUP.
Code_Aster
®
Version
7.4
Titrate:
Taking into account of thermal dilation and the creep of desiccation
Date:
03/01/05
Author (S):
Y. The POPE
Key
:
V6.04.180-A
Page:
7/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
3.3 Functionalities
tested
Controls
Key word
DEFI_MATERIAU ELAS_FO
BETON_UMLV_FP
K_DESSIC
B_ENDOGE
FONC_DESORP
K_RS
K_IS
K_RD
V_RS
V_IS
V_RD
V_ID
CREA_CHAMP “AFFE”
TYPE_CHAM=' NOEU_TEMP_R'
NOM_CMP=' TEMP'
CREA_RESU “AFFE”
TYPE_CHAM=' NOEU_TEMP_R'
NOM_CMP=' TEMP'
AFFE_CHAR_MECA DDL_IMPO
LIAISON_UNIF
FORCE_NODALE
SECH_CALCULEE
HYDR_CALCULEE
STAT_NON_LINE COMP_INCR
RELATION= `BETON_UMLV_FP'
3.4
Sizes tested and results
The component
xx
with node NO6 was tested.
Moment Reference
Aster %
difference
64800
- 4.081E-04
- 4.0854E-04
0.108
648000
- 5.250E-04
- 5.2533E-04
0.063
6480000
- 9.065E-04
- 9.0689E-04
0.043
64800000
- 22.990E-04
- 23.0189E-04
0.126
Code_Aster
®
Version
7.4
Titrate:
Taking into account of thermal dilation and the creep of desiccation
Date:
03/01/05
Author (S):
Y. The POPE
Key
:
V6.04.180-A
Page:
8/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
4
Summary of the results
The values obtained with Code_Aster are in agreement with the values of the numerical solution of
reference.