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 Key POPE
:
V6.04.180-A Page:
1/8
Organization (S): EDF-R & D/MMC
Handbook of Validation
V6.04 booklet: Non-linear statics of the voluminal structures
Document: V6.04.180
SSNV180 - Prise in 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.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
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 Key POPE
:
V6.04.180-A Page:
2/8
1
Problem of reference
1.1 Geometry
Z
E
H
y
X
L
Height:
H = 1,00 [m]
Width:
L = 1,00 [m]
Thickness: E = 1,00 [m]
1.2
Properties of material
E = 31 [GPa]
modulus of elasticity
=,
0 2
Poisson's ratio
kre = 60 [µm/m]
endogenous coefficient of withdrawal
krd = 10 [µm/Mr. m3/L]
coefficient of withdrawal of desiccation
=10 [µm/m/°C]
thermal dilation coefficient
Here one informs also the curve sorption-desorption which connects the water content C to the hygroscopy h.
In this case one supposed that the two quantities were connected by the following linear relation:
C [L/m3] = H [%].
Parameters specific to clean creep:
K Sr =,
1 20th + 5 [MPa]
spherical part: rigidity connects associated with the skeleton formed by
blocks of hydrates on a mesoscopic scale
K if =,
6 22E + 4 [MPa]
spherical part: rigidity connects intrinsically associated with
hydrates on a microscopic scale
K Dr. = 86
,
3
E + 4 [MPa]
deviatoric part: rigidity associated with the capacity with water adsorbed with
to transmit loads (load bearing toilets)
S
R =,
2 21E +10 [MPa.s]
spherical part:viscosity connects associated with the mechanism with
diffusion within capillary porosity
S
I =
16
,
4
E +10 [MPa.s]
spherical part: viscosity connects associated with the mechanism with
diffusion interlamellaire
D
R =
19
,
6
E +10 [MPa.s]
deviatoric part:viscosity associated with the water adsorbed by
layers of hydrates
D
I = 64
,
1
E +12 [MPa.s]
deviatoric part: viscosity of interstitial water.
Parameters specific to the creep of desiccation:
= 30
.
5
E + 4
fd
[MPa.s]
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
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 Key POPE
:
V6.04.180-A Page:
3/8
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% with the 750ème day.
The degree of hydration varies linearly from 0 to 1 between the initial moment and the 28th day.
The temperature of reference is worth 20°C. The thermal loading corresponds to a rise 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.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
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 Key POPE
:
V6.04.180-A Page:
4/8
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 = K
.
Re
where the degree of hydration of material indicates
· the deformations of withdrawal of desiccation are given starting from the relation:
-
& = K C
. &
rd
rd
where C indicates the water content of material
· the deformations of thermal dilation are given starting from the relation:
-
HT = (T - ref.
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:
1
-
& =
h&
fd
where H = F (C) indicates the moisture of material
fd
The results of calculation with Scilab are presented in the figure below.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
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 Key POPE
:
V6.04.180-A Page:
5/8
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 de Code_Aster, [R7.01.06] 16 p (2002).
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
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 Key POPE
:
V6.04.180-A Page:
6/8
3 Modeling
With
3.1
Characteristics of modeling
Modeling 3D
Z
NO7
NO6
NO8
NO5
NO2
NO3
y
NO4
NO1
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:
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.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
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 Key POPE
:
V6.04.180-A Page:
7/8
3.3 Functionalities
tested
Commands
Key word
DEFI_MATERIAU ELAS_FO
K_DESSIC
BETON_UMLV_FP
B_ENDOGE
FONC_DESORP
K_RS
K_IS
K_RD
V_RS
V_IS
V_RD
V_ID
CREA_CHAMP “AFFE”
NOM_CMP=' TEMP'
TYPE_CHAM=' NOEU_TEMP_R'
CREA_RESU “AFFE”
NOM_CMP=' TEMP'
TYPE_CHAM=' NOEU_TEMP_R'
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
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
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
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 Key POPE
:
V6.04.180-A Page:
8/8
4
Summary of the results
The values obtained with Code_Aster are in agreement with the values of the numerical solution of
reference.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
Outline document