Code_Aster
®
Version
6.4
Titrate:
HSNA100 - Drying of a concrete enclosing wall
Date:
23/06/03
Author (S):
G. DEBRUYNE
Key
:
V7.20.100-C
Page:
1/10
Manual of Validation
V7.20 booklet: Thermodynamic nonlinear statics of the axisymmetric structures
HT-66/03/008/A
Organization (S):
EDF-R & D/AMA
Manual of Validation
V7.20 booklet: Thermomechanical nonlinear statics of the structures
axisymmetric
V7.20.100 document
HSNA100 - Drying of a concrete enclosing wall
Summary:
This case test is intended to not validate the calculation of the drying of the concrete, developed in the operator of thermics
linear of Code_Aster. The studied case corresponds to the simulated drying of the chamber of Flamanville. Data
geometrical and the characteristics materials result from the thesis of Laurent Granger “Behavior
differed from the concrete in the chambers of nuclear thermal power stations " published by the Central Laboratory of the Bridges and
Roadways (1996, pages 185 to 204).
Drying is carried out by exchange with outside, on the walls internal and external of the wall, in modeling
axisymmetric 2D. It is carried out over one 54 years duration.
The coefficient of dissemination of drying depend on the temperature, the analysis is made up of the chaining of one
thermal calculation and of a calculation of drying. One carries out then a mechanical calculation of withdrawal in elasticity
linear and in Von Mises plasticity with an isotropic work hardening.
Code_Aster
®
Version
6.4
Titrate:
HSNA100 - Drying of a concrete enclosing wall
Date:
23/06/03
Author (S):
G. DEBRUYNE
Key
:
V7.20.100-C
Page:
2/10
Manual of Validation
V7.20 booklet: Thermodynamic nonlinear statics of the axisymmetric structures
HT-66/03/008/A
1
Problem of reference
1.1 Geometry
The chamber is modelized on a Lint height = Lext = 1 m
Radius external of the chamber: Rext = 23,4 m
Interior radius of the chamber: Rint = 22,5 m
Rint
Rext
L_int
L_ext
X (R)
Y
1.2
Material properties
For thermal calculation:
Thermal coefficient of diffusion process:
=
°
8000 W m C
//
Voluminal heat:
C
J m
C
p
=
°
2 4 10
6
3
.
/
/
For the calculation of drying:
In the equation of drying:
()
[
]
cd.
dt
Div D C T GradC
-
=
,
0
the coefficient of dissemination
D
will be form recommended by Granger [bib1], [bib2]:
D C T
With
BC T
T
Q
R T
T
With
m
S
B
T
K
Q
R
K
S
S
(,)
exp (
)
exp
,
/
,
=
-
-
=
×
=
=
°
=
-
-
0
0
13
2
0
1
1
1
3 8 10
0 05
273
4700
Code_Aster
®
Version
6.4
Titrate:
HSNA100 - Drying of a concrete enclosing wall
Date:
23/06/03
Author (S):
G. DEBRUYNE
Key
:
V7.20.100-C
Page:
3/10
Manual of Validation
V7.20 booklet: Thermodynamic nonlinear statics of the axisymmetric structures
HT-66/03/008/A
1.3
Boundary conditions and loadings
For thermal calculation:
The temperatures are imposed on the walls interior and external of the enclosing wall (groups
meshs
l_ int
and
l_ ext.
).
During the first five years, the imposed temperature is of 15°C on each wall:
T
T
C
ext.
int
=
= °
15
From the fifth year, the temperature in internal wall passes to 35°C:
T
C
T
C
int
ext.
= °
= °
35
15
and
In practice, the scales of time of drying being much higher than that of thermics, one can
to consider that thermal balance is quasi immediate. Calculation is carried out in linear thermics.
For the calculation of drying:
The boundary conditions are expressed in term of normal flow of moisture on the walls internal and
external of the chamber (groups of meshs
l_ int
and
l_ ext.
). The option is used
FLUX_NL
of the operator
AFFE_CHAR_THER_F
. Normal flow is expressed generally, in a calculation of drying, in
function of the initial concentration
0
C
and of the external concentration
C
eq
, in the form:
(
)
[
]
(
)
W
D C T
C
N
C
C
C
C C
C C
eq
eq
eq
= -
=
-
-
-
-
(,)
,
(
)
0 5
2
0
2
with
= 3.41557.10
8
The data retained in the case of the chamber of Flamanville are as follows:
C
L m
0
3
105 7
=
,
/
(initial concentration)
On the interior face:
of
0
with
5
years,
C
L m
eq
=
69 1
3
,
/
of
5
with
54
years,
C
L m
eq
=
51 6
3
,
/
On the outside:
C
L m
eq
=
69 1
3
,
/
The expression of flow is interpolated by Code_Aster, according to the current price of
water concentration, (variable of calculation). One uses an interpreted function, to define sound
expression, according to the formulation above (operator
FORMULATE
), and the operator
CALC_FONC_INTERP
to define the corresponding tabulée function.
The calculation of drying is carried out in nonlinear thermics, by chaining with thermal calculation
linear.
1.4 Conditions
initial
The initial conditions are consisted the initial temperature, which one takes with 15°C, and
initial water concentration, which is worth
C
L m
0
3
105 7
=
,
/
.
Code_Aster
®
Version
6.4
Titrate:
HSNA100 - Drying of a concrete enclosing wall
Date:
23/06/03
Author (S):
G. DEBRUYNE
Key
:
V7.20.100-C
Page:
4/10
Manual of Validation
V7.20 booklet: Thermodynamic nonlinear statics of the axisymmetric structures
HT-66/03/008/A
2
Reference solution
2.1
Method of calculation used for the reference solution
The reference solution is consisted the calculation carried out with a similar modeling by
L. Granger, within the framework of its thesis [bib1]. The case test relates to the calculation carried out with the data
experimental corresponding to the chamber of Flamanville. The implementation and the results are there
described pages 185 to 204.
Drying is carried out over 54 years, by taking account of the change of boundary conditions at the time of
the fifth year.
2.2
Results of reference
Water concentration in the middle of the chamber, at the end of 5, 15, and 54 years.
2.3
Uncertainty on the solution
One does not have that water concentrations calculated within the framework the thesis of Laurent
Granger, without numerical data on uncertainty of the solution, with regard to the chamber of
Flamanville.
2.4 References
bibliographical
[1]
L. GRANGER: “Behavior differed from the concrete in the chambers of nuclear thermal power stations”
published by the Central Laboratory of the Highways Departments (1996).
[2]
G. DEBRUYNE, B. CIREE: “Modeling of the thermo hydration, drying and the withdrawal
concrete “, manual of Code_Aster Reference, [R7.01.12] (2001).
Code_Aster
®
Version
6.4
Titrate:
HSNA100 - Drying of a concrete enclosing wall
Date:
23/06/03
Author (S):
G. DEBRUYNE
Key
:
V7.20.100-C
Page:
5/10
Manual of Validation
V7.20 booklet: Thermodynamic nonlinear statics of the axisymmetric structures
HT-66/03/008/A
3 Modeling
With
3.1
Characteristics of modeling
It is about an axisymmetric modeling.
Cutting in 10 elements of variable size on the thickness, 2 elements on the height.
10 subdivisions in
R
Y (Z)
X (R)
With
3.2
Characteristics of the mesh
A number of nodes: 85
A number of meshs and type: 20 QUAD8
3.3
Characteristics of the temporal discretization
Thermal calculation (years)
Calculation of drying (years)
0.1
1
5
5.1
6
10
54
0.001
0.1
1
4.9
5
5.001
5.1
6
10
50
54
Code_Aster
®
Version
6.4
Titrate:
HSNA100 - Drying of a concrete enclosing wall
Date:
23/06/03
Author (S):
G. DEBRUYNE
Key
:
V7.20.100-C
Page:
6/10
Manual of Validation
V7.20 booklet: Thermodynamic nonlinear statics of the axisymmetric structures
HT-66/03/008/A
3.4
Functionalities tested
Controls Options
“THERMAL” AFFE_MODELE
“AXIS” “ALL”
AFFE_CHAR_THER_F “FLUX_NL”
“GROUP_MA”
DEFI_MATERIAU “SECH_GRANGER”
THER_NON_LINE “COMP_THER_NL”
“SECH_GRANGER”
“EVOL_THER_SECH”
4
Results of modeling A
4.1 Values
tested
Water concentration at point a:
Identification Reference Aster %
difference
concentration at 5 years
104.
104.818
0.951
concentration at 15 years
95.
96.161
1.540
concentration at 54 years
78.
78.276
0.568
Radial displacement with 54
years (elasticity)
- 0.2759 - 0.2758 0.011
Radial displacement with 54
years (plasticity)
- 0.1840 - 0.1840 0.005
Code_Aster
®
Version
6.4
Titrate:
HSNA100 - Drying of a concrete enclosing wall
Date:
23/06/03
Author (S):
G. DEBRUYNE
Key
:
V7.20.100-C
Page:
7/10
Manual of Validation
V7.20 booklet: Thermodynamic nonlinear statics of the axisymmetric structures
HT-66/03/008/A
5 Modeling
B
5.1
Characteristics of modeling
It is about a modeling 3D
Rext
Rint
X
y
Z
N6
N7
GM72 (in front of)
GM71 (bases)
GM73 (behind)
GM69 (interior surface)
GM70 (surface external of
roll)
5.2
Characteristics of the mesh
The mesh is carried out with the graphic tool gmsh.
A number of nodes:456.
The voluminal meshs are tetrahedral meshs tetra4.
A number of meshs and types: 929 TETRA4, 410 TRIA3, 8 SEG2, 2 POI1.
5.3
Functionalities tested
Controls Options
DEFI_MATERIAU “SECH_GRANGER”
“THERMAL” AFFE_MODELE
“3D”
“ALL”
AFFE_CHAR_THER_F “FLUX_NL”
“GROUP_MA”
DEFI_MATERIAU “SECH_GRANGER”
THER_NON_LINE “COMP_THER_NL”
“SECH_GRANGER”
STAT_NON_LINE “COMP_INCR” “GRANGER_FP”
Code_Aster
®
Version
6.4
Titrate:
HSNA100 - Drying of a concrete enclosing wall
Date:
23/06/03
Author (S):
G. DEBRUYNE
Key
:
V7.20.100-C
Page:
8/10
Manual of Validation
V7.20 booklet: Thermodynamic nonlinear statics of the axisymmetric structures
HT-66/03/008/A
6
Results of modeling B
6.1 Values
tested
Reference AUTRE_ASTER corresponds to the results of modeling A.
Water concentration with the N6 node:
Identification
Water concentration
Reference
AUTRE_ASTER
Aster %
difference
at 5 years
104.818
107.094
2.171
at 15 years
96.161
98.459
2.390
at 54 years
78.276
79.693
1.810
Water concentration with the N6 node:
Identification
Water concentration
Reference
AUTRE_ASTER
Aster %
difference
at 10 years
100.071
102.345
2.273
at 20 years
92.787 95.056
2.445
at 30 years
87.224 89.290
2.368
at 40 years
82.893 84.673
2.147
at 50 years
79.460 80.970
1.901
Water concentration with the N7 node:
Identification
Concentration
Reference
NON_REGRESSION
Aster %
difference
at 5 years
104.818
105.773
0.912
at 15 years
96.161
97.597
1.494
at 54 years
78.276
79.558
1.638
Water concentration with the N7 node:
Identification
Water concentration
Reference
NON_REGRESSION
Aster %
difference
at 10 years
100.071
101.571 1.499
at 20 years
92.787 94.185
1.507
at 30 years
87.224 88.571
1.543
at 40 years
82.893 84.202
1.579
at 50 years
79.460 80.746
1.619
Dx displacement with the node elastoplastic N6 calculation:
Identification
Dx displacement
Reference
AUTRE_ASTER
Aster %
difference
at 54 years
- 0.184
- 0.184 0.126
Dx displacement with the node elastoplastic N7 calculation:
Identification
Dx displacement
Reference
NON_REGRESSION
Aster %
difference
at 54 years
- 0.181
- 0.184 - 1.592
Code_Aster
®
Version
6.4
Titrate:
HSNA100 - Drying of a concrete enclosing wall
Date:
23/06/03
Author (S):
G. DEBRUYNE
Key
:
V7.20.100-C
Page:
9/10
Manual of Validation
V7.20 booklet: Thermodynamic nonlinear statics of the axisymmetric structures
HT-66/03/008/A
Dx displacement with the node N6 elastic design:
Identification
Dx displacement
Reference
AUTRE_ASTER
Aster %
difference
at 54 years
- 0.275
- 0.275
- 0.073
Dx displacement with the node N7 elastic design:
Identification
Dx displacement
Reference
NON_REGRESSION
Aster %
difference
at 54 years
- 0.271
- 0.275
- 1.626
Code_Aster
®
Version
6.4
Titrate:
HSNA100 - Drying of a concrete enclosing wall
Date:
23/06/03
Author (S):
G. DEBRUYNE
Key
:
V7.20.100-C
Page:
10/10
Manual of Validation
V7.20 booklet: Thermodynamic nonlinear statics of the axisymmetric structures
HT-66/03/008/A
7 Modeling
C
7.1
Characteristics of modeling
It is a question here of comparing the mechanical fields resulting from the controls
MECA_STATIQUE
and
STAT_NON_LINE
. Those must be identical provided that the initial water concentration is
null. Indeed, the withdrawal of dessication is equal to
)
)
(
(
)
(
0
C
T
C
T
-
=
for incremental calculation
(
STAT_NON_LINE)
and
)
(
)
(
T
C
T
=
in
MECA_STATIQUE
since calculation does not take account of
history of material. One affects a water preconcentration then equalizes with
0
C
by the operator
CREA_CHAMP
and one replaces the running water concentration
)
(T
C
by
0
C
T
C
-
)
(
using
the operator
COMB_CHAM_NO
.
One uses same axisymmetric modeling as A, with the same space discretization and
temporal. Only the mechanical loading is modified, one removes the mechanical pressures
exerted on the chamber as well as thermal dilation (by cancelling the expansion factor) so
to isolate the withdrawal from with drying.
7.2
Functionalities tested
The functionalities tested are those of other modelings plus the following ones:
Controls Options
CREA_CHAMP “AFFE”
“NOEU_TEMP_R”
CREA_CHAMP “EXTR”
“NOEU_TEMP_R”
COMB_CHAM_NO
CREA_RESU “EVOL_THER”
8
Results of modeling C
8.1 Values
tested
Displacement at the A2 point:
Identification Reference Stat_Non_Line Aster
Aster Méca_Statique %
difference
DX (N47)
8.7688E-4
8.9645E-4 8.7688E-4
2.2
The value of reference selected is that obtained by the operator
MECA_STATIQUE
.
9
Summary of the results
For modeling A, the precision of the results reaches approximately 1.5% for the water concentration
compared to the reference solution which one does not know the proper precision.
The test was also carried out on a mesh much coarser (4 elements in the direction
radial), and the results are also good in the center of the concrete structure.
For modeling B, the difference reaches 2.5% on the concentrations because of a mesh 3D
relatively coarse.
This test makes it possible of more than check nonthe regression of the code for the calculation of drying in
the nonlinear operator of mechanics. The law of behavior chosen, as well as the field of moisture
resultant do not make it possible to know simple analytical solution. Convergence in thermics
nonlinear is delicate with the first pitch of time, to find the first state of balance, because of
the important scale of the pitches of time. Modeling C makes it possible to take account of a concentration
out of nonnull initial water in a calculation carried out with the operator
MECA_STATIQUE
.