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Code_Aster
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Titrate:
Relation of behavior of Bazant for the creep of desiccation
Date:
30/01/03
Author (S):
J. EL GHARIB
Key
:
R7.01.05-A
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:
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Manual of Reference
R7.01 booklet: Modelings for the Civil Engineering and the géomatériaux ones
HT-66/02/004/A
Organization (S):
EDF-R & D/AMA















Manual of Reference
R7.01 booklet: Modelings for the Civil Engineering and the géomatériaux ones
R7.01.05 document



Relation of behavior of Bazant
for the intrinsic creep of desiccation of the concrete




Summary:

Contrary to the clean creep which is the share of the creep measured on a test-tube protected from
external desiccation, the creep of desiccation is calculated on a mechanically charged test-tube and
subjected to drying simultaneously.
This document presents the model of intrinsic creep of desiccation of Bazant (1985). One details there
also the writing and digital processing of the model.
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Code_Aster
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Titrate:
Relation of behavior of Bazant for the creep of desiccation
Date:
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Author (S):
J. EL GHARIB
Key
:
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:
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Count
matters
1
Introduction ............................................................................................................................................ 3
2
Partition of the deformation ....................................................................................................................... 4
3
Constitutive law ....................................................................................................................................... 5
4
Discretization ......................................................................................................................................... 5
5
Integration of the law of behavior ................................................................................................... 6
5.1.1
Deviatoric part .................................................................................................................. 6
5.1.2
Hydrostatic part ................................................................................................................ 7
6
Stamp tangent .................................................................................................................................... 8
6.1
Phase of prediction ......................................................................................................................... 8
6.2
Reactualization of the tangent matrix ........................................................................................... 8
6.3
Variables of state .............................................................................................................................. 10
7
Implementation of a calculation of creep of desiccation ......................................................................... 10
8
Bibliography ........................................................................................................................................ 11
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Titrate:
Relation of behavior of Bazant for the creep of desiccation
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1 Introduction
One points out the deformations differed from a concrete structure to locate the share of the deformation
calculated in this document:
·
at the youth:
- endogenous withdrawal (1j - 1 year),
caused by a reaction of thermo hydration
- thermal withdrawal (1h ­ 1j).
·
in the medium term without load: withdrawal of desiccation (qq m ­ qq year) according to dimensions' of
structure caused by the drying which results in an evaporation of part of water not
used in the process of hydration.

·
long-term under load:
- clean creep (without exchange of moisture with outside thus without drying),
- the creep of desiccation (with drying which assigns the behavior of the concrete to the scale
microscopic, which is translated the macroscopic scale by creep of desiccation).
The differed deformations constitute a significant part of the deformations which appear in
concrete during its life. Among its differed deformations, withdrawals endogenous and thermal with short
term, withdrawal of desiccation caused by medium-term drying. One quotes also them
deformations differed under long-term load like clean creep and creep from desiccation.
The model presented here relates to the modeling of the deformation differed associated creep from
intrinsic desiccation. The creep of desiccation in complement to clean creep is the share of
total creep directly related to the water departure affecting the concrete which undergoes a mechanical loading
on the one hand and drying on the other hand. In other words, the deformation which one measures in one
test-tube which dries is directly related to the drying under stresses which carries not of creep of
desiccation.
The model suggested here is that of Bazant (1985) and adopted by L. Granger in its thesis (1995).
It is a law of the viscoelastic type linear which holds in account of the effect of the variation of
the hygroscopy. One presents the details of the numerical integration of this law in Code_Aster.
In Code_Aster, this model is used under the name of
BAZANT_FD
.
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Code_Aster
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Titrate:
Relation of behavior of Bazant for the creep of desiccation
Date:
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Author (S):
J. EL GHARIB
Key
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2
Partition of the deformation
Into small deformations, the increment of the total deflection is broken up into several terms
relating to the mechanisms considered. If one holds account in the partition of the increments of
deformations, thermics, associated the thermal, endogenous withdrawal and with the withdrawal of desiccation, then:
fl
Re
as of
Re
end
HT
E
+
+
+
+
=
éq
2-1
The increment of the deformation of creep
fl
breaks up into two components, corresponding
with clean creep and the creep of desiccation:
fl
as of
fl
Pr
fl
+
=
éq 2-2
The creep of desiccation
fl
as of
as for him, breaks up into two intrinsic and structural part:
fl
struc
as of
fl
as of
fl
as of
_
int
_
+
=
It is agreed that the structural deformation is not a component of deformation in oneself,
thus in this document the only component of the creep of desiccation relates to the part
intrinsic:
fl
as of
fl
as of
int
_
=
éq 2-3
with:
H
E
=
(
)
I
T
T
ref.
HT
-
=
I
Re
end
-
=
:
hydration
Ci
Re
as of
-
=
:
C
water concentration
,
,
,
H
: stamp elastic, thermal dilation, coefficients related on the withdrawals endogenous and the withdrawal
of desiccation are data material.
Here, one wants to modelize
fl
as of
.
Note:
This partition of the deformations is purely numerical. For the calculation of each one of these
components, the research workers consider a combination different from
components of deformation (See [bib1] and [bib2]).
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Code_Aster
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Titrate:
Relation of behavior of Bazant for the creep of desiccation
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3 Law
constitutive
Bazant et al. (1985) suggest that the drying and the application of a loading in compression
at the same time are responsible for the microcomputer-dissemination of the molecules between the macro-pores and them
micropores. The microcomputer-dissemination of the water molecules would support the rupture of the connections between
particles of gel inducing the deformation of creep of desiccation. It is one of the phenomena
physicochemical most intricate to modelize resulting from a coupling between the stress, it
clean creep and drying. They propose the following equation to take into account the creep of
intrinsic desiccation at the elementary level:
H
fl
as of
&
&
=
éq 3-1
with:
,
fl
as of
deformation of the intrinsic creep which evolves/moves in time,
,
a parameter material
[]
1
-
AP
,
,
H
the relative humidity which evolves/moves in time, fact of the case of evolution.
This expression is similar to the rheological model of the shock absorber:
=
fl
as of
&
éq 3-2
Note:
By preoccupation with a lightening of notations, one uses
fl
to replace
fl
as of
in the continuation of
document.


4 Discretization
The evolution of the relative humidity is approached by a function closely connected per pieces (Benboudjema and
Al, 2001d). This discretization according to (Bazant, 1982) makes it possible to increase the precision of calculations
numerical in a considerable way compared to an approximation by bearing (Heaviside function)
especially if the size of the pitch of time is important:
()
(
)
[
]


-
=
-
+
=
+
+
N
N
N
N
N
N
N
N
N
H
H
H
T
T
T
H
T
T
T
H
T
H
1
1
,
with
éq
4-1
according to the equation [éq 3-1], one can write:
(
)
[]
1
,
0
.
1
1
+
-
+
=
+
+
with
T
T
H
H
N
N
N
fl
N
fl
N
éq
4-2
For
2
/
1
=
, semi-implicit diagram which makes it possible to have a better quadratic convergence of
solution, one obtains:
(
)
2
.
2
.
1
1
1
1
1
+
+
+
+
+
+
-
+
=


+
-
+
=
N
N
N
N
fl
N
fl
N
N
N
N
fl
N
fl
N
H
H
H
H
or
éq
4-3
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Code_Aster
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Titrate:
Relation of behavior of Bazant for the creep of desiccation
Date:
30/01/03
Author (S):
J. EL GHARIB
Key
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R7.01.05-A
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R7.01 booklet: Modelings for the Civil Engineering and the géomatériaux ones
HT-66/02/004/A
5
Integration of the law of behavior
As in this document one is interested in integration of the intrinsic creep of desiccation, one goes
to consider for creep the only component
fl
as of int
_
but to simplify the writing one goes
to call
fl
. One poses in the same way:
Re
as of
Re
end
HT
With
+
+
=
éq
5-1
By employing the following notations:
With
With
With
-
,
,
for the quantity
With
evaluated at the known moment
N
T
, with
the moment
1
+
N
T
and its increment
T
, respectively.
It is a question of expressing the stress at time + according to the stress at time ­ and of the increment
of deformation at time -. One seeks initially the expression of the deviatoric component and then
the expression of the hydrostatic component of the stress.
5.1.1 Part
deviatoric
One seeks a relation between the deviatoric stress
~
and variation of the deformation
deviatoric
~
at time +:
The stress at time + is written:
E
E
µ
µ
µ
µ
~
2
~
2
2
~
2
~
+
=
=
-
-
éq
5.1.1-1
The elastic prediction of the deviatoric stress is written:
µ
µ
µ
~
2
~
2
2
~
+
=
-
-
E
éq
5.1.1-2
Like the component
With
do not have a deviatoric part, one can write:
fl
µ
µ
µ
µ
~
2
~
2
~
2
2
~
-
+
=
-
-
éq
5.1.1-3
While using [éq 4-3], one obtains:
µ
µ
µ
µ
µ
~
2
2
~
2
2
~
2
~
2
2
~
~
H
H
E
-
-
+
=
-
-
-
4
4 3
4
4 2
1
éq
5.1.1-4
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Relation of behavior of Bazant for the creep of desiccation
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from where,




+
-
=




+
-
+
=
-
-
-
-
2
2
1
~
2
2
~
2
2
1
~
2
2
~
2
~
2
2
~
H
H
H
H
E
µ
µ
µ
µ
µ
µ
µ
éq
5.1.1-5
5.1.2 Part
hydrostatic
One seeks a relation enters
()
tr
and
()
tr
at time +:
The stress at time + is written:
()
()
()
()
E
E
Ktr
tr
K
K
Ktr
tr
+
=
=
-
-
3
3
3
3
éq
5.1.2-1
The elastic prediction of the hydrostatic stress is:
()
()
()
+
=
-
-
Ktr
tr
K
K
tr
E
3
3
3
éq
5.1.2-2
from where,
()
()
()
()
()
()
With
fl
E
Ktr
Ktr
Ktr
tr
K
K
Ktr
tr
-
-
+
=
=
-
-
3
3
3
3
3
3
éq
5.1.2-3
According to [éq 4-3], one can express the hydrostatic part of
fl
:
()
()
()
()
()
()
tr
H
K
tr
H
K
Ktr
Ktr
tr
K
K
tr
With
2
3
2
3
3
3
3
3
-
-
-
+
=
-
-
-
éq 5.1.2-4
from where,
()
()
()
()
() ()
()
()




+
-
-
=




+
-
-
+
=
-
-
-
-
2
3
1
2
3
3
2
3
1
2
3
3
3
3
3
H
K
tr
H
K
Ktr
tr
H
K
tr
H
K
Ktr
Ktr
tr
K
K
tr
With
E
With
éq 5.1.2-5
One thus deduces the total stress from it by combining the two components deviatoric and
hydrostatic at time +:
()
ij
ij
tr
3
~
+
=
éq
5.1.2-6
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Relation of behavior of Bazant for the creep of desiccation
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J. EL GHARIB
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6 Matrix
tangent
6.1
Phase of prediction
The option used is
RIGI_MECA_TANG
, the tangent operator calculated in each point of Gauss is known as
in speed:
kl
ijkl
ij
D
&
&
=
,
in this case,
ijkl
D
is a viscoelastic operator calculated starting from the not discretized equations.
6.2
Reactualization of the tangent matrix
The option used is
FULL_MECA
, when one reactualizes the tangent matrix with each iteration in
updating the internal stresses and variables:
kl
ijkl
ij
D
With
D
=
,
in this case,
ijkl
With
is a viscoelastic operator calculated starting from the discretized equations
implicitly.
()
D
I
tr
+
=
3
1
~
éq
6.2-1
()
() ()
D
I
tr
tr
tr
+
=
3
1
~
~
~
éq
6.2-2
()
kl
ij
jl
ik
kl
ij
kl
ij
kl
ij
tr
3
1
3
1
~
-
=
-
=
()
kl
ij
kl
ij
tr
=
According to [éq 5.1.1-5]:
µ
µ
2
2
2
1
~
~
=


+
H
éq
6.2-3
According to [éq 5.1.2-5]:
()
()
K
H
K
tr
tr
3
2
3
1
=


+
éq
6.2-4
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Relation of behavior of Bazant for the creep of desiccation
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Writing of speed:
T
H
T
=


+
µ
µ
~
.
2
2
2
1
~
éq
6.2-5
()
()
T
tr
K
H
K
T
tr
=


+
.
3
2
3
1
éq
6.2-6
Thus while returning to [éq 6.2-2], one can deduce the writing of speed:
(
)
D
D
D
D
D
I
I
H
K
K
I
I
I
H




+
+


-




+
=
2
3
1
3
3
1
3
1
2
2
1
2
4
µ
µ
éq
6.2-7
Linearization:
µ
µ
~
.
2
2
2
1
~
=


+
H
éq
6.2-8
()
()
tr
K
H
K
tr
=


+
.
3
2
3
1
éq
6.2-9
Like
H
is independent of the stress, it is the same writing that one finds afterwards
linearization from where the form of the tangent matrix:



























































+




+




+




+
+
+




+
-
+




+
-
+




+
-
+




+
+
+




+
-
+




+
-
+




+
-
+




+
+
+
=








31
23
12
33
22
11
31
23
12
33
22
11
2
2
2
2
2
1
2
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
2
2
1
3
4
2
3
1
2
2
1
3
2
2
3
1
2
2
1
3
2
2
3
1
0
0
0
2
2
1
3
2
2
3
1
2
2
1
3
4
2
3
1
2
2
1
3
2
2
3
1
0
0
0
2
2
1
3
2
2
3
1
2
2
1
3
2
2
3
1
2
2
1
3
4
2
3
1
2
2
2
µ
µ
µ
µ
µ
µ
µ
µ
µ
µ
µ
µ
µ
µ
µ
µ
µ
µ
µ
µ
µ
µ
µ
µ
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
3
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
2
1
H
H
H
H
H
K
K
H
H
K
K
H
H
K
K
H
H
K
K
H
H
K
K
H
H
K
K
H
H
K
K
H
H
K
K
H
H
K
K
In this case, the tangent operator is the same one for
RIGI_MECA_TANG
and for
FULL_MECA
:
ijkl
ijkl
D
With
=
. It has a writing similar to the elastic matrix with dependant coefficients
of
H
and of
.
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Code_Aster
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Titrate:
Relation of behavior of Bazant for the creep of desiccation
Date:
30/01/03
Author (S):
J. EL GHARIB
Key
:
R7.01.05-A
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:
10/12
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R7.01 booklet: Modelings for the Civil Engineering and the géomatériaux ones
HT-66/02/004/A
6.3 Variables
of state
The variables of state are:
·
: tensor of the stresses,
·
: tensor of the deformations,
·
C
: water concentration.
The internal variables of this law of behavior is the value of the hygroscopy at the current moment.


7
Implementation of a calculation of creep of desiccation
In a way similar to the clean model of creep of Granger,
GRANGER_FP
, established already in
Code_Aster, this law constitutive depends on
,
H
the relative humidity, which evolves/moves in time.
1)
To make a mechanical calculation of creep of desiccation with this law, it is necessary to have
relative humidity. The user can confront himself with two situations:
Has
The user knows moisture
H
or water content
C
structure at various moments,
initial and final in the majority of the cases.
In this case, it can with
CREA_CHAM
and the key word
AFFE
to affect the field of
temperature
“TEMP”
with the structure. It must repeat the control
CREA_CHAM
with each
desired moment. Then, with the control
CREA_RESU
, creates a structure of
data result starting from the fields already defined in the corresponding moments.
B
The user does not know the distribution of the field of moisture of the structure.
In this case, it must carry out a calculation of drying. The field of drying is given
thanks to the control
THER_NON_LINE
, but which is comparable in term of variable with
a temperature (standard
TEMP
) of the field
NOEU_TEMP_R
.
Once defined (A) or calculated (B) a field of temperature “compared to a field of drying”, it
is necessary to begin mechanical calculation:
2)
Initially by creating the loading corresponding under
AFFE_CHAR_MECA
and the key word
SECH_CALCULEE
. On the level of
STAT_NON_LINE
, which one put in
SECH_CALCULEE
is
regarded from now on as a field of drying with the variable
“SECH”
.
However the law is written according to the hygroscopy
H
and not according to the water content
C
,
They is the same the case of the clean law of creep of Granger. One proceeds in the same way, it
is necessary:
3)
To define the curve sorption-desorption which allows the passage of the water content
C
with
the hygroscopy
H
. This curve must be indicated by the user with
DEFI_FONCTION
and
NOM_PARA = SECH
.
4) To define
under
DEFI_MATERIAU
, the key word
BAZANT_FD
in which it is necessary to give like words
obligatory keys:
LAM_VISC
who is a parameter material and
FONC_DESORP
who is one
function defined before and which connects
H
the hygroscopy with
C
water content.
5)
Mechanical calculation is carried out thanks to the control
STAT_NON_LINE
with like relation
in the key word
COMP_INCR = _F
(
RELATION = “BAZANT_FD”
).
One of the evolutions to be envisaged is the use in
RELATION_KIT
of the two laws of creep of
Granger:
GRANGER_FP
and
BAZANT_FD
.
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Code_Aster
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Titrate:
Relation of behavior of Bazant for the creep of desiccation
Date:
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Author (S):
J. EL GHARIB
Key
:
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Page
:
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R7.01 booklet: Modelings for the Civil Engineering and the géomatériaux ones
HT-66/02/004/A
8 Bibliography
[1]
L. GRANGER: Behavior differed from the concrete in the chambers of nuclear thermal power stations:
analyze and modeling. Thesis of Doctorate of the ENPC (1995).
[2]
F. BENBOUDJEMA, F. MEFTAH, J.M. TORRENTI, Y. LE-PAPE: Taking into account of the effects
drying on the deformations of the concrete noncharged and charged. Note HS-DG/AA/NNN/A
(2002).
[3]
A. RAZAKANAIVO: Modeling of the behavior of Granger for the clean creep of
concrete. Doc. [R7.01.01], Code_Aster (2001).
[4]
G. DEBRUYNE, B. CIREE: Modeling of the thermo hydration, drying and the withdrawal
concrete. Doc. [R7.01.12], Code_Aster (2001).
[5]
J. EL GHARIB: Comparison of the processing of the deformations differed between the model from
Granger and model LGCU. CR-AMA-02.125.
background image
Code_Aster
®
Version
6.0
Titrate:
Relation of behavior of Bazant for the creep of desiccation
Date:
30/01/03
Author (S):
J. EL GHARIB
Key
:
R7.01.05-A
Page
:
12/12
Manual of Reference
R7.01 booklet: Modelings for the Civil Engineering and the géomatériaux ones
HT-66/02/004/A


























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