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SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 1
F. Pesavento, B.A. Schrefler, G. Sciumè
Dept. of Civil, Environmental and Architectural EngineeringUniversity of Padova – ITALY
D. Gawin
Department of Building Physics and Building MaterialsTechnical University of Lodz – POLAND
A multiphase concrete model with application
to high temperature, structural repair,
leaching and Alkali-Silica reaction
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 3
Layout
� Introduction
� Mathematical model of concrete as multiphase porous material
� (Numerical model)
� Applications of the model and numerical examples
� Modelling of concrete at early ages and beyond
� Modelling of concrete leaching
� Modelling of ASR in concrete structures
� Concrete at high temperature
� (Simplification of the model and its application to concrete structures repair)
� Conclusions & final remarks
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 4
� Concrete treated as a deformable, multiphase porous material
� Phase changes and chemical reactions (hydration, leaching, etc) are
taken into account
� Full coupling:
hygro-thermo-mechanical (stress – strain) ⇔ chemical reaction(cement hydration, leaching, ASR, etc)
� Transport mechanisms of moisture- and energy- typical for the specific phases of concrete are considered.
� Evolution in time (aging) of material properties, e.g. porosity, permeability,strength properties according to the hydration degree.
� Non-linearity of material properties due to temperature, gas pressure,moisture content and material degradation.
Theoretical ModelFundamental hypotheses
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 5
Capillary water (free water):� advective flow (water pressure gradient)
Physically adsorbed water:� diffusive flow (water concentration gradient)
Chemically bound water:� no transport
Water vapour:� advective flow (gas pressure gradient)� diffusive flow (water vapour concentration gradient)
Dry air:� advective flow (gas pressure gradient)� diffusive flow (dry air concentration gradient)
Ions (Ca++, Na+):� advective flow(water pressure gradient)� diffusive flow (calcium ions concentration gradient)� electrical flow (electrical potential gradient)
Theoretical ModelTransport Mechanisms
E=0
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 6
� Dehydration: solid matrix + energy ⇒ bound water
� Hydration: chemically bound water ⇒ solid matrix + energy
� Evaporation: capillary water + energy ⇒ water vapour
� Condensation: water vapour ⇒ capillary water + energy
� Desorption: phys. adsorbed water + energy ⇒ water vapour
� Adsorption: water vapour ⇒ phys. adsorbed water + energy
� Leaching: calcium in solid skeleton ⇒ calcium in liquid solution
� ASR: silica+alkali+water ⇒ hydrophilic gel+absortpion
Theoretical ModelChemical reactions & Phase Changes
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 7
Balance equations:
local formulation (micro- scale)
upscaling
Volume Averaging Theory
by Hassanizadeh & Gray, 1979,1980
macroscopic formulation
(macro- scale)
Rational Thermodynamics
Theoretical ModelMicro- ⇒ macro- description
Model development:
� Lewis & Schrefler, 1998; Schrefler, 2002;
�Gray & Schrefler, 2007; Gray, Pesavento, Schrefler, 2 009;
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 8
� The dry air and skeleton mass balance
� The water species and skeleton mass balance
� The multiphase medium enthalpy balance
� The calcium mass conservation equation
� Electrical charge balance equation
� The multiphase medium momentum balance (mechanical equilibrium)
� Evolution equation for hydration/dehydration
� Evolution equation for mechanical damage
� Evolution equation for thermo-chemical damage (leaching, etc.)
� Evolution equation for ASR process
Theoretical ModelMacroscopic balance equations & evolution equations
Electrical field neglected
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 9
( )
( )
ρβρ ρ
ρρρ
− − − + + + +
= −ɺ
11
1
s gas sg gasw
s g g gga ga
ga gs disg gga s
S nD S D T Dn n S S div divDt Dt Dt
mdiv nS S
v J
v
Dry air (and skeleton) mass balance equation
( ) ( )1 1
s s shydr disss
s s s
mn D D n mn div
Dt Dt− ρ − + − = −ρ ρ ρ
vɺ ɺ
Solid skeleton mass balance equation
Mathematical modelMacroscopic balance equations
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 10
Water species (liquid+vapor) (and skeleton) mass ba lance equation
Mathematical modelMacroscopic balance equations
( ) ( )
( ) ( ) ( ) ( )
( )
ρρ ρ ρ ρ α β
ρρ ρ ρ ρρ
ρ ρρ
− + + − + + +
− Γ+ − + = Γ
− +ɺ
*
1
s gws sgw gw gww w sw
w g swg g g
ss sgw gs gww ls w leach
w g w g sleach
gw wdiss
g ws
D S D T Dn S S div S n div
Dt Dt Dt
n DDdiv nS div nS S S
D Dt
mS S
v J
v v
Energy balance equation (for the whole system)
( ) ( ) ( )ρ ρ ρ χ∂ + + ⋅ − = − ∆ + ∆∂
ɺ ɺg gw w
p w p g p eff vap vap dis diseff
TC C C gradT div gradT m H m H
tv v
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 11
Mathematical modelMacroscopic balance equations
( )
( )
ρ αρ ρ
ρρ ρ ρ
Γ− + + + + +
Γ
−ɺ ɺ
1 11
1=
s s ss ss Caleach w Ca
Ca w Ca w Ca w ds wleach
w ls dis disCa w Ca ww w s
D D S D CDn C S nC nS C S div div
D Dt Dt Dt
m mdiv C nS C S
v J
v
Calcium mass balance equation
( ) ρ =ɺ ɺ+ 0totaldiv t g
Linear momentum balance equation (for the multipha se system)
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 12
� Gas pressure – pg
� Capillary pressure – pc
� Temperature – T;
� Calcium concentration – cCa
� Displacement vector – [ux, uy , uz]
� Hydration/Dehydration degree – Γhydr
� Mechanical damage degree – d
� Themo-chemical damage degree – V
� ASR reaction extent – ΓASR
� Leaching degree – Γleach
Theoretical ModelState variables & internal variables
Theoretical fundamentals and model development:
� Gawin, Pesavento, Schrefler , CMAME 2003, Mat.&Struct. 2004, Comp.&Conc. 2005
�Gawin, Pesavento, Schrefler , IJNME 2006 (part 1, part2)
�Gawin, Pesavento, Schrefler , IJSS 2008 (part 1, part2), CMAME 2009
�Pesavento et al. CMAME 2012
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 14
Modelling of concrete at early ages and beyond
Creep in concrete
� Bazant, Wittmann (eds)- 1982
� Bazant et al. - 1972-2002
� Harmathy - 1969
� Bazant, Chern – 1978 - 1987
� Hansen - 1987
� Bazant, Prasannan - 1989
� De Schutter, Taerwe - 1997
� Sercombe, Hellmich, Ulm, Mang - 2000
Hydration of cement
� Jensen - 1995
� van Breugel - 1995
� De Schutter, Taerwe - 1995
� Singh et al. – 1995
� Ulm, Coussy -1996
� Bentz et al. – 1998, 1999
� Sha et al. - 1999
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 16
hydrhydr
hydr
m
m∞ ∞Γ = =χ
χ
( ) ( ), exphydr ahydr hydr
d EA
dt RTΓΓ = Γ Γ −
ɶ ϕβ ϕ
( ) ( ) ( )21 1 exphydr hydr hydr hydr
AA AΓ ∞
∞
Γ = + κ Γ − Γ −ηΓ κ ɶ
where
- hydration degree-related, normalized affinity, χ - hydration extent,
Ea – hydration activation energy, R – universal gas constant, t – time.
( )hydrAΓ Γɶ
� from: [Cervera, Olivier, Prato, 1999]
Effect of relative humidity
Chemo - hygrothermal interactionsEvolution of the hydration process
Evolution of the hydration degree ΓΓΓΓhydr[Gawin, Pesavento, Schrefler, IJNME 2006 part 1 and part 2]
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 17
Chemo- mechanical interactionsStrain components
ch ch hydrd d= β Γε I
In general, a total strain of maturing concrete, εεεεtot, can be split into the following components:
1. free thermal strain2. thermo-chemical strain3. creep strain4. mechanical strain (caused by mechanical load and shrinkage)
Shrinkage strain Thermo-chemical strain
Free thermal strain strain
t sd dTβ=ε I
( )3
ws c ws csh
Td d p dp
Kα χ χ= − +ε I
mech tot c th chd d d d d= −ε ε ε − ε − εε ε ε − ε − εε ε ε − ε − εε ε ε − ε − εStrain decomposition
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 18
Capillary pressure & disjoining pressure Forces:
in waterCapillary pressure
Disjoining pressure
in skeletonCapillary pressure
Disjoining pressure
Hygro-mechanical interactionsShrinkage of concrete
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 19
Effective stress principle:
where is the solid surface fraction in contact with the wetting film,
I - unit, second order tensor, α - Biot’s coefficient,
ps - pressure in the solid phase and pc is given by
with - disjoining pressure
Hygro-mechanical interactionsShrinkage of concrete
wssx
Coefficient x
0,0E+00
5,0E-02
1,0E-01
1,5E-01
2,0E-01
2,5E-01
3,0E-01
3,5E-01
0,0 0,2 0,4 0,6 0,8 1,0
Saturation [-]�[Gray & Schrefler, 2001]�[Gray & Schrefler 2006]�[Gray, Pesavento, Schrefler 2009]
c f wg wwgp s J= Π −
fΠ
0,0E+00
1,0E-04
2,0E-04
3,0E-04
4,0E-04
5,0E-04
6,0E-04
7,0E-04
8,0E-04
0% 20% 40% 60% 80% 100%
RELATIVE HUMIDITY [%]
SH
RIN
KA
GE
ST
RA
IN [m
/m] OC - experiment
OC - theory
HPC - experiment
HPC - theory
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 20
Evolution of concrete porosity & permeability:
Hygro-structural - chemical interactionsEvolution of the material properties
0,0E+00
1,0E-01
2,0E-01
3,0E-01
4,0E-01
5,0E-01
6,0E-01
0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1
HYDRATION DEGREE [-]
PO
RO
SIT
Y [
-]
1,0E-21
1,0E-20
1,0E-19
1,0E-18
1,0E-17
1,0E-16
1,0E-15
1,0E-14
0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1
HYDRATION DEGREE [-]
PE
RM
EA
BIL
ITY
[m
2 ]
k = f (hydr)
k = f (porosity)
( ) 10 k hydrAhydrk k ΓΓ
∞Γ = ⋅( ) ( )10 knA n nk n k ∞−∞= ⋅( ) ( )1hydr n hydrn n A∞Γ = + Γ −
[Halamickova, Detwiler, Bentz, Garboczi, 1995] [Halamickova et al., 1995, Kaviany, 1999]
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 21
Evolution of concrete strength properties:[De Schutter, 2002]
Hygro-structural - chemical interactionsEvolution of the material properties
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 22
Mathematical modelConstitutive law for creep strain
Details:� [Bazant Z.P. Prasannan S.,Solidification theory for concrete creep I: formulation, J. Eng. Mech., 115(8), 1989]
where ( ) ( )( )v
hydr
tt
t
γε =
Γɺ
ɺ ( ) ( )( )
se
f
tt
t
σε
η=ɺ
- creep strains (as sum of viscoelastic and viscous (flow) term);
- viscoelastic term;
- flow term;
- viscoelastic microstrain;
- apparent macroscopic viscosity
c
v
f
εεεγη
ɺ
ɺ
ɺ
Solidification theory for basic creep
Effective stress
Hydration degree
c v fd d d= +ε ε ε( )
( )
se c th ch
c th ch
d d d d d
d
= −
+ −
D
D
σ ε ε − ε − εσ ε ε − ε − εσ ε ε − ε − εσ ε ε − ε − ε
ε ε − ε − εε ε − ε − εε ε − ε − εε ε − ε − ε
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 23
� Cubic specimen – 50x50x200 mm;
� Initial conditions:To= 293.15 K, ϕo= 99.0% RH, Γhydr=0.1;
� Boundary conditions:
- convective heat and mass exchange: sealed (adiabatic)- surface mechanical load: unloaded
� Properties of the cement paste:- Elastic modulus measured prior the test (1, 3 and 7 days), curing temperature 20°C
Numerical example Autogenous shrinkage in High Performance Cement Paste
(Lura, Jensen, van Breugel test)
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 24
Numerical example Autogenous shrinkage in High Performance Cement Paste
(Lura, Jensen, van Breugel test)
0.93
0.94
0.95
0.96
0.97
0.98
0.99
1
0 24 48 72 96 120 144 168
TIME [h]
RE
LAT
IVE
HU
MID
ITY
[-]
RHb=4, fc=10b=2.8, fc=10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 12 24 36 48 60 72
TIME [h]H
YD
RA
TIO
N D
EG
RE
E [-
]
Experimental
b=4 or 2.8, fc=10
R.H. development in time Hydr. Degree development in time
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 25
Numerical example Autogenous shrinkage in High Performance Cement Paste
(Lura, Jensen, van Breugel test)
Effect of shrinkage – creep coupling
-3.0E-04
-2.5E-04
-2.0E-04
-1.5E-04
-1.0E-04
-5.0E-05
0.0E+00
0.93 0.94 0.95 0.96 0.97 0.98 0.99 1
RELATIVE HUMIDITY [-]
TO
TA
L S
TR
AIN
[-]
total - experiment
shrinkage - experiment
total - numerical
shrinkage - numerical
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 26
Numerical example Tests of Bryant and Vadhanavikkit (1987)
� Slab – thickness=30 cm; concrete: C50
� Material: concrete C50� - final porosity: 0.122, density: ρ= 1900 kg/m3,
� - intrinsic permeability: ko= 5·10-19 m2,
� - Young modulus: E= 49.2 GPa,
� - water/cement ratio w/c=0.45.
� Initial conditions:To= 293.15 K, ϕo= 99.8% RH, Γhydr=0.3;
� Boundary conditions:
Shrinkage (from day 7)
- convective heat and mass exchange: αc=5W/m2K; Tamb=293.15K; βc=0.002m/s; RHamb=60%
- surface mechanical load: unloaded or load=7 MPa at 8,28,84,182 days
Sealed (for the first 7 days and basic creep)
- convective heat and mass exchange: αc=5W/m2K; sealed - surface mechanical load: unloaded or load=7 MPa at 8,28,84,182 days
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 27
Numerical example Tests of Bryant and Vadhanavikkit (1987)
Drying & Load
-1.8E-03
-1.6E-03
-1.4E-03
-1.2E-03
-1.0E-03
-8.0E-04
-6.0E-04
-4.0E-04
-2.0E-04
0.0E+00
1 10 100 1000
TIME [days]
TO
TA
L S
TR
AIN
[-]
exp. shrinkageshrinkageexp. 8 daystotal 8 daysexp. 28 daystotal 28 daysexp. 84 daystot. 84 daysexp. 182 daystot. 182 days
-2.0E-03
-1.8E-03
-1.6E-03
-1.4E-03
-1.2E-03
-1.0E-03
-8.0E-04
-6.0E-04
-4.0E-04
-2.0E-04
0.0E+00
1 10 100 1000
TIME [days]S
TR
AIN
[-]
exp. Sealed - load sealed - loadexp. shrinkageshrinkageexp. total creepdrying & load
Pickett’s effect (8 days)
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 28
Modelling of concrete leachingD
em
ine
rali
ze
d
wa
ter
Picture of a leached cement paste sample, obtained by means of microscopic analysis in a fluorescent light.
Equilibrium based models: Gérard (1996), Kuhl et al. (2004), Kuhl and Meschke (2007)
Process kinetics based models:Ulm, Torrenti, Adenot – J. Engineering. Mechanics, 1999
Gawin, Pesavento, Schrefler - Part 1 & Part 2 , Solids and Structures, 2008Gawin, Pesavento, Schrefler, CMAME 2009.
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 30
Concrete leaching process kinetics Curve describing equilibrium between solid and liquid calcium
Calcium conc. in the pore solution [mol/m3]
Ca
lciu
m c
on
cte
nt
in t
he
so
lid
sk
ele
ton
[k
mo
l/m
3]
Calcium leaching
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 31
Concrete leaching process kinetics Curve describing equilibrium between solid and liquid calcium
Calcium conc. in the pore solution [mol/m3]
Ca
lciu
m c
on
cte
nt
in t
he
so
lid
sk
ele
ton
[k
mo
l/m
3]
Calcium leaching
0
2
4
6
8
10
12
14
16
0 2 4 6 8 10 12 14 16 18 20 22
Ca ions concentr. [mol/m 3]
Sol
id C
a co
ncen
tr. [
kmol
/m3 ]
0.00E+00
5.00E-07
1.00E-06
1.50E-06
2.00E-06
2.50E-06
dSC
a/dc
Ca
[mol
/m3 s]
SCa-Ca,T=25°C
source,T= 25°C
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 32
Kinetics of leaching processThermodynamic description of the process
η- parameter dependent on micro-diffusion of Ca2+,
µs – chemical potential of liquid calcium,
Γ – chemical potential of solid calcium.
[Ulm, Torrenti, Adenot – J. Engng. Mech. 1999]
dA
s= RT
dcCa
cCa
− B : dεεεε − dεεεε p( )+ kdχ −κ dsCa
Effect of Caconcentration
Effect of the material elastic properties
Effect of micro-cracking
Effect of Ca content in skeleton
A
s= µ s − Γ = η
dsCa
dt
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 33
Kinetics of leaching processThermodynamic description of the process
η- parameter dependent on micro-diffusion of Ca2+,
µs – chemical potential of liquid calcium,
Γ – chemical potential of solid calcium.
[Ulm, Torrenti, Adenot – J. Engng. Mech. 1999]
dA
s= RT
dcCa
cCa
− B : dεεεε − dεεεε p( )+ kdχ −κ dsCa
Effect of Caconcentration
Effect of the material elastic properties
Effect of micro-cracking
Effect of Ca content in skeleton
A
s= µ s − Γ = η
dsCa
dt
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 34
τ
s= η
RT Characteristic time of the process
R – universal constant of gas,
κ – process equilibrium constant,
η - parameter dependent on micro-
diffusion of Ca2+
Kinetics of leaching processThermodynamic description of the process
∂sCa
∂t= 1
ηκ s ,T( )ds − κ s ,T( )ds
sCa0
sCa
∫sCa0
sCa*
∫
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 35
cCa
ef T( )= cCa × exp −Eleach
R
1
T− 1
Tref
dAs = RT
dcCa
cCa
− κ dsCa = 0
The values of the equilibrium constant
can be found from the thermodynamic equilibrium condition at temperature T, which can be written in the incremental form as
κ sCa ,T( )
κ sCa ,T( )=
RT
cCa
dsCa
dcCa T
−1
in this way we get
and taking into account the expression
one can write
κ sCa ,T( )=κ sCa ,Tref( ) T
Tref
This allows writing the general relationship describing the thermodynamic of the process as:
∂sCa
∂t= 1
τ leach T( )1
RTref
κ s ,Tref( )ds − κ s ,Tref( )dssCa
0
sCa
∫sCa0
sCa*
∫
i.e. the dependence on the temperature is concentrated in the function τ leach T( )
Kinetics of leaching processExtension to the non-isothermal conditions
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 37
Evolution of a material porosity & permeability:
Chemo - hygral interactionsEvolution of the material properties
[Kuhl et al. - 2004] [Saito and Deguchi - 2000]
( )0 10 leachAk k n ΓΓ= ⋅
( )0 ,ch leachn n n= + ∆ Γ
0dissch Ca leachdiss
Mn s
ρ∆ = ⋅ Γ
** 10 nA nk B= ⋅
k = k n
0( )⋅10An∆nch*
Effect of mechanical and chemical damage
[Gawin et al. - 2009, CMAME accepted]
AΓ = An
∆nch
Vpaste
=A
n
Vpaste
Mdiss
ρdisss
Ca0
with
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 38
Hygral - chemical interactionsCalcium transport
0CaD2,0E-10
3,0E-10
4,0E-10
5,0E-10
6,0E-10
7,0E-10
8,0E-10
9,0E-10
0 2 4 6 8 10 12 14 16 18 20 22 24
Ca++ IONS CONCENTRATION [mol/m 3]
Ca+
+ IO
NS
DIF
FU
SIV
ITY
[m
2 /s]
T= 298.15 K
T= 283.15 K
T= 313.15 K
0,0E+00
1,0E-10
2,0E-10
3,0E-10
4,0E-10
5,0E-10
0 2 4 6 8 10 12 14 16 18 20 22
Ca++ IONS CONCENTRATION [mol/m 3]C
a++
ION
S T
HE
RM
OD
IFF
. [m
2 /s]
T= 298.15 K
T= 283.15 K
T= 313.15 K
Ions thermo-diffusionIons diffusion
( )0 expCa Ca Ca CaT T w T T refD
cn S D T T
Tτ α = = ⋅ − D I I
[Samson et al. - 2007]
D
dCa = D
dCaI = n S
wτ D
d 0Ca ⋅exp A
4T − T
ref( )
I
[Samson et al. - 2007, Kuhl and Meschke - 2003 ]
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 39
Numerical simulation resultsModeling of a wall subject to reaction-diffusion-advection process
Boundary Conditions
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 40
Numerical simulation resultsReaction-diffusion-advection process: 25°C and 60°C-25°C cases (2 and 3)
Ca ions concentration Calcium content Solid skeleton
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 41
Numerical simulation resultsReaction-diffusion-advection process: 25°C and 60°C-25°C cases (2 and 3)
Ca ions concentration Calcium content Solid skeleton
Chemical Damage
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 42
Numerical simulation resultsReaction-diffusion-advection process: 60°C and 25°C-60°C cases (1 and 4)
Ca ions concentration Calcium content Solid skeleton
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 43
Numerical simulation resultsReaction-diffusion-advection process: 60°C and 25°C-60°C cases (1 and 4)
Ca ions concentration Calcium content Solid skeleton
Chemical Damage
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 44
Numerical simulation resultsModeling of a wall subject to reaction-diffusion-advection process
Leaching front evolution
14
2
3
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 45
Modelling of Silica Alkali ReactionIntroduction
Difficulties related to ASR process simulation
� The reaction between alkali and the aggregates takes place at microscopic level and consists in the formation of a hydrophilic gel from the chemical combination of the silica contained in the aggregates, the alkali in the cement klinker (ions K+ and Na+ mainly) and the saline water solution, which fills partly or fully the pores of the material.
� While the first stage of the ASR (i.e. the dissolution of the silica) is known and can be simulated by means of a first order kinetic law, the second part of the process is less clear. In particular the mechanism of the formation of the amorphous gel, its combination with water and the related swelling, which leads to the macroscopically observable expansion and deterioration of the concrete structures, is under discussion.
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 46
Existing models and model proposed
� The existing models can be classified essentially into two classes: models which attribute the process progression to the water imbibitions (temperature independent) [1, 2] and models which consider temperature as the main parameter, i.e. ASR is considered as a pure thermally activated process [3, 4].
� In the present model the ASR is modelled as a two-stage process, involving chemical reactions causing first silica dissolution and then gel formation, [1]. The effect of moisture content on the kinetics of the first process is considered similarly as in [1, 2] and effect of temperature following approach proposed in [3, 4]. It is assumed that the gel formation process causes expansion of the material skeleton and the maximal chemical strain is dependent on the moisture content and to a much lesser extent on the temperature value. The gel is assumed to be in equilibrium with moisture in its pores, hence any variation of relative humidity causes an immediate change of chemical strains, also during decrease of water content.
① A. Steffens et al., Aging Approach to Water Effect on Alkali–Silica Reaction Degradation of Structures, Journal of Engineering Mechanics, 129, 50-59, (2003).
② F. Bangert et al., Chemo-hygro-mechanical modelling and numerical simulation of concrete deterioration caused by alkali-silica reaction, Int. J. Numer. Anal. Meth. Geomech., 28(78), 689-714, (2004).
③ Larive, C. Apports combinés de l'expérimentation et la modélisation à la compréhension de l'alcali-réaction et de ses effets mécaniques, Monograph LPC, 0A28, Laboratoire Central des Ponts et Chaussées, Paris (1998).
④ F-J Ulm et al., Thermo-chemo-mechanics of ASR expansion in concrete structures, Journal of Engineering Mechanics, 126(3), 233-242, (2000).
Modelling of Silica Alkali ReactionIntroduction
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 47
First stage of the process: evolution of the reaction extent ΓΓΓΓASR
tr = kr/A0 is the reaction time (A 0 is the initial chemical affinity and kr is the kinetic coefficient)
Mathematical modelModel of Silica Alkali Reaction
where (at constant T and Sw):
The chemical affinity is:
The reaction time is: where
with
Influence of saturation level
Latency time
Characteristic time
� Ref.: Larive et al , Journal of Engineering Mechanics 2000
τ L0 ,τ r 0 , AL , BL are material parameters
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 48
Mathematical modelStrain components
ch ch hydrd d= β Γε I
In general, a total strain of concrete, εtot, can be split into the following components:
1. free thermal strain2. ASR strain3. thermo-chemical strain4. creep strain5. mechanical strain (caused by mechanical load and shrinkage)
Shrinkage strain Thermo-chemical strain
Free thermal strain strain
t sd dTβ=ε I
( )3
ws c ws csh
Td d p dp
Kα χ χ= − +ε I
Strain decomposition
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 49
Mathematical modelModel of Silica Alkali Reaction
� Ref.: Steffens et al , Journal of Engineering Mechanics 2003
Second stage of the process: evolution of ASR strain εεεεASR
The water-gel combination rate is now:
with
Due to peculiar physico-chemical processes a loss of swelling potential is experimentally observed; this loss can be considered as a sort of “material aging”:
Water Aging
in which is the water combination coefficient at saturation level SwM ASR Sw( )
� Ref.: Pesavento et al , Comp. Methods in Appl. Mech. and Eng. 2012
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 50
Mathematical modelModel of Silica Alkali Reaction
Hence, the ASR strain evolution law is now:
After some mathematical transformations Steffens showed that:
Second stage of the process: evolution of ASR strain εεεεASR
M ASR Sw( ) = M ASR0ɶAASR ⋅ Sw + ɶBARS( ) linear formulation
M ASR Sw( ) = M ASR0 ⋅ exp ɶCASR ⋅ Sw + ɶDASR( ) power formulation
� Ref.: Steffens et al , Journal of Engineering Mechanics 2003
�Ref.: Bangert et al , IJNME 2004
M ASR0 = M ASR Sw = 1( )in which and and are material parametersɶAASR, ɶBARS, ɶCASRɶDASR
� Ref.: Pesavento et al , Comp. Methods in Appl. Mech. and Eng. 2012
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 51
� Density of the solid phase:
Mathematical modelModel of Silica Alkali Reaction: constitutive relationships
Const. relationships for the solid density
� In general the constitutive relationship for the solid skeleton has the form :
� Rate of the first invariant of the effective stress tensor:
Variation of the pore volume
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 52
Mathematical modelModel of Silica Alkali Reaction: constitutive relationships
Const. relationships for the intrinsic permeability
k = k mASR,d( ) = ko ⋅ 10Ak mASR/mASR∞( )10Add
Const. relationships for the porosity
n = constant
Sorption isotherms
� Suction curve for “unreacted” and for “fully reacted” material (Van Genuchten type):
� Evolution of the sorption isotherm during ASR process:
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 53
Mathematical modelModel of Silica Alkali Reaction: additional shrinkage
Evolution of the solid surface fraction due to ASR
with
Solid pressure
New microstructure due to the gel formation ⇒ modification of the solid pressure formulation by means a new form of the solid surface fraction
This allows of taking into account an additional shrinkage due to water loss from the ASR gel during the drying phases (the gel occupies less volume)
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 56
Modelling Silica Alkali ReactionExperimental-Numerical results comparison
� Material properties as in:
S. Poyet, Etude de la dégradation des ouvrages en béton atteints de la réaction alcali–silice: approcheexpérimentale et modélisation numérique multi-échelle des dégradations dans un environnement
hydrochemo–mécanique variable, PhD thesis, Université de Marne la Vallée, France (2003).
� Size of the specimens:
Cylindrical specimens – radius=1cm, height=16cm
� Boundary conditions:
- convective heat and mass exchange:
� RH∞=82%, and then 59%, 76%, 82%, 96% or 100% kept constant in time
with βc=0.002 m/s (drying cases) and βc=0.002 m/s (swelling cases)� T=60°C with αc=5 W/Km2
- surface mechanical load: unloaded
Poyet’s experimental tests at constant relative humidity
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 57
Modelling Silica Alkali ReactionExperimental-Numerical results comparison
Poyet’s experimental tests at constant relative humidity
Mass variation
ASR strain evolution
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 58
Modelling Silica Alkali ReactionExperimental-Numerical results comparison
� Material properties as in:
S. Poyet, Etude de la dégradation des ouvrages en béton atteints de la réaction alcali–silice: approcheexpérimentale et modélisation numérique multi-échelle des dégradations dans un environnement
hydrochemo–mécanique variable, PhD thesis, Université de Marne la Vallée, France (2003).
� Size of the specimens:
Cylindrical specimens – radius=1cm, height=16cm
� Boundary conditions:
- convective heat and mass exchange:
� RH∞=59-96% variable in time with
two different cycles: short (14 days) and long (28 days)βc=0.002 m/s (drying phases) and βc=0.002 m/s (swelling phases)
� T=60°C with αc=5 W/Km2
Poyet’s experimental tests at variable relative humidity
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
Modelling Silica Alkali ReactionExperimental-Numerical results comparison
Poyet’s experimental tests at variable relative humidity (long cycle)
Mass variation
ASR strain and react. extent evolution
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
Modelling Silica Alkali ReactionExperimental-Numerical results comparison
Poyet’s experimental tests at variable relative humidity (short cycle)
Mass variation
ASR strain and react. extent evolution
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 67
Modelling of concrete at high temperature
Concrete at high temperature
� Bazant, Thonguthai – 1978
� Thelandersson – 1987
� England, Khoylou - 1995
� Bazant, Kaplan – 1996
� Gerard, Pijaudier-Cabot, Laborderie - 1998
� Gawin, Majorana, Schrefler - 1999
� Bentz – 2000
� Nechnech, Reynouard, Meftah
- 2001
Thermal spalling
� Phan – 1996
� Ulm, Coussy, Bazant – 1999
� Sullivan – 2001
� Phan, Lawson, Davis - 2001
� HITECO project – 1995-2000
� NIST workshop – 1997
� UPTUN project – 2002-2006
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 68
Dehydration of concrete
Thermo-chemical interactionsConcrete at high temperature
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
0 200 400 600 800 1000
Temperature [ oC]
Deh
ydra
tion
degr
ee [
-]
0
0,005
0,01
0,015
0,02
0,025
0,03
0,035
0 0,2 0,4 0,6 0,8 1
Dehydration degree [-]
Deh
ydra
tion
rate
[1/
s]( ) ( )[ ]maxdehydr dehydrt T tΓ = Γ ( )
−⋅Γ=∂Γ∂
Γ RT
EexpA
ta
AΓ – chemical affinityT –temperature of concrete
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 69
Non-local isotropic damage theory
[Mazars & Pijaudier-Cabot, 1989]
Mechanical – mat. degradation interactionsMechanical material degradation description
2
2( ) exp
2oc
x sx s
l
−Ψ − = Ψ −
1( ) ( ) ( )
( )r V
x x s s dvV x
ε = Ψ − ε∫ ɶ
( )3 2
1i
i+
=
ε = ε∑ɶ
Ko
Koc
Fct
Fcc
εmax
σ−
ε−
t t c cd d d= +α α
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 70
Chemo - mechanical interactionsConcrete at high temperature
Correlation of dehydration degree & thermo-chemical damage
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
0 0,1 0,2 0,3 0,4
Dehydration degree [-]
The
rmo-
chem
ical
dam
age
[-]
( )1
( )o
o a
E TV
E T= −
( ) ( )( ) ( ) ( )1 1 1 1 1
( ) ( ) ( )o
o a o o a
E T E T E TD d V
E T E T E T= − = − = − − ⋅ −
0 0(1 )(1 ) : (1 ) :e ed V D= − − = −σ Λ ε Λ εσ Λ ε Λ εσ Λ ε Λ εσ Λ ε Λ ε
( ) ( )1 1S
d VS= =
− −σσσσσ σσ σσ σσ σɶ
ɶ
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 71
Effect of thermo- chemical material degradation on the stress – strain curves for C-60 concrete
Thermochemical - mechanical interactionsConcrete at high temperature
-70
-60
-50
-40
-30
-20
-10
0
-0.006 -0.005 -0.004 -0.003 -0.002 -0.001 0
Strain [-]
Str
ess
[MP
a]
20°C200°C
300°C
400°C
500°C
Experimental results from the EURAM-BRITE “HITECO” project
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 72
Intrinsic permeability – damage relationship
1.E-18
1.E-17
1.E-16
1.E-15
1.E-14
1.E-13
0 0.2 0.4 0.6 0.8 1
Damage parameter [-]
Wat
er in
tr.
perm
eabi
lity
[m2 ]
C-60
C-60 SF
C-70
C-90
Mechanical - hygral interactionsConcrete at high temperature
( )10 10p
D
Agf T A D
o go
pk k
p
= ⋅ ⋅ ⋅
Details:[Gawin, Pesavento & Schrefler,CMAME 2003]
Experimental results from the EURAM-BRITE “HITECO” project
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 73
Stress and strains of concreteStrain decomposition
Mechanical strain
mech tot th tchem trd d d d d= − − −ε ε ε ε ε
� mechanical strain (contains also shrinkage strain)
� total strain
� thermal strain
� thermo-chemical strain
� thermal transient strain
mech
tot
th
tchem
tr
ε
ε
ε
ε
ε
Where:
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 74
Shrinkage strain
LFTS model according to: [Gawin, Pesavento, Schrefler, Materials and Structures, 2004]
Stress and strains of concreteLoad Free Thermal Strain (LFTS) model
( )ws c ws csh
Td d p dp
Kα χ χ= +ε I tchem tot th shd d d d= − −ε ε ε ε
By using Load Free Thermal Strain (LFTS, i.e. irreversible part of thermal strain) model we get:
1. free thermal strain2. shrinkage strain3. thermo-chemical strain
( )tchem tchemd V dVβ=εConstitutive relationship for εεεεtchem
Thermo-chemical strain assessment
Free thermal strain strain
( )th sd T dTβ=ε
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
> 76
3-D modelling of LITS:
[Thelandersson, 1987]
βtr(V) relation according to:
[Gawin, Pesavento & Schrefler, Mat&Struct 2004]
c
( )f ( )
tr str e
a
Vd dT
Tβ=ε Q : σ
( ) ( )11
2ijkl ij kl ik jl il jkQ = − + + +γδ δ γ δ δ δ δ
Transient thermal creep of C-90
15% load
30% load45% load60% load
0% load
-1,00E-02
-7,50E-03
-5,00E-03
-2,50E-03
0,00E+00
2,50E-03
5,00E-03
7,50E-03
1,00E-02
0 100 200 300 400 500 600 700 800
Temperature [oC]
Line
ar s
trai
n [m
/m]
Stress and strains of concreteLoad Induced Thermal Strain (LITS) model
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
AIM: qualitative analysis of the effect of cooling processes on the hygro-thermo-chemo-mechanical state of a square column, manufactured with HSC, during thedevelopment of a natural fire in a high-rise building.
Numerical simulationsAnalysis of cooling processes in HSC square columns
> 79
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
Cooling Rates of the Air:�“Slow cooling”: – 0.20 ºC/s� “Fast cooling”: – 20.0 ºC/s
C60 (HSC)
HEATING PARAMETRIC CURVE:- Slow fire curve-Eurocode 1, Part 1-2 is used (O = 0,013 m1/2)
(Θg [ºC] , t [h])
0,0077
0,06545 0,7315
20 1.325 (1 0,324
0,204 0,472 )
tg
t t
e
e e
− ⋅
− ⋅ − ⋅
Θ = + ⋅ − ⋅ −
− ⋅ − ⋅
+2 TYPES OF ENVIRONMENTAL COOLING:
> 80
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
Par. 82 min. from fire start – at the beginning of cooling 122 minutes from fire start – at the end of slow cooling
Analysis of cooling processesSLOW (40 min) ENVIRONMENTAL COOLING
> 82
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
Par. 82 min. from fire start – at the beginning of cooling 122 minutes from fire start – at the end of slow cooling
Analysis of cooling processesSLOW (40 min) ENVIRONMENTAL COOLING
> 83
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
ZONES WITH AN INCREASE OF DAMAGE DUE TO COOLING (ESPECIALLY CLOSE TO
THE SURFACE)
Param. 82 min. fromfire start – at the beginningof slow cooling 122 minutesfromfire start – at the end of slow cooling
Analysis of cooling processesSLOW (40 min) ENVIRONMENTAL COOLING
> 84
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
DURING COOLING PHASE IN THE ZONES
CLOSE TO THE EXTERNAL SURFACES WE
OBSERVE AN INCREASE OF DAMAGE D
Analysis of cooling processesFAST (20 sec) ENVIRONMENTAL COOLING
> 85
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
Param. 82 min. fromfire start – at the beginningof fast cooling≈100 mins from fire start –at the end of the phase at constant ambient temperature
TO
TAL
DA
MA
GE
[-]
Zones of the squares column with Total Damage higher than 0.75, at the beginning of the fast environmental cooling and at the end of the phase at constant ambient temperature
Analysis of cooling processesFAST (20 sec) ENVIRONMENTAL COOLING
> 86
SSCS 2012 - Aix-en-Provence, France , May 29-June 1, 2012
A multiphase concrete model with application to high temperature, structural repair, leaching and Alkali-Silica reaction
� A general model based on the mechanics of multiphase porous media for the analysis of thermo-hygral-chemical and mechanical behaviour of concrete has been presented.
� Some relevant applications of this model have been shown:
� Concrete maturing/hardening process (i.e. hydration) and long term behaviourof concrete structures (i.e. creep development);
� Concrete structures under extreme conditions in terms of pressure and temperature (high temperature);
� Concrete exposed to chemical degradation by pure water (i.e. leaching) in both isothermal and non-isothermal conditions;
� Concrete subject to Alkali-Silica Reaction;
� The leaching model considers not only the diffusive calcium transport, as other existing models, but additionally also the advective calcium flow.
� Calcium leaching process is modeled by considering thermodynamic imbalance of the calcium in solid and liquid phases, what allows for the description of process kinetics;
� The ASR model accounts for both water content (i.e. saturation) and temperature influence on the reaction evolution and the strain development;
� A simplified version of the model suitable for practical engineering application (e.g. concrete structures repair) has been formulated.
Conclusions
Recommended