moisture curling of concrete slabs for airfield applications illinois university of illinois at...
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MOISTURE CURLING OF CONCRETE SLABS FOR AIRFIELD APPLICATIONS
ILLINOISUniversity of Illinois at Urbana-Champaign
PIs:David A. Lange
Jeffery R. Roesler
RAs:Chang Joon Lee
Yi-shi LiuBenjamin F. Birch
November, 2005
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OUTLINE
• Objective of the Project• Computer Modeling • Laboratory Tests for FAA Material• Prediction of NAPTF Single Slab• Technology Transfer of Results• Future Works
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OBJECTIVE OF PROJECT
• To develop a better understanding of concrete material behavior that leads to moisture curling
• To develop guidelines for future concrete materials selection for airport pavement applications.
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COMPUTER MODELING
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WHY IS OUR MODELING CONCEPT USEFUL?
ABAQUS DIANA ICON
Gradient excitations YES YES YES
Aging concrete properties
NO YES YES
Hygrothermal model for shrinkage
NO NO YES
Aging effect on creep NO SIMPLE SOLIDIFYING
NOTE: Assessments are based on the built-in functions of the codes
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“Instantaneous” response- Static
“Delayed” response - Creep
Hygrothermal Model
Material ModelsConcrete is an Aging Material
Linear Elastic Continuum
Solidification Theory[Bazant 1977]
“Hygrothermal” response - Shrinkage & Thermal Expansion
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Stress is a function of porosity and humidity
Pc
Vapor Diffusion
1m
50 nm
Drying shrinkage is a mechanical response of porous microstructure to the capillary pressure due to internal humidity reduction
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Kelvin-Laplace Equation relates RH directly to capillary pressure
– surface tensionr – mean pore radius
RH – Relative humidityR – Universal gas
constantT – Temperature
v’ – molar volume of water
Capillary pore pressure as a function humidity
Pc
Vapor Diffusion '
)ln(2
v
RTRH
rp
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Two concepts for hygrothermal models
Stress Approach:Internal stress based hygrothermal model
Strain Approach:Strain based
hygrothermal model
'
)ln(2
v
RTRH
rp
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Internal stress based hygrothermal model
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Average stresses in porous media:Converts pore pressure to average bulk stress!
σaverage = p x pc = (pore pressure) x (porosity)
Pc = 9%
σaverage = 90.1psi
Pc = 16.3%
σaverage = 162.8psi
Pc = 22.5%
σaverage = 225.2psi
NOTE: σaverage = average hydrostatic stress assuming that out-of-plan behavior of the porous medium shows the same behavior with the in-plan behavior
pore pressure = 1000psi,
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Stress in concrete for a given humidity & porosity
conreteconcreteaverage pv
RTRHpp
'
)ln(
As applied to Concrete…
hydration ofdegree
rationtwater/ceme
ncalibratiofor constant
aggregatesoffractionvolume32.0/
)36.0/( pastecement ofPorosity
)1(concrete ofPorosity
cw
P
Vcw
cwP
PVPP
cal
a
paste
calapasteconcreteWhere,
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1/8 model
Finite Element Analysis for a free drying prism
Aging Material properties
(Porosity, Elastic & Creep response)
Humidity History at different depth from drying surface
50
55
60
65
70
75
80
85
90
95
100
0 10 20 30
Time (day)
Re
lati
ve
Hu
mid
ity
(%) 0.1"
0.3"
0.7"
1.5"
conreteaverage pv
RTRH
'
)ln(
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1/8 model, stress in z direction at age of 30days
Deformation and stress distribution in a free drying prism
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Best fit with the parameter Pcal
Free drying shrinkage of prism
0.00E+00
2.00E-04
4.00E-04
6.00E-04
8.00E-04
0 5 10 15 20 25 30
Time(Day)
Dry
ing
Sh
rin
ka
ge
(in
/in)
Experiment
Predicted
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Strain based hygrothermal model
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t
pHT v
v
kkpS
03
1
3
1
Strains in a solid with spherical pores under negative pore pressure
(A linear elastic solution)
[ Grasley et al., 2003]
P
volumelpaste/totacement /vv
skeleton solid theof modulusbulk
pastecement theofmodulusbulk
factorsaturation
presurepore
,
tp
0
k
k
S
p
where
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t
pHT v
v
kkpS
03
1
3
1
3
98.0175.01
RHS
))(
1()ln()25.0)(75.0( 3
tK
bTRHRHa HT
HTHT
Saturation factor (Approximation)[Bazant & Kim, 1991]
'
)ln(
v
RTRHp
t
pHT v
v
kk
RH
v
RTRH
0
3
3
1
3
1
98.01(75.01
'
)ln(
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Fit to experimental data (RH, T, shrinkage)
))(
1()ln()25.0)(75.0( 3
tK
bTRHRHa HT
HTHT
-5.0E-05
0.0E+00
5.0E-05
1.0E-04
1.5E-04
2.0E-04
2.5E-04
3.0E-04
3.5E-04
0 10 20 30 40 50 60
Time(day)
Sh
rin
kag
e(i
n./i
n.)
drying_shrinkage
simple linear model
strain based hygrothermal model
RHaRHRHNOTE: simple linear model for shrinkage
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LABORATORY TESTS TO CALIBRATE MODELFOR FAA HIGH-FA CONCRETE
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Lab Test: Strength Development Rate
0
1000
2000
3000
4000
5000
0 20 40 60 80 100 120
Age(day)
Un
iax
ial c
om
pre
ss
ive
str
en
gth
(ps
i)
0
100
200
300
400
500
600
0 20 40 60 80 100 120
Age(day)
Sp
rit t
en
sile
str
en
gth
(psi
)
Uniaxial Compressive Strength Split Tensile Strength
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Lab Test : Stress-strain & Young’s modulus
0.E+00
1.E+06
2.E+06
3.E+06
4.E+06
5.E+06
6.E+06
0 20 40 60 80 100 120
Age(day)
Yo
un
g's
mo
du
lus
(ps
i)
0
500
1000
1500
2000
2500
3000
0 0.0005 0.001 0.0015 0.002 0.0025 0.003
Axial strain(in.in)
Co
mp
res
siv
e s
tre
ss
(ps
i)
0
500
1000
1500
2000
2500
3000
3500
-0.03 -0.025 -0.02 -0.015 -0.01 -0.005 0
Lateral dilation(in.)
Co
mp
res
siv
e s
tre
ss
(ps
i)
Uniaxial compressive test with axial & lateral strains
Stress-strain Stress-lateral dilation
Young’s modulus
28 days
7 days
28 days
7 days
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Lab Test: Temperature, RH & shrinkage
10
15
20
25
30
0 10 20 30 40 50 60
Age(day)
Te
mp
era
ture
(oC
)
ambient
surface
quarter
center
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60
Age(day)
Re
lati
ve
Hu
mid
ity
(%)
ambient
surface
quarter
center
0.0E+00
5.0E-05
1.0E-04
1.5E-04
2.0E-04
2.5E-04
3.0E-04
3.5E-04
0.00 10.00 20.00 30.00 40.00 50.00 60.00
Age(day)
Sh
rin
ka
ge
str
ain
(in
./in
.)
Free drying shrinkage test+ internal temperature &
relative humidity
Drying
Internal temperature
Drying shrinkage
Internal humidity
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0.E+00
1.E-04
2.E-04
3.E-04
4.E-04
5.E-04
6.E-04
0 20 40 60 80
Age(day)
Str
ain
(in
./in
.)
Lab Test - Creep
0.E+00
5.E-05
1.E-04
2.E-04
2.E-04
3.E-04
3.E-04
4.E-04
0 20 40 60 80
Age(day)
Cre
ep
str
ain
(in
./in
.)
Sealed test Exposed to ambient
DryingSealed
Basic creep Total deformation
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PREDICTION OF NAPTF SLAB
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“Instantaneous” response - Static
“Delayed” response - Creep
Material Models for Prediction
Shrinkage & Thermal Expansion
Linear Elastic Model
Bazant’s Solidification Theory
Const. creep Poisson’s ratio
Strain based Hygrothermal Model for Shrinkage
92.0~88.0),()( mdryingmwetting HTHT Different shrinking & expanding rates for drying & wetting
Linear relation for thermal expansion
TaTT
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¼ modeling using symmetric boundary conditions
INPUTS – Finite Element Mesh & Boundary Conditions
7.5ft7.5ft
11 in.
Non-linear spring for base contact
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INPUTS – Material Parameters from Lab. tests
0.E+00
1.E+06
2.E+06
3.E+06
4.E+06
5.E+06
6.E+06
0 20 40 60 80 100 120
Age(day)
Yo
un
g's
mo
du
lus
(ps
i)
0.0E+00
2.0E-07
4.0E-07
6.0E-07
8.0E-07
1.0E-06
1.2E-06
1.4E-06
0 50 100 150
Time(day)
Sp
ec
ific
cre
ep
(in
./ps
i)
Parameters for the material model set were calibrated based on the Lab. material
test results.
-5.0E-05
0.0E+00
5.0E-05
1.0E-04
1.5E-04
2.0E-04
2.5E-04
3.0E-04
3.5E-04
0 10 20 30 40 50 60
Time(day)
Sh
rin
kag
e(i
n./i
n.)
drying_shrinkage
strain based hygrothermal model
BASIC CREEP
ELASTIC MODULUS
SHRINKAGE
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INPUTS – Internal Temperature & RH from NAPTF test
12 22 32 42 52 62 72 8218
20
22
24
26
28
30
32
Time (day)
Tem
pera
ture
( o C
)
1" 10.5"
5.5"
12 22 32 42 52 62 72 8275
80
85
90
95
100
105
Time (day)
Rel
ativ
e H
umid
ity (
%)
1"
10.5"
5.5"
TEMPERATURE RELATIVE HUMIDITY
Internal humidity and temperature measured at the NAPTF were applied to the FE model
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OUTPUTS - Deformation & Stresses
-20
0
20
40
60
80
100
120
14 21 28 35 42 49 56 63 70
Time(day)
Dis
pla
ce
me
nt(
in. x
10
-3)
A
B
A
B
Age = 68days, Mag. = 100x Age = 68days
Deformation map Max. Principle stress
234 psi
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Lift-off displacement
Deformation Comparison
A
VD-1
VD-4
CL-3
VD-5
CL-4
CL-2
-50
0
50
100
150
200
14 21 28 35 42 49 56 63 70
Time(day)
Dis
pla
ce
me
nt(
in. x
10
-3CL-2
CL-3
CL-4
VD-1
VD-4
VD-5
A
CL = Clip gauge
VD = Vertical Displacement Transducer
CL
VD
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Lift-off displacement
Deformation Comparison
B
VD-2
-50
0
50
100
150
200
14 21 28 35 42 49 56 63 70
Time(day)
Dis
pla
ce
me
nt(
in. x
10
-3)
VD-2
B
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TECHNOLOGY TRANSFER OF RESULTS
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Finite Element Analysis Code
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ICON ver 0.1.0
Finite Element Analysis Code
1. ICON is a FEA code written in C++ for deformation and stress prediction. OOP (Object Oriented Programming) Effective in code maintenance, update
2. ICON is specialized for aging concrete & time dependent excitations Material properties as functions of time Internal humidity & temperature as functions of time Loads & BCs, as functions of time
3. ICON is a Standalone code Previous version required MATLAB engine for a sparse matrix solver. Current version uses TAUCS( a library for a sparse matrix solver).
ICON can be run as a standalone program.
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ICON ver 0.1.0
Finite Element Analysis Code
ELEMENTS:• 20-node solid element• 8-node solid element• 2-node spring• 2-node bar-element
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ICON ver 0.1.0
Finite Element Analysis Code
MATERIAL:• Linear elastic • Solidifying material model for creep• Internal stress based hygrothermal model • Strain based hygrothermal model
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Structure of ICON input file
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1. NODE section nodal coordinates
2. ELEMENT section element connectivity, properties
3. GROUP section group info. (node & element set)
for easy access to the model
4. MATERIAL section material info.
5. CONDITION section loads, BCs, RH, temperature, age
6. ASSIGN section CONDITIONs are ASSIGNed to GROUPs
7. CONTROL section analysis duration, time interval,
convergence criterion, etc.
Structure of ICON input file
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NODE:
<# of nodes>
<node_id> <x> <y> <z>
<node_id> <x> <y> <z>
…
ELEMENT:
<# of elements>
<element_id> <element_type> <node_id> … <node_id>
<element_id> <element_type> <node_id> … <node_id>
…
GROUP:
<# of groups>
<group_id> <group_label> <id_type>
<# of ids in this group> <id> … <id>
<group_id> <group_label> <id_type>
<# of ids in this group> <id> … <id>
…
Input file format
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MATERIAL:
<# of materials>
<material_id> <material_type>
<material_property_set>
<material_property_set, VAR_SET > for <material_type_EL>
< E > < nu >
<material_property_set, VAR_SET > for <material_type_SLDFB>
<fc28> <ft28> <E28> <nu>
<a_T> <a_HT> <b_HT>
<# of KM> [<Tu> <Au>]
<m> <alpha><q4>
CONDITION:
<# of conditions>
<condition_id> <condition_type> < # of time step>
<time> <condition_value_set>
<time> <condition_value_set>
…
ASSIGN:
<# of assigns>
<assign_id> <assign_type> <material _id or condition_id> <group_id>
<assign_id> <assign_type> <material_id or condition_id> <group_id>
…
Input file format
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CONTROL:
<# of controls>
<control_id>
<analysis_duration> <analysis_time_step>
<max_iteration> <convergence_creterion>
<num_monitor_node> <node_id> … <node_id>
<num_monitor_element> <element_id> … <element_id>
<monitor_writing_frequency>
Input file format
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Modeling Procedure
MSC.Patran- modeling geometry
model.inp
ICON – Finite Element Analysis
Generate mesh data for ICON
Read input file
model.res
Write analysis results
MSC.Patran- graphical postprocessing
Read result file
Add materials & other conditions(BC, RH, T)
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Modeling Procedure
MSC.Patran- modeling geometry
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Modeling Procedure
model.inp
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Modeling Procedure
ICON – Finite Element Analysis
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Modeling Output Filemodel.res
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Modeling Results
MSC.Patran- graphical post-processing
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FUTURE WORK
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FUTURE WORK
Lab Tests:Drying/Wetting test Scale-down single slab test
Computer Modeling:Modeling Twin slabs Application with the models using various drying scenario
Technology Transfer of Results:Users Manual for ICON
Anticipated Completion:Summer 2006
Future Features?Prediction of internal temperature & humidityGraphical pre- and post-processor user interface