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

OUTLINE

• Objective of the Project• Computer Modeling • Laboratory Tests for FAA Material• Prediction of NAPTF Single Slab• Technology Transfer of Results• Future Works

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.

COMPUTER MODELING

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

“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

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

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

Two concepts for hygrothermal models

Stress Approach:Internal stress based hygrothermal model

Strain Approach:Strain based

hygrothermal model

'

)ln(2

v

RTRH

rp

Internal stress based hygrothermal model

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,

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,

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(

1/8 model, stress in z direction at age of 30days

Deformation and stress distribution in a free drying prism

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

Strain based hygrothermal model

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

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(

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

LABORATORY TESTS TO CALIBRATE MODELFOR FAA HIGH-FA CONCRETE

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

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

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

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

PREDICTION OF NAPTF SLAB

“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

¼ modeling using symmetric boundary conditions

INPUTS – Finite Element Mesh & Boundary Conditions

7.5ft7.5ft

11 in.

Non-linear spring for base contact

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

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

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

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

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

TECHNOLOGY TRANSFER OF RESULTS

Finite Element Analysis Code

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.

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

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

Structure of ICON input file

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

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

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

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

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)

Modeling Procedure

MSC.Patran- modeling geometry

Modeling Procedure

model.inp

Modeling Procedure

ICON – Finite Element Analysis

Modeling Output Filemodel.res

Modeling Results

MSC.Patran- graphical post-processing

FUTURE WORK

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