All Rights Reserved,
Copyright(C)2011,National Institute forLand and Infrastructure Management

Study on Effects of Nonlinear Temperature
Distribution and Slab Thickness on Thermal
Stress of Airport Concrete Pavement

TSUBOKAWA, Y., MIZUKAMI, J. and SAITOU, Y.
National Institute for Land and Infrastructure Management,
Ministry of Land, Infrastructure, Transport and Tourism,
Japan
1Background
Aircraft gear load

Daily temperature changeHigh Temp.
Low Temp.

Concrete SlabLoading StressThermal StressBase

Design of airport concrete pavement in Japan (until 2008) isempirical design method based on U.S. PCA method.
loading stress: stress at slab center is calculated.
thermal stress: considered by Safety Factor (1.7 – 2.2).
fatigue damage:21

All Rights Reserved,Copyright(C)2011,National Institute forLand and Infrastructure Management

BackgroundWestergaard (1927)
Theoretical thermal (warping) stress equation for
linear temperature gradient.
High temp.
temp

TopEα
σ=
θ2(1 −ν )Bottom
Low temp.

Thermal stress σ increases with temperature difference θ.

σ : thermal stressθ : temperature differential between top and bottom
E, α, ν : property of concrete
3

BackgroundWestergaard (1927)
Theoretical thermal (warping) stress equation for
linear temperature gradient.
High temp.
temp

TopEα
σ=θ2(1 −ν )Bottom
Low temp.

Iwama (1964)
Practical thermal (warping and internal) stress equation
for nonlinear temperature distribution(used for road pavement design in Japan) High temp.
TopEαθσ = 0.72(1 −ν )Bottom
Low temp.

42All Rights Reserved,Copyright(C)2011,National Institute forLand and Infrastructure Management

Background
Iwama’s Observation

Sttress

1.0Internal Stress-0.3

compressivetensile

Warping Stress0 AM

8 AM

4 PM

Internal stress tend to be-30 % off daily maximum
warping stressfor 20 and 25 cm thickness

TimeIwama (1964)
Practical thermal (warping and internal) stress equation
for nonlinear temperature distribution(used for road pavement design in Japan) High temp.
TopEαθ
σ = 0.7
2(1 −ν )Bottom
Low temp.

5

Objective
Can the coefficient 0.7 be used for thicker airport pavement ?
Is nonlinearity of temperature distribution same ?

?
Road concrete pavement(20-30cm)

Airport concrete pavement(30-50cm)

Coefficient = 0.7

Coefficient = ?

Practical thermal stress equation
for thicker airport concrete pavement63All Rights Reserved,Copyright(C)2011,National Institute forLand and Infrastructure Management

Contents
1. Observation of 42cm thick concrete pavement
Temperature and strain were measured for 1 year.
2 Relationship2.
R l ihi b
between warpingi stress andd iinternall stress
Thermal stress equation for 42cm slab thickness
was developed.
3. Relationship between thermal stress and thickness
By means of heat balance analysis,
temperature distributions and thermal stressof various thicknesses are estimated.
4. Comparison of thicknesses

7Observation of Experimental Pavement
Slab Size
Measurement

length 8.5m, width 8.5m, thickness 42cm
strain and temperature at slab center
every hour for one year.

.

8500

8500

4250

4250

30
180420Concrete
Slab85000

18030
Asphalt Stabilized
Base Course 150mm
Granular Materials
Subbase 230mm

Direction ofConstruction

Subgrade

Strain gauge with thermocouples(Unit : mm)

PlanSection
84All Rights Reserved,Copyright(C)2011,National Institute forLand and Infrastructure Management

Contents
1. Observation of 42cm thick concrete pavement
Temperature and strain were measured for 1 year.
2 Relationship2.
R l ihi b
between warpingi stress andd iinternall stress
Thermal stress equation for 42cm slab thickness
was developed.
3. Relationship between thermal stress and thickness
By means of heat balance analysis,
temperature distributions and thermal stressof various thicknesses are estimated.
4. Comparison of thicknesses

9Thermal Stress Equation (42cm thick)Hourly Thermal Stress, σt (MPa)32Tensile StressCompressive Stress

10-1

σt = 0.53-2

Eαθt-3hour2(1-ν)

2R =0.921-3-15
15-1010-5505101520o

Hourly Temperature Differential, θt-3 ( C)

Coefficient is 0.53 for a slab 42cm thick.
The coefficient is smaller than 0.7 for 20 and 25cm
105

All Rights Reserved,Copyright(C)2011,National Institute forLand and Infrastructure Management

Contents
1. Observation of 42cm thick concrete pavement
Temperature and strain were measured for 1 year.
2 Relationship2.
R l ihi b
between warpingi stress andd iinternall stress
Thermal stress equation for 42cm slab thickness
was developed.
3. Relationship between thermal stress and thickness
By means of heat balance analysis,temperature distributions and thermal stressof various thicknesses are estimated.
4. Comparison of thicknesses

11Heat Balance Analysis
Temperature distribution in various slab thicknesses
was estimated through heat balance analysis(heat conduction, heat transfer, solar radiation
are considered in 2D FEM)
FEM).
60oTempera
ature ( C)

50

3cm

Analysed
3cm
21cm
39cm

Measured
3cm
21cm
39cm

42cm
thick

21cm
39cm

40

30

20

68

10

12

14

16

18

20

22

24

Time

126

All Rights Reserved,
Copyright(C)2011,National Institute forLand and Infrastructure Management

Temperature Distribution in VariousSlab Thicknesses0.0Top
Normalized Depth

020.2
Thickness 42cm

0.4

Thickness 50cm

Thickness 26cm

Thickness 58cm

Thickness 34cm

0.6

thick0.8
1.025

thinBottom

30354045
oTemperature in Slab ( C)5055

Nonlinearity of temperature distribution increased
along with slab thickening.
13

Practical Thermal Equation

Eασ =βθ2(1 −ν )Coefficcient of thermal stress equattion, β

1.2
1.0

Long-term observation by Iwama (1964)
Long-term observation in this paper
C l l iCalculation

0.8
0.60.4β = - 0.772h + 0.854

0.20.0

0.2

0.3
0.4
0.5
Slab Thickness, h (m)0.6

The coefficient tended to decrease withan increase in slab thickness.

.

147

All Rights Reserved,Copyright(C)2011,National Institute forLand and Infrastructure Management

Contents
1. Observation of 42cm thick concrete pavement
Temperature and strain were measured for 1 year.
2 Relationship2.
R l ihi b
between warpingi stress andd iinternall stress
Thermal stress equation for 42cm slab thickness
was developed.
3. Relationship between thermal stress and thickness
By means of heat balance analysis,
temperature distributions and thermal stressof various thicknesses are estimated.
4. Comparison of thicknesses

15

Comparison of Thicknesses
Design of Airport Concrete Pavement in Japan was revised
based on this research results.
Previous design method : Empirical method
CCurrent
design method : Mechanistic-Empirical method
Design coverage (traffic volume)
10,00020,00040,000Previous
42 cm
Current
39 cm
41 cm
43 cm
Previous design method
Slab thicknesses are 42 cm in all cases
because safety factors are same in 3 conditions.
Current design method
Slab thicknesses are 39 to 43 cm
because safety factor is not used.
168

All Rights Reserved,Copyright(C)2011,National Institute forLand and Infrastructure Management

Summary and Conclusion(1) The coefficient of thermal stress equation decreases
as the slab thickness increases because internal
stress due to nonlinearity of temperature distribution
across the slab is larger with increasing of slabthickness.
(2) We propose practical thermal stress equation forvarious thicknesses of slabs.

σ =βEαθ2(1 −ν )β = −0.772 + 0.854h

17

Thank you for your attention !

189