Temperature Distribution Within Asphalt

Pavements and Its Relationship to

Pavement Deflection
HERBERT F. SOUTHGATE and ROBERT C. DEEN, Kentucky Department of Highways,
Lexington

A method has been developed to estimate the temperatures at depth in

an asphaltic concrete pavement utilizing the measured pavement sur-
face temperature and the 5-day average air temperature history.
Temperature prediction nomographs were developed for each hour
between 6 a. m. and 5 p. m. This temperature prediction method is
independent of the season of the year. A method for adjusting Benkel-
man beam deflections for temperature effects has been developed and
is presented. This enables the deflections taken at any temperature
to be adjusted to a reference temperature, thus making possible di-
rect comparisons of deflections.
An analysis of AASHO Road Test data was made using the Boussinesq
and Burmister equations and charts. The results indicate that the
temperature-modulus of elasticity relationship is curvilinear, has the
same basic shape found by Kallas in the laboratory, and has the same
basic shape as the temperature-deflection adjustment factor curve.
There appears to be a linear relationship between deflection adjust-
ment factors and modulus of elasticity. Therefore, there seems to
be a temperature-deflection-modulus of elasticity correlation be-
tween field test data and theory.

•ASPHALTS "soften" as the temperature increases and "stiffen" as the temperature

decreases, and measurements have shown that the deflection and rebound of asphalt
pavements in response to loads are affected to a significant degree by temperature.
Historically, pavements that deflect greatly under traversing loads are short-lived.
Pavements that undergo minimal deflection at some maximum load are either inherently
more rigid or are more firmly supported than those that undergo greater deflection.
The rigidity or "stiffness" of asphaltic concrete is not a direct measure of strength, nor
is deflection an inverse measure of the strength of a pavement structure. strength is
usually expressed as the load or stress that causes overt failure, whereas stiffness or
rigidity is concerned only with load-deflection (or stress-strain) relationships. It seems
reasonable that the deflection of a pavement decreases as the thickness of the asphaltic
concrete is increased, and that the strength of the pavement structure is thereby in-
creased. Therefore, in the case of a pavement that has a more or less uniform degree
of support, deflection and thickness are empirical indicators of strength and structural
adequacy. For lesser but uniform degrees of support, greater thicknesses of asphaltic
concrete are compensating, effectively reducing deflection and strengthening the pave-
ment system. Of course, the supporting capabilities of underlying soil or base courses
may be improved and/or thickened to accomplish the same effect. Elastic and visco-
elastic theories have been extended and perfected, fatigue theories of failure have been
studied, and each of these has been related with some degree of confidence to load and
deflection.

Paper sponsored by Committee on Flexible Pavement Design and presented at the 48th Annual Meeting.
116
 117

Surface deflection (or rebound) remains the most measurable response of a pavement
to an applied load. Adjustment of measured deflections to a common (or base) tempera-
ture offers further hope of reducing the temperature variate and improving the correla-
tion between load-deflection and classical theory.
Pavement surface temperature alone does not suffice to account for the dependency
of deflection on temperature; and, because temperatures at depths are known to influ-
ence deflections, subsurface temperatures must be either measured in situ or estimated
from other correlations. The purpose of this research (1) is (a) to develop a method
for estimating the temperature at any depth in a flexible pavement up to 12 in. thick, and
(b) to analyze the temperature-deflection data generated in the AASHO Road Test (2) to
show that temperature adjustment factors are generally applicable to Benkelman beam
deflection measurements of bituminous pavements and to determine the magnitude of
these adjustment factors.

METHOD AND ANALYSIS

Analysis of Temperature Records
The data used to develop the temperature distributions and the prediction criterion
were those recorded in 1964 and 1965 at the Asphalt Institute's laboratory at College
Park, Maryland (3).
In this analysis, data for 12 consecutive months were punched on cards to facilitate
data processing and analysis. A study of the data revealed that in normal weather and
at a given hour, the temperature at a given depth was approximately the same percentage
value of the surface temperature, even though the surface temperatures fluctuated from
day to day. For a given depth, temperature fluctuations followed an orderly pattern and
were influenced primarily by the surface temperature.
The data showed that a short period of rain or extensive cloud cover reduced the sur-
face temperature and influenced the temperatures at shallow depths. However, extended
periods of inclement weather reduced the surface temperature to nearly the level of the
air temperature and proportionately decreased the temperature throughout the 12-in.
pavement thickness. Air temperatures generally dropped and recovered more slowly
than the pavement surface temperature. Therefore, air-temperature history was an
indication of previous long-term influences on the temperatures at various depths.
Mean daily air temperatures, a measure of the air-temperature history, were com-
puted as the average of the highest and lowest air temperatures for each day. This
particular method was chosen for the following reasons:
1. The U.S. Weather Bureau uses this system for each reporting weather station,
and thus air temperature data would be readily available;
2. The U.S. Weather Bureau report does not contain air temperatures for each hour
of the day;
3. This method has some precedence in engineering work.
Consideration of air-temperature history provided an interesting and valuable result,
as shown in Figures 1 and 2. In Figure 1, a linear relationship between mean pavement
temperatures (average of temperatures at the 0.125-, 4.0-, and 8.0-in. depths) and
0.125-in. depth temperatures is shown for each calendar month. The relationship of the
months, their temperature ranges, and the seasonal changes in temperatures can be
readily seen. The addition of mean monthly air temperature to each respective monthly
line in Figure 1 produced Figure 2. The addition of air-temperature history to each
respective month reduced the scatter of the data such that one straight line could replace
all of the monthly lines. Similar analyses for 4- and 12-in. thick pavements indicated
the same general relationships.

Regression Analysis of Temperatures With Respect to Depth

The only daily temperature data that were deleted prior to regression analysis were
eliminated for one of two reasons: either the recorder was out of operation because of
maintenance, or the first two days of recorded pavement temperatures after a missing
118

"" 120 APR 65

• OCT 64
l&I
a:: MAY 65
::>
SEP 64
!4 100
JUN 6 4
ffi
IL
2
l&I
I-
80
I-
z
l&I
:::E
l&I
ii
IL 60
z
cl
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2
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~0~~~~
80
~~~~10L0~~~12L0~~~1~
40~~~~
16-
0 ~~---'
18-
0~~-2
~00
'-:--~~~
220

TEMPERATURE AT THE 0.125-INCH DEPTH, •F

Figure 1. Mean pavement temperature by calendar month for an 8-in. thick pavement at 1:00 p.m. vs
temperature at the 0.125-in. depth.

day of data were eliminated because the antecedent air temperatures were also missing
from the source data. This resulted in the elimination of 47 days of data. Therefore,
data for 318 days were used in the final analysis.
To develop relationships to be used in later analyses, a regression analysis was made
of the temperature-depth data. Because the method of estimating temperatures would
ultimately be used to adjust Benkelman beam deflections, data taken from 6 a. m. through
5 p. m. were analyzed because most deflection tests would be performed during these
hours.
To approximate the temperature-depth relationships for a given hour, a review of the
data suggested the need for a polynomial equation of the form
Y = C1 + C2 X + C3 X2 + ... + Cnxn-l (1)
where
Y = temperature in degrees F at depth X,
X = depth in inches from the pavement surface, and
Cu <;, C3 , • • • Cn = coefficients determined by the method of least squares.

"" 12 0

l&I
a::
::>
!4 100
a::
l&I
IL
2
l&I
I-
80
I-
z
l&I
2
l&I
~
Q. 60
z PR 65
cl
w
:::E
40
40 60 80 100 120 140 160 180 200 220
TEMPERATURE AT THE 0.125-INCH DEPTH + MEAN MONTHLY AIR TEMPERATURE, °F

Figure 2. Mean pavement temperature by calendar month for an 8-in. thick pavement at 1:00 p.m. vs
temperature at the 0.125-in. depth plus 30-day mean air-temperature history.
 119

Results showed that at 6, 7, and 8 a. m., a third-order polynomial provided the best fit,
and a fourth-order polynomial was very nearly as accurate. For the remaining hours,
a fifth-order polynomial gave the best fit, and again the fourth-order was very nearly as
accurate. Therefore, a fourth-order polynomial was chosen to approximate data for all
hours.
Standard errors of estimate were calculated and the maximum difference between the
observed temperature value and the value calculated from the polynomial was recorded.
Analysis showed that the average standard error of estimate was approximately 0.50 F-
the least being 0.09 F and the maximum being 2.20 F. The maximum difference between
the observed and calculated temperatures ranged from 0.17 F to 4.54 F and an average
of 318 values yielded 0.95 F. The large differences, such as the 4.54 F, were verified
by inspection of the temperature-depth data and revealed that the real distribution was
erratic. Days of data were picked at random, and further checks between observed and
calculated values indicated that the curves were smooth and in close agreement with
measured temperatures at the respective depths.
The temperatures at the surface and at each Y:i-in. increment of depth through 12 in.
were calculated by means of the fourth-order polynomial equation determined for the
respective day. Temperatures so calculated were plotted as ordinate values vs the
measured surface temperature plus an average air-temperature history preceding the
day of record (a separate graph for each depth was prepared). The plot for the 6-in.
depth is shown in Figure 3. The average air-temperature history was computed for 5
days prior to the day of record. The optimum number of days for the air-temperature
history was determined by further investigations described below.
The addition of an average air -temperature history to the surface temperatures was
found to produce a favorable shift in the abscissa values in relation to the fixed ordinate
values . Average air temperatures were computed for 1, 2, 3, 5, 7, and 10 days pre-
ceding each day of record. Each set of data was adjusted and evaluated in terms of
standard error of estimate. The standard error of estimate decreased to a minimum
when 2 days of air-temperature history were added and then increased as the number of
antecedent days increased. The minimum standard error of estimate for the 6-in. depth
and for the hours 6 a.m. through 9 a.m . and 6 p.m. and 7 p.m . occurred when a 10-day

100 319 DATA POINTS

IL
0
Y• 2 . 6409 + 0 .445 4 X
:I:
I-
Q.. 80
l&J
0
:I:
0
z
I 60
CD

0
40 60 80 100 120 140 160 180 200 220
PAVEMENT SURFACE TEMPERATURE+ 5-0AY MEAN AIR-TEMPERATURE HISTORY, °F
Figure 3. Temperature at the 6-in. depth vs measured pavement surface temperature at 1:00 p.m. plus
5-day mean air-temperature history.
120
4.4

~ 4.2
Cl
2
j::
en
"'
IL 4.0
0
cc
0
cc
cc
Ill 3.8
0
cc
"'z
0

~
en 3.6

34
• 0 2 3 :I 7 10
NUMBER OF DAYS OF AIR-TEMPERATURE HISTORY

Figure 4. Standard error of estimate for all depths and all hours vs number of days of air-temperature
history.

average air-temperature history was added, and for the hours of 10 a. m. through 5
p. m., a 2- to 5-day average air -temperature history was optimum.
Figure 4 was drawn to find the number of days of average air temperatures that gave
the least standard error of estimate for all depths and all hours under consideration.

DEPTH IN PAVEMENT, INCHES

160

140

...
•
:r.' 120
I-
Q.
Ill
O 100

~
~ 80
::>
~
a:
"'
Q. 60
:::E
"'
I-
40

20

20 40 60 80 100 120 140 160 180 200 220 240 260

SURFACE TEMPERATURE+ !I-DAY MEAN AIR - TEMPERATURE HISTORY, °F
Figure 5. Temperature-depth prediction graph at 1:00 p.m. for pavements greater than 2 in. thick.
 121

As can be seen, accuracy does not increase significantly beyond the 5-day point. There-
fore, only the 5 previous days are considered to be significant. Further analysis of the
standard errors of estimate showed that the 5-day average air-temperature history suf-
ficed for all depths greater than 2 in. The least standard errors of estimate for the
depths 0 in. through 2 in. indicated that the best estimate was obtained by the use of the
surface temperature alone. Pavement temperatures in the top 2 in. of the pavement
are more directly dependent on the hour of the day and the amount of heat absorption,
whereas temperatures at depths greater than 2 in. are assumed to be a function of the
surface temperature, amount of heat absorption, and the past 5 days of temperature
history.
A complete set of curves giving the best estimate of temperature at the several depths
and by hour of the day was developed. Because of space limitations, only the set of
curves for 1 p. m. is shown in Figure 5 as a typical example.

Development of Deflection Adjustment Factors for Temperature Effects

Two types of adjustment factors were considered. The first was to assign an incre-
mental deflection to each degree of temperature difference between the pavement tem-
perature and the reference or standard temperature. This type of correction was em-
ployed by Kingham and Reseigh (4) and by Sebastyan (5); however, the m~gnitude of sug-
gested corrections differed. The second method considered was the use of a dimension-
less, multiplicative factor that could be applied to a measured deflection at some known
surface temperature or a known mean temperature of the pavement. No known refer-
ence in the literature mentions the second method.
Inspection of the AASHO Road Test curves (2, Figs. 89a, 89b, 89c, and 90a) sug-
gested that the dimensionless, multiplicative factor method might be more appropriate.
Therefore, in this study, the aboveAASHO Road Test curves were transformed to semi-
logarithmic plots, temperature being the logarithmic scale. The data plotted as straight
lines, and the slopes of the individual curves for each loop were very nearly parallel.
However, the slopes for the several loops were not parallel. The equation for the
straight lines was

(2)

where
M = slope of the straight line,
Yll Y2 =deflection values, and
Tu T 2 = mean pavement temperatures in degrees F corresponding to the Y1 and Y2
deflection values respectively.
After the slope had been determined, the deflections were computed for mean pave-
ment temperatures of 30 through 150 F, at 10 F-intervals, by the equation

(3)

where
Y3 = deflection at the temperature T 3 ,
Y1 =same Y1 used in Eq. 2,
M =slopes as determined in Eq. 2,
T3 = temperature at which the deflection was computed, and
T1 =same T 1 used in Eq. 2.
A mean temperature of 60 F was chosen as the reference temperature, T 60 •
The adjustment factors were derived from the equation

(4)
122

where
AF = the adjustment factor used to adjust measured deflections due to temperature
effects,
Y60 =computed deflection in inches for the mean pavement temperature 60 F from
Eq. 3, and
Y3 = computed deflection in inches for a particular- mean pavement temperature T 3
from Eq. 3.
Table 1 shows the results of calculations for the 4-in. pavement on Loop 5. Each of the
12 adjustment factor curves in Figure 6 are the results of computations according to
Eqs. 2, 3, and 4, and the curves are plotted arithmetically with mean pavement tempera-
ture, T 3 , on the ordinate axis and the adjustment factor, AF, on the abscissa axis. De-
flections, Y3 , computed from the 12 individual curves at a given mean pavement tem-
perature, T 3 , were added and averaged to obtain the final adjustment factor curve shown
in Figures 6 and 7.
Further analysis showed that there may be a relationship among average structures
within a given loop-that is, except for the 8.6-in., asphalt-treated base curve, which
for some unknown reason was an outlier. There was no consistent relationship between
loops and substructures as evidenced by the 2-in. surfacing on Loop 3 and the 6-in. sur-
facing on Loop 6, where the total structural thicknesses were 9 and 24 in. respectively;
yet each had the same adjustment factor curve. The same situation was present with
regard to the 4-in. surfacing on Loop 3 and the 16.1-in., asphalt-treated base section
that had total structural thicknesses of 11 and 24.1 in. respectively. These structural
relationships may have been obscured by the AASHO approach of averaging deflections
for a given surfacing thickness within a loop; however, theAASHO structural-equivalency
equation showed that in some cases the structural indexes were vastly different. Fur-
ther analyses might be made of the AASHO data (2, Figs. 89a, 89b, 89c, and 90a) with
the raw data grouped according to surfacing thicknesses and structural indexes without
regard to locations.
The adjustment factor curve for temperature effects is applicable only to creep-
speed deflections because the source data used in the analysis were taken at creep speed.
Further analysis would be required to establish applicability to deflections taken at other
than creep speed. The adjustment factor curve is applicable to any loading as long as
the deflection is to be adjusted to the reference temperature for that same loading.

Relationship Between Temperature-Adjustment Factors and

Modulus of Elasticity of Asphalti.c Concrete
Reflection on the Boussinesq equation for deflections at the center of a flexible plate
y = 1.5 Pa (5)
E
where Y = surface deflection in inches, P =unit load on circular plate, a = radius of
plate, and E = modulus of elasticity of the material, discloses that the deflection is a

TABLE 1
RESULTS OF CALCULATIONS SHOWING DEVELOPMENT OF DEFLECTION ADJUSTMENT FACTORS FOR
THE 4-INCH PAVEMENT ON LOOP 5 OF THE AASHO TEST ROAD

Deflecl!on, Y,, at Deflec llon, Y,, at

Temperature, T 3 (F) Tempernture T, Adjua1ment Temperature, T, (F) Adjustment
Pac tor Temperature T,
(In.) (in.l Factor

40 0.01562 1.7106 100 0.04071 0 .6563

50 0.02173 1.2293 110 0 .04333 0.6167
60 0.02672 1.0000 120 0.04571 0.5846
70 0.03094 0.8636 130 0.04790 0.5578
80 0.03460 0.7723 140 0.04993 0.5351
90 0.03783 0.7063 150 0.05182 0.5156
T1 = 52 F = average pavement temperature, TA Y 1 = 0.0228 = deflection corresponding to T1
T2 = 80 F = overage fXJVement temperature, TA Y2 = 0.0346 = deflection corresponding to T2
 123
150
1-8.6" BASE
140 2-4" ON LOOP 3
16.1" BASE
I&. 130 3-3•; 4': 5" ON LOOP 5
• 12.4" BASE
.... 120
0:: 4-AVERAGE
:I 3" ON LOOP 3
!;i 110
0:: 5-2" ON LOOP 3
....
Q. 6" ON LOOP 6
::IE 100
.... 6-5" ON LOOP 6
....
90 7-4" ON LOOP 6
....
z
.... 80
::IE
....
: 70

z
c 60
....
2
50

40

30
0 1.0 2,0 3 .0
DEFLECTION ADJUSTMENT FACTOR

Figure 6. Mean pavement temperature vs deflection adjustment factors for various loops.

150

140

.... 130

..; 120
0::
:::>
~ 110
....
0::
0..

........::IE 100

90
....z
.... BO
....::IE
~ 70

z
<l 60
....
::IE
50

40

30
0 5 10 15 20 25 30
DEFLECTION ADJUSTMENT FACTOR

Figure 7. Mean pa vement temperature vs average deflection adjustment factor.

124

8 BASES AT 50"
•
... Q
BASES - 8 114"

0 >C LOO
7
>- UI
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u
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UI Ill
C( a: BASES AT 10•
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Ill u 5
... a:
j BASES AT so•
0 I-
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UI 4
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~Ill
0 2 3
2""
~
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111111
a: I-
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... v.

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I

0
u
0
0 2 4 s 8 10 12 14 IS 18 20 22 24
THICKNESS OF ASPHALT MATERIALS, INCHES

Figure 8. Apparent modulus of elasticity of composite pavement structure vs pavement thickness.

linear function of load as well as the modulus of elasticity of the material, which may
be affected by temperature. In turn, Burmister's equation for deflections under a flexi-
ble plate, using a two-layered elastic system (§),

(6)

where E 2 =modulus of elasticity of lower layer, and F 2 =dimensionless factor depend-

ing on the ratio of moduli of elasticity of the subgrade and pavement as well as the
depth-to-radius ratio, indicates that deflections are also a function of pavement thick-
ness and the modulus of elasticity of the pavement layer and the underlying material.
The load and the radius of contact area could be considered constant for a given axle
load and tire pressure.
The surface deflections (2, Figs. 89a, 89b, 89c, and 90a) were used to calculate the
modulus of elasticity by the Boussinesq equation (Eq. 5). This was an apparent modulus,
Ee, of the composite structure of the pavement. When these values were plotted against
respective thicknesses of asphaltic concrete (Fig. 8), a straight line could be passed
through the data points for a given loop section at each temperature; and, upon extrap-
olation to zero thickness (or temperature-affected thickness, in the case of asphalt-
treated bases), the respective lines converged at an approximate value of 8,400 psi. This
was considered to be the subgrade modulus E 2 of Burmister's two-layered, elastic theory
equation. The Fw factors were obtained by

(7)

where Fw = Burmister's settlement coefficient.

Burmister's influence curves (6) were used to obtain the ratio of E 1 to E 2 • The mod-
ulus of elasticity of the asphaltic concrete was obtained from

E1 =N x E 2 (8)
 125

where

The foregoing calculations were made using the deflections at various temperatures
and the E 1 values were avaraged for each temperature. Simultaneous solution of the
equation

A
log E =- + B (9)
io i TA

where
TA =absolute temperature (degrees R =degrees F + 460),
E 1 = average modulus of elasticity of asphaltic concrete at TA• and
A, B = constants,
for two different temperatures determined the values A and B. Extrapolated values for
E 1 at 30 F, 40 F, 100 F, 120 F, and 140 F were then calculated. Figure 9 shows that
the resulting modulus of elasticity of the asphaltic concrete pavement has a curvilinear
relationship with temperature. Note that the shape of the curve is very similar to the
adjustment factor curve shown in Figure 7. The shape of the temperature-modulus
curve derived by elastic theory clearly substantiates the adjustment factor curve derived
by statistical procedures. A correlation graph is shown in Figure 10. It is seen that
the adjustment factor and modulus of elasticity are related at any stated temperature by
the equation given in Figure 10.

Comparison of Derived Temperature Distributions and

Adjustment Factors With Data From Other Test Roads
Data are being gathered by the Asphalt Institute (7) from a test site at San Diego,
California. The flexible pavement at this test site contains thermocouples embedded in

140

.... 130

w 120
er
::::>
'er.« 110
w
IL
:E 100
w
I-
90
1-
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~ 80
w
~ 70

z
<( 60
w
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50

40

30 ol _ _ _o-1_5_____ _i1_0=------, L. ~:------:2:1.:o:-_--=~2~-s=-======?3_::=0_=-"",__-:!3_5 x 106

E 1, MODULUS OF ELASTICITY, PSI

Figure 9. Mean pavement temperature vs modulus of elasticity for asphaltic concrete pavement.
126

4 .0
a:
0
t 1
~ AF• 0 .699E X 10- + 0.!583 0
... 3.0
z
w
Iii::::>
.,
.
0 2 .0

.
....
0 o'--- - - -
o.'-
,_- - - -,'-
.o-- - - - - - ',.',_
-- - - -2.'-o- - - - - -2.._.$_-_ ___3L..
.o_-_ _ __.3.$ K106
E 11 MODULUS OF ELASTICITY, PSI

Figure 10. Correlation between deflection adjustment factor and modulus of elasticity for an asphaltic
concrete pavement.

the pavement, and temperatures are being recorded. Two days of temperature distri-
butions, October 6, 1966, and February 17, 1967, together with their respective 5 days
of high and low air temperatures have been received from the Asphalt Institute and
checked by the temperature prediction procedure described in this report. The pre-
dicted temperatures varied generally within ±6 F from the observed temperatures at
the various levels. The Asphalt Institute also furnished temperature distribution data
for the Colorado test pavement reported by Kingham and Reseigh (4). Table 2 contains
the summary of the analyses for both California and Colorado data; each compared to
the temperatures predicted by the method reported herein and developed from the Col-
lege Park data. A few temperatures fell outside two standard errors of estimate; how-
ever, most of the data are well within these tolerances.

TABLE 2
COMPARISON OF MEASURED PAVEMENT TEMPERATURES AT
SAN DIEGO AND COLORADO TEST SITES WITH ESTIMATION OF
TEMPERATURES BY METHOD BASED ON COLLEGE PARK DATA

Average Difference
Depth Number of Between Observed and Standard
Location (In.) Deviation
Observations Estimated Temperatures (F)
(F)

Colorado 2.00 59 -2.68 5.03

4.60 4 -4.75 6.61
5.50 5 -1.40 3.55
5.75 25 +1.72 5. 51
6.00 25 +1.96 5.94
7.50 4 -0.25 3.71
9.00 5 +1.60 4.24
10.50 50 +2.82 7.09
San Diego 3.00 2 0.00 0.00
3.10 2 -2.00 1.41
3.40 2 -6.00 6.00
3.50 11 -3.50 4,69
6.50 2 -2.50 2.55
9.40 11 +0.09 2.50
9.50 2 -2.50 2.55
10.80 2 -2.50 2.55
11.50 2 -3.50 3.54
 127
30 An interesting comparison between modulus
ASPHALT CONCftETE of elasticity of a sphaltic concrete, E 1 , derived
BASE from the AASHO da ta (Fig. 9) and laboratory
2!1
measurements of the complex modulus, IE* I,
is also pr ovided by Kallas and Riley' s tests
20 (8) on asphaltic concretes used 0 11 the Col o1·ado
test pavement (4) . In F igur e 11 (from 8, Fig .
"'2 3b ), showing IE* I plotted against temper a-
.. 15
tur e, IE* I was determ ined by sinusoidal ten-
1 sion and compression loading. The most fa-
..!: IO vorable agreement is with respect to the 1-cps
loading frequency. The similarity between
•l&I this curve and the curve in Figure 7 seems
5 extraordinary.

0 SUMMARY AND RECOMMENDATIONS

20 40 60 IO 100 120
A practical and reasonably accurate method
TEMPERATURE (°F) of estimating the temperature distributions
within flexible pavements has been developed.
Figure 11. Relationship Between IE* I and
This method can be used to analyze deflection
temperature for various loading frequencies
data at any time if the hour of the day and the
@1 p. 933). surface temperature are included in the re-
corded data.
The relationship between mean pavement
temperature and deflection allows any deflec-
tion test value to be adjusted to a reference temperature if the mean temperature of the
pavement at the time of testing is known or is estimated by the method outlined herein .
Further study is needed to test the assumption that the average air-temperature his-
tory allows this system of estimating pavement temperature distributions to be used in
other areas of the world. Additional data are needed to determine whether the average
air-temperature history adequately takes into account the effects of latitude and altitude
on pavement temperatures.
Theoretical analysis of the AASHO Road Test pavement deflection data by the two-
layered elastic theory shows a curvilinear relationship between modulus of elasticity
of asphaltic concrete and temperature. The magnitude of the moduli are such that a
straight-line relationship exists between moduli and the multiplicative, temperature-
deflection adjustment factors.

ACKNOWLEDGMENTS
This report has been prepared as a part of Research Study KYHPR 64-20, "Flexible
Pavement Study Using Viscoelastic Principles," sponsored cooperatively by the Kentucky
Department of Highways and the U.S. Department of Transportation, Federal Highway
Administration, Bureau of Public Roads. The opinions, findings, and conclusions in this
report are not necessarily those of the Bureau of Public Roads.

REFERENCES
1. Southgate, H. F. An Evaluation of Temperature Distribution Within Asphalt Pave-
ments and Its Relationship to Pavement Deflection. MSCE thesis, Univ. of Ken-
tucky, 1968.
2. The AASHO Road Test: Report 5-Pavement Research. HRB Spec. Rept. 61E, pp.
86-111, 1962.
3. Kallas, B. F. Asphalt Pavement Temperatures. Highway Research Record 150,
pp. 1-11, 1966.
4. Kingham, R. I., and Reseigh, T. C. A Field Experiment of Asphalt-Treated Bases
in Colorado. Proc. Second Internat. Conf. on Structural Design of Asphalt Pave-
ments, Univ. of Michigan, pp. 909-930, 19 67.
128
5. Sebastyan, G. Y. The Effect of Temperature on Deflection and Rebound of Flexible
Pavements Subjected to the Standard CGRA Benkelman Beam Tests. Proc. 42nd
Convention, Canadian Good Roads Association, pp. 143-161, 1961.
6. Burmister, D. The Theory of Stresses and Displacements in Layered Systems and
Applications to the Design of Airport Runways. HRB Proc., Vol. 23, pp. 126-148,
1943.
7. Laboratory Activity Report No. 67-2. The Asphalt Institute, Aug. 1967.
8. Kallas, B. F ., and Riley, J. C. Mechanical Properties of Asphalt Pavement Ma-
terials. Second Internat. Conf. on the Structural Design of Asphalt Pavements,
Univ. of Michigan, pp. 931-952, 1967.

Discussion
N. K. VASWANI, Virginia Highway Research Council-The authors are to be compli-
mented on their attempt to account for the effect of temperature on pavement deflection.
Clarification of two points may prove to be helpful.
Some of the most important data that led to the authors ' conclusions are an analysis
of the AASHO data given in Figures 89a, 89b, and 89c and Figure 90a of the AASHO
Road Test Report 5. The authors do not seem to have taken the actual data points, but
instead the generalized curve for which the correlation and standard deviation values
are not known.
In Figure 6 of the paper, seven curves are shown, each based on the AASHO data
mentioned. The degree of correlation (or amount of error) existing between the data
obtained from the AASHO curves and the curves given in Figure 6 is also not known.
Figure 7 is the average of the seven curves in Figure 6. In Figure 6, the further
the distance from the base point (i.e., 60 F of deflection adjustment factor = 1.0 ), the
greater the error in averaging. It is therefore believed that, although this investigation
shows the trend, the percentage error is unknown.
The AASHO Road Test and any number of field and laboratory investigations have
shown that the pavement strength is the sum of the strengths of each layer, and that this
strength can be generalized as

deflection, y, is a function of (E1 h 1 + E 2 h 2 + ... )

where E1 and Ka are the str~ngth coellicients of the materials in each layer of the pave-
ment with thickness h 1 and h2 respectively. According to the authors, the modulus of
asphaltic concrete, E1 , ifl a function of the temperature. Thus it follows that, according
to the above equation, the change in temperature resulting in the change in the value of
E1 should be an additive quantity for correlating with y, the deflection, as indicated by
Kingham and Reseigh (4), rather than a quantity to multiply by (E1 h 1 + E 2 h2 + ... ), which
in effect would change the contributing strength of other layers too. The reason that the
authors used the multiplying quantity in their analysis may be the result of the adoption
of Burmister' s elastic theory.

R. 1AN KINGHAM, The Asphalt Institute-Southgate and Deen are to be commended fo1·
reducing the enormous built of temperature data obtained by Kallas on thick asphalt
pavements to a mathematical form that can be used to predict pavement temperatures
at any depth in an asphalt pavement layer. With such predictions, a mean pavement
temperature can be determined for use in correcting Benkelman beam deflections to a
60 F standard temperature. This discussion is limited to the derivation of the adjustment
 129
.075
factors that the authors suggest can be used
to correct beam deflections for temperature.
To derive adjustment factors for cor-
.oeo
recting beam deflections to 60 F, the au-
thors were limited to data published from
.oze the AASHO Road Test. They assumed that
.i...:

~
the mean pavement temperature for the
AASHO data was the average of the top,
0 middle, and bottom of the pavements being
Ci
c
.075 tested. It is believed that the top, middle,
.2 and bottom temperatures of an asphalt con-
u
..
~
0
.oeo
crete layer 4-in. thick were used. For this
reason, temperatures reported for thicker
asphalt layers may have been subject to
bias .
.oze
This would explain in part why the ef-
fect of temperature on deflection seemed
to decrease at higher temperature ranges.
.02!5 .oeo .01e .100 This trend influenced the authors' choice
Deflection at Designalld Temperature, in. of a mathematical model to fit the data. In
order to compute deflection adjustment
Figure 12. Colorado deflection-temperature data. factors for temperatures other than those
measured at the AASHO Road Test, extrap-
olations from 90 to 140 F had to be made
using the mathematical model, and thus
the correction factors were highly dependent on the choice of mathematical model. An-
other limitation of the adjustment factors was the reference temperature of 60 F. It is
believed that 70 F would have been a better choice because it represents more nearly
the median for the temperatures normally experienced in deflection testing throughout
the United States and Canada.
For several years this discussant has been concerned with developing technology for
correcting Benkelman be!tm deflections to a standard temperature (10). Such correc-
tions are very important when deflections are used to determine asphalt concrete over-
lay thicknesses (11). Data from two full-scale experimental base projects, which were
in Colorado (4) and San Diego County, California (12), were collected to explore this
problem. These data, plu s some published by the Canadian Good Roads Association (5,
13) and the Road Research Laboratory (14), shed further light on the relationship be- -
tween mean pavement temperature and the Benkelman beam deflection measurement.
All the data considered were obtained by measuring deflections at a point while pave-
ment temperatures varied throughout the course of a day. Deflections plotted against
the mean asphalt layer temperature showed a linear relationship for the temperature
ranges that can be expected over a 24-hour period. This finding for full-depth asphalt
pavements from the Colorado Experimental Base Project has been reported previously
by this discussant (10). Also, more nearly linear relationships were found for the
AASHO Road Test data when mean temperatures were determined without the known
bias. A theoretical analysis also suggested that the relationship is approximately linear
for a 30 to 40 F temperature span. For temperatures ranging from 30 to 140 F, how-
ever, the trend was curvilinear with greater temperature influence at higher tempera-
tures.
As a result of the field measurements and theoretical studies, this discussant selected
a linear mathematical model to fit measurement data for each pavement point. The re-
sulting equations were used to compute deflections for certain designated temperatures.
Extrapolations greater than 10 F were avoided. Deflections at these selected tempera-
tures were then plotted against the 70 F deflection as shown in Figure 12. The excel-
lence of fit of the data to a straight line through the origin shows that a multiplying fac -
tor, of the type proposed by Southgate and Deen, is a good method of adjusting beam de-
flections. The slope of the linear fit through the origin is, of course, the adjustment or
multiplying factor for the temperature in question.
130
120 ~~--.
\ ~~-.-.,....-,.-----.-__,.~...---.------,.---"T""""--r~,--.---.---.

\ Dato Source :
\ • Colorado
\ >< Great Britain ( RRL)
\
100 • o Canada ( CGRA)
4 Son Oie90 County
CJ AASHO Road Test
0
IJ..:
*
Canada (Welsh)
f
.2 80
..
::!
CL
E
~

60

40'-----'----'~-'---'-~'---'-----'-~~&.L.~'---'---'-~-'--'---'~
0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
Adjustment Factor

Figure 13. Derivation of adjustment factor curves.

Plots similar to Figure 12 were made for dat a from each source. The resulting
slopes were plotted against their respective temperatures. These results are' shown
in Figure 13. Two relationships are evident. The Curve A included data primarily
from granular base pavements and represents strong support to the thin asphalt layer
(less than 4 in.). Curve B represents test data from thick aspn;Ut pavements (4 in. or
more) laid directly on weak subgrades.
Figure 13 provides two adjustment factor curves for use in correcting beam deflec-
tions to a standard temperature of 70 F. The choice of curves involves some judgment.
Considering the data sources for each curve, it is recommended that Curve A, the curve
representing the smaller correction factors, be used in the majority of instances. The
second curve, Curve B, providing large correction factors, represents an extreme situ-
ation where the asphalt layer is thick and weakly supported.

References
9. Benkelman, A. C ., Kingham, R. I., and Fang, H. Y. Special Deflection Studies
on Flexible Pavement. HRB Spec. Rept. 73, pp. 102-125, 1962.
10. Kingham, R. I. A New Temperature Correction Procedure for Benkelman Beam
Rebound Deflections. Asphalt Institute Research Report 69-1, 1969.
11. Asphalt Overlays and Pavement Rehabilitation. The Asphalt Institute, Manual
Series No. 17, 1969.
12. Kingham, R. I. Full-Scale Experimental Base Construction in San Diego County.
ASCE National Meeting on Transportation Engineering, San Diego, 1968.
13. Welch, D. A. Use of the Benkelman Beam in Municipal Street Design, Maintenance
and Construction. Proc. 42nd Convention, Canadian Good Roads Association,
1961.
14. Road Research, 1965-1966. Report of the Director of Road Research. Road Re-
search Laboratory, Ministry of Transport, United Kingdom, 1967.

H. F. SOUTHGATE and R. C. DEEN, Closure-The authors appreciate the interest

shown in the paper by Vaswani and Kingham. The comments made by Vaswani are well
taken and offer the opportunity to reemphasize points mentioned in the paper.
 131

Because the study reported in the paper was of a feasibility and pilot nature, and be-
cause of certain pressing needs to analyze field deflection measurements, the actual
data points represented by the curves in Figures 89a, 89b, and 89c and Figure 90a of
the AASHO Road Test-Report 5 were not used. fustead, the generalized curves were
analyzed and therefore the correlations and deviations are not known . The authors in-
dicated that a more precise analysis might be made in the future by considering the
actual data points instead of the generalized curves.
The authors did assume that the definition for surfacing temperature given on page
104 of Report 5 on the AASHO Road Test was correct. Because the term " surfacing
temperature" was not redefined for Figures 89 and 90 of the r eport, it must be assumed
that the surfacing temperature was the average of the top, middle, and bottom tempera-
tures of the actual layer thickness rather than of a 4-in. layer.
By definition, the adjustment factor at 60 F was taken to be one and is so indicated in
Figures 6 and 7. This does not necessarily suggest that the error in estimat ing the de-
flection adjustment factor is less at this temperature than at other temper atures. Much
of the scatter indicated by the various curves in Figure 6 may be, in part, due to the av-
eraging effect of the AASHO curves over pavements of various structural thicknesses
and components. Selection of the reference temperature seems to be somewhat arbi-
trary and analyses of deflection measurements should not be altered by use of adjust-
ment factor curves based on different reference temperature s. Figure 7 can be easily
adjusted to any other temperature that one desires to u se as a reference or base.
It is interesting to note that the adjustment facto1· curve s hown in Figure 7 of the
paper falls bet ween Kingham 's Curves A a nd B (Fig. 13), which may be c onsidered ex-
treme cases of pavement construction. Because the adjustment factor curve in the
paper was based on Figures 89 and 90 of the AASHO Road Test report, and the r efore in-
cluded averaging effect s, it is not surprising that the curve of Figure 7 falls between
Curves A alld B of Kingbam's discussion.
Further analysis of field deflection measurements since the paper was submitted
have been made using the deflection adjustment factor curve given in Figure 7 of the
paper. Amazingly good a greement has been found between the deflections as adjusted
for temperature and the theoretical deflections computed by an n-layered computer
program for the analysis of elastic-layered pavement systems. This comparison in-
creased the authors' confidence in the adjustment factor curve and, more importantly,
in the shape of the temperature adjustment factor curve.
To repeat what was indicated by the authors in the paper and by Vaswani in his dis-
cussion, further analysis of the AASHO Road Test data is needed to determine the actual
magnitude of the adjustment factors and to develop the proper and precise relationship
between temperature and adjustment factor with respect to the structural makeup of the
pavement system. Until this more detailed analysis of actual field data points can be
made, it is felt that the adjustment factor curve in Figure 7 provides an adequate first
approximation of the temperature effects on pavement deflections.