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Mix Code Poisson's ratio does not need to be known for an analysis
4-1 4-2 4-3 4-4 4-5 4-6 of thermal stresses in asphalt concrete pavement, so there is
no need to determine it as part of a uniaxial creep test. It is,
Critical Pavement Temp., C
0
however, an essential part of the IDT creep test.
-10 The SHRP equation for estimating the coefficient of ther-
mal expansion of asphalt concrete mixtures is not accurate. A
-20 simple and reasonably accurate alternative method has been
developed that uses the volumetric composition of the mixture
-30 and the mixture m-value (log-log creep compliance slope with
respect to time) to estimate the coefficient of thermal contrac-
-40 tion of the mixture. This approach appears to be similar in
Tc Prony 0°C Prony -10°C Prony -20°C accuracy to the laboratory measurement of the coefficient of
thermal contraction.
Figure 10. Errors in critical cracking temperature The Prony series method of calculating relaxation modulus
resulting from using Prony series approach to estimate from creep compliance, in general, works acceptably well, but
relaxation modulus. can result in significant errors for stiff mixtures when the max-
imum relaxation time for the series is exceeded during the
analysis. To avoid this problem, test temperatures should be
varied according to the binder grade used in producing a mix-
although not as theoretically elegant, produces more robust
ture. The current test temperatures should continue to be used
estimates over a wide range of conditions. The third approach
for PG XX-22 and PG XX-28 binders. For mixtures made
is the simplest and most direct: adjust IDT (or uniaxial) creep
using softer binders, all test temperatures should be lowered by
test temperatures to avoid collecting exceedingly stiff com-
10°C; for mixtures made using harder binders or heavily aged
pliance data. Based upon this analysis and general experience
binders, all test temperatures should be raised by 10°C.
with low-temperature creep data, the following protocol is
suggested:
COMPARISON OF COMPLIANCE VALUES
AS DETERMINED USING UNIAXIAL TENSION,
· For mixtures made using PG XX-22 and PG XX-28
UNIAXIAL COMPRESSION, AND THE IDT TEST
binders, creep tests should be performed at -20, -10 and
0°C; tensile strength should be determined at -10°C. An experimental test program was designed and executed
· For mixtures made using PG XX-34 binders (or softer), to answer several important questions related to the determi-
creep tests should be performed at -30, -20 and -10°C; nation of the low-temperature creep compliance of asphalt
strength tests should be performed at -20°C. concrete mixtures:
· For mixtures made using PG XX-16 binders (or harder),
or severely aged mixtures, creep tests should be per-
formed at -10, 0, and +10°C; strength tests should be · Is the low-temperature creep compliance of asphalt con-
performed at 0°C. crete similar in tension and compression?
· Does the IDT creep test provide creep values similar to
those determined in uniaxial tension or compression?
This approach should ensure that the compliance data col- · If the creep compliance values as determined in uniaxial
lected will not be prone to excessive errors when the maxi- tension, uniaxial compression, and with the IDT creep
mum relaxation time for the Prony series is exceeded. This
test are not similar, what is the nature of the relationship
will have the added benefit of producing more uniform data,
among these data?
which should help improve the precision of the test. This pro-
· How does the precision of test data compare for compli-
tocol is also consistent with that presented earlier, based on
ance determined using uniaxial tension, uniaxial com-
more practical considerations.
pression, or the IDT test?
Summary and Findings on Theory This section of this report discusses the design, execution,
of Testing and Analysis results, and findings of this test program.
Under the loads normally used in the IDT creep test and
likely to be used for uniaxial creep testing, asphalt concrete Materials, Methods, and Experiment Design
behaves essentially as a linear viscoelastic material. Data at
this time suggest that IDT specimens are large enough to Table 8 lists the four aggregate types and gradations
provide for a reasonable degree of homogeneity for most used in the laboratory testing performed as part of Phase III
asphalt concrete mixtures, though additional research needs of NCHRP Project 9-29. Nominal maximum aggregate
to be done in this area. size ranged from 9.5 mm to 25 mm, and the mineralogy was
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TABLE 8 Aggregate gradations cent by volume--and a similarly wide range of VFA--68
Aggregate Type: to 77 percent by volume.
Sieve 9.5-mm 12.5-mm 19-mm 25-mm The experiment consisted of measuring both the creep com-
Size VA MD VA PA pliance and tensile strength of the mixtures at low temperature,
mm Limestone Diabase Granite Gravel
Percent Passing by Weight:
using various procedures. The creep compliance was mea-
37.5 100 100 100 100 sured by indirect tensile, uniaxial tension, and uniaxial com-
25.0 100 100 100 97 pression. The IDT creep compliance tests were performed fol-
19.0 100 100 96 86 lowing procedures outlined in AASHTO T322. Specimens
12.5 100 97 76 63
9.5 97 75 54 46 having a diameter of 150 mm and a thickness of 50 mm were
4.75 63 38 33 35 sawn from standard Superpave gyratory specimens. The spec-
2.36 42.0 29.3 24.0 25.0 imens for uniaxial tension and uniaxial compression tests were
1.18 26.7 22.7 18.8 14.0 100 mm in diameter and 150 mm high and were cored and
0.600 17.2 18.5 15.0 9.0
0.300 11.2 11.9 10.8 5.0 sawn from high (165-mm) gyratory specimens. The procedure
0.150 7.9 7.2 6.1 4.0 used in the uniaxial tests followed as much as possible the
0.075 6.3 5.6 3.2 3.9 same protocol as described in AASHTO T322 for IDT tests,
except where the different geometry made changes necessary.
TABLE 9 Binder grades and bending beam rheometer test data The LVDTs used in the IDT creep tests were as described in
Binder Grade AASHTO T322--two transducers on each face, one vertical
Temperature PG 58-28 PG 64-22 PG 76-16 PG 76-22 and one horizontal, all with a gage length of 37.5 mm. For the
°C Stiffness (MPa)/m-value (PAV Residue): uniaxial tests, two LVDTs were mounted in diametrally oppo-
78/
-6
0.321
site locations at the specimen midheight with a gage length of
214/ 158/ 179/ 100 mm. For the uniaxial tension test, the ends of the specimen
-12
0.359 0.285 0.349 were fastened to the loading platens using epoxy cement. For
216/ 507/ the compression tests, rubber loading pads were used between
-18
0.373 0.275
548/ the specimen ends and platens to distribute the load and avoid
-24
0.278 stress concentrations. All creep tests were 100 seconds in dura-
tion and were performed at three temperatures for each mix-
ture. Most of the specimens were tested at -20, -10 and 0°C.
Specimens made with the PG 76-16 binder were however
distinctly different for each aggregate type. The four binders tested at -10, 0 and 10°C, because of the hardness of the binder
used in the study are given in Table 9. The grades included used in specimens (as recommended previously).
were PG 58-28, PG 64-22, PG 76-16, and PG 76-22. The first Two types of strength tests were performed: IDT strength,
three of these asphalt binders were unmodified; the PG 76-22 per AASHTO T322, and uniaxial tension. The tests were per-
was an SBS modified binder. formed at the middle creep temperature, usually -10°C, except
A total of 16 mixtures were designed with these materials-- that the specimens with the PG 76-16 binder were tested at
each of four aggregate types with each of four binder types. All 0°C. The IDT strength tests were instrumented so that the
were designed according to Superpave procedures, with an exact procedure described in AASHTO T322 could be used to
Ndesign of 100 gyrations. The resulting design volumetric com- determine the point of failure. In analyzing the data, this pro-
position of the mixtures is given in Table 10 (the design air cedure was used along with the more direct approach of sim-
void level was in all cases 4 percent by volume). The resulting ply using the maximum load to determine the IDT strength.
mixtures covered a wide range of VMA--12.6 to 17.6 per- Hereafter, these are referred to as the corrected IDT strength
TABLE 10 Volumetric properties of mixtures
Aggregate Type:
VA MD VA PA
Binder Property Limestone Diabase Granite Gravel
AC, Wt. % 6.2 4.75 4.4 4.4
PG 58-28 VMA, Vol. % 17.3 13.7 14.3 12.6
VFA, Vol. % 76.9 70.7 72.1 68.2
AC, Wt. % 6.2 4.75 4.4 4.4
PG 64-22 VMA, Vol. % 17.3 13.5 14.2 12.6
VFA, Vol. % 76.9 70.5 71.7 68.3
AC, Wt. % 6.2 4.75 4.4 4.4
PG 76-16 VMA, Vol. % 17.6 13.7 15.0 12.8
VFA, Vol. % 77.2 70.8 73.3 68.8
AC, Wt. % 6.2 4.75 4.4 4.4
PG 76-22 VMA, Vol. % 17.0 13.5 14.4 12.7
VFA, Vol. % 76.5 70.3 72.1 68.6
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and the uncorrected IDT strength. The IDT strength tests 1.E-04
Compliance,Tension, 1/psi
were performed using a loading rate of 12.5 mm per minute. 1.08
y = 4.48x
The uniaxial tension strength tests were performed at a load- 2
R = 86 %
1.E-05
ing rate of 3.75 mm/min, which provides a strain rate roughly
equivalent to that in the standard IDT strength test. MD DBASE
The experiment designs for both creep and strength can be 1.E-06 PA GRVL
VA GRNT
considered full factorials. For the creep experiment, there are VA LMSTN
Equality
five factors--test type, aggregate type, binder type, temper-
ature, and loading time--at 4, 4, 3, and 2 levels, respectively 1.E-07
1.E-07 1.E-06 1.E-05 1.E-04
(loading times analyzed were 10 and 100 seconds). For the
strength experiment, there are only three factors--test/analysis Compliance, IDT, 1/psi
type, aggregate type, and binder type--at 3, 4, and 4 levels, Figure 12. Comparison of compliance as measured in
respectively. As described in the following section, a variety uniaxial tension and as measured using IDT test.
of graphical and statistical methods were used in analyzing
the data. The primary problem in both experiments involved
comparing test data produced on the same set of materials
using different methods of testing. Many of the comparisons In Figure 12, the compliance values measured in uniaxial
were done using regression analysis, often with log-log trans- tension are compared to those determined using the IDT pro-
formations. A more rigorous comparison of compliance test cedure. The compliance values in tension again appear to be
data was done by treating compliance values as paired mea- significantly higher, exhibiting a very similar relationship to
surements. For both sets of tests, estimates were made of test that between compliance in uniaxial tension and compression.
variability, presented as both standard deviation and coefficient However, in this case it appears that the nature of the relation-
of variation. ship varies slightly among the different aggregates used. The
difference in compliance values appears largest for the Vir-
ginia limestone mixtures, whereas the difference for the Vir-
ginia granite mixtures appears to be negligible. This suggests
Results of Low-Temperature
Creep Compliance Experiment
that the compliance as measured using the IDT can be affected
by the aggregate used; it is possible, for example, that because
The most straightforward comparison of data involves of the high stresses at the point of loading that some aggregate
graphical methods and basic regression analysis. In Figure 11, particles are being crushed, resulting in substantial redistribu-
the compliance as measured in uniaxial compression is com- tion of stresses. It is also possible that the anisotropy is in fact
pared to that measured in uniaxial tension. As might be caused by preferential orientation of asymmetric aggregate
expected, the compliance in tension is usually higher than particles and that the degree of such orientation varies depend-
that measured in compression. The difference between these ing upon the specific aggregate used in a mixture.
two measurements is smaller at low temperatures/low compli- Based upon Figures 11 and 12, it should be expected that the
ance values and increases at higher temperatures/compliance compliance as measured in uniaxial compression and as mea-
values. At high compliance values, the value in tension is often sured using the IDT procedure will compare closely. This is
two or more times the value as determined in compression. confirmed in Figure 13, where these values are plotted against
There is no obvious trend in terms of aggregate--the relation- one another. Note that this relationship appears to vary depend-
ship between the two tests appears to be similar for the four ing on aggregate type, with the softer aggregates exhibiting
different aggregates used. somewhat lower compliance values in the IDT test compared
to the harder aggregates (the Maryland aggregate is a relatively
1.E-04
Compliance,Tension, 1/psi
1.E-04
Compliance, IDT, 1/psi
1.08
y = 4.24x y = 0.857x
1.E-05 2
R = 90 % 2
R = 93 %
1.E-05
MD DBASE
PA GRVL MD DBASE
1.E-06 VA GRNT 1.E-06 PA GRVL
VA LMSTN VA GRNT
Equality VA LMSTN
Equality
1.E-07 1.E-07
1.E-07 1.E-06 1.E-05 1.E-04 1.E-07 1.E-06 1.E-05 1.E-04
Compliance, Compression, 1/psi Compliance, Compression, 1/psi
Figure 11. Comparison of compliance as measured in Figure 13. Comparison of compliance as measured in
uniaxial compression and as measured in uniaxial tension. uniaxial compression and as measured using IDT test.
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hard diabase). To confirm this, Figure 14 is shown, which is characterizing the low-temperature stiffness of asphalt con-
identical to Figure 13, but only includes the hard aggregates crete mixtures.
(Virginia granite and Maryland diabase). Although the regres- A more rigorous comparison of data generated by the three
sion line is slightly closer to equality, and the R2 value is actu- low-temperature test methods is given in Tables 11 through 16,
ally lower, the relationship appears to be more uniform and which summarize the result of statistical pair-wise compar-
indicative of a better relationship between these test data. isons for creep compliance, master curve parameters, and
Because of the possibility of crushing aggregate and the result- critical cracking temperature. Table 11 compares the compli-
ing non-linear behavior, caution should be used in applying ance measured in uniaxial compression and uniaxial tension.
the IDT test to mixtures made using soft, friable aggregates. This table includes comparisons at loading times of 10 and
Two findings stand out in the graphical comparison of
compliance values: (1) compliance values in tension and
compression are not equal, as assumed in the analysis of the
TABLE 11 Statistical test for equality of compliance measured
IDT test; and (2) compliance values as determined using the
in uniaxial compression and as measured in uniaxial tension
IDT procedure tend to agree very well with those determined
Test
in uniaxial compression but not with values determined using
D(Tens.) D(Tens.) Stat. Sig.
uniaxial tension. In interpreting these findings, it must be Parameter D(Comp.) D(Comp.) |t*| Diff.?
remembered that the axes in which compliance is determined 1/psi %
in these three tests are not the same--the uniaxial tests eval- Temp. 1, 10 s 1.08E-07 19.3 2.228 YES
uate compliance along the length (or height) of the gyratory Temp. 1, 100 s 1.01E-07 9.9 1.295 NO
specimen, whereas the IDT evaluates compliance along the Temp. 2, 10 s 3.76E-07 30.6 2.559 YES
diameter of the specimen. Furthermore, the air void distribu- Temp. 2, 100 s 5.29E-07 23.4 2.126 NO
Temp. 3, 10 s 1.26E-06 34.5 2.175 YES
tion in typical gyratory specimens is not uniform, but tends to
Temp. 3, 100 s 2.16E-06 23.4 1.773 NO
be higher near the center of the specimen. Because the strain
measurements in the IDT test are made near the center of the
specimen, the effective air void content for the IDT tests TABLE 12 Statistical test for equality of master
curve parameters and critical temperatures
is lower than that for the uniaxial tests. Therefore, there are from uniaxial compression data and uniaxial
two possible sources for the higher compliance values de- tension data
termined in the IDT test compared to uniaxial tension: Diff.: Test
anisotropy and differences in air void content. It is possible Tens. Stat. Sig.
that the orientation of aggregate particles during compaction Parameter Comp. |t*| Diff.?
causes anisotropy in laboratory compacted specimens, so
Log (D0) 0.093 1.574 NO
that the compliance along the specimen diameter--as deter- Log (D1) 0.260 2.125 NO
mined with the IDT test--is lower than as determined in uni- M -0.094 3.345 YES
axial tests. The somewhat lower effective air void content in d log a(T)/d T -0.038 3.584 YES
the IDT specimens is also expected to produce lower compli-
ance values. However, an analysis of creep modulus values as TABLE 13 Statistical test for equality of compliance measured
predicted using the Hirsch model (4) indicates that differences in uniaxial tension and as measured using the IDT procedure
in air void levels probably only account for a few percent of Test
the observed differences. Because of the apparent presence of D(IDT) D(IDT) Stat. Sig.
substantial anisotropy in asphalt concrete specimens, the IDT Parameter D(Tens.) D(Tens.) |t*| Diff.?
creep test should be retained as the preferred procedure for 1/psi %
Temp. 1, 10 s -1.69E-07 -50.0 2.787 YES
Temp. 1, 100 s -1.98E-07 -45.6 2.053 NO
1.E-04 Temp. 2, 10 s -4.58E-07 -74.9 2.677 YES
Temp. 2, 100 s -5.98E-07 -51.7 2.188 YES
Compliance, IDT, 1/psi
y = 0.897x Temp. 3, 10 s -1.54E-06 -102.4 2.260 YES
1.E-05 R2 = 88 % Temp. 3, 100 s -2.42E-06 -55.4 1.766 NO
MD DBASE
TABLE 14 Statistical test for equality of master
1.E-06
VA GRNT curve parameters and critical temperatures
Equality from uniaxial tension data and IDT data
1.E-07 Diff.: Test
IDT Stat. Sig.
1.E-07 1.E-06 1.E-05 1.E-04
Parameter Tens. |t*| Diff.?
Compliance, Compression, 1/psi
Log (D0) -0.201 2.117 NO
Figure 14. Comparison of compliance as measured in Log (D1) -0.308 2.345 YES
uniaxial compression and as measured using IDT test, hard M 0.123 3.417 YES
aggregates only. d log a(T)/d T 0.046 3.597 YES
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TABLE 15 Statistical test for equality of compliance The final set of statistical comparisons is given in Tables 15
measured in uniaxial compression and as measured using and 16. In examining the compliance values, the difference
the IDT procedure between compliance values determined in uniaxial compres-
Test sion and using the IDT test is statistically significant in two of
D(IDT) D(IDT) Stat. Sig.
Parameter D(Comp.) D(Comp.) |t*| Diff.?
six cases. The compliance values determined in compression
1/psi % range from about 8 to 20 percent higher than those determined
Temp. 1, 10 s -6.10E-08 -16.5 1.973 NO using the IDT test. The only master curve parameter for which
Temp. 1, 100 s -9.71E-08 -21.2 2.200 YES the difference is statistically significant is the shift constant.
Temp. 2, 10 s -8.21E-08 -14.6 2.130 NO
In general, the compliance values determined using the IDT
Temp. 2, 100 s -6.90E-08 -8.2 1.284 NO
Temp. 3, 10 s -2.85E-07 -20.6 2.394 YES test and those determined using uniaxial compression com-
Temp. 3, 100 s -2.66E-07 -8.3 1.205 NO pare favorably, but they are not entirely interchangeable.
The statistical analysis presented above agrees with the
TABLE 16 Statistical test for equality of master
graphical comparison presented earlier and confirms that
curve parameters and critical temperatures the observed differences in compliance values determined
from uniaxial compression data and IDT data using the three procedures are statistically significant. As
Diff.: Test Sig.
discussed, the IDT creep compliance values are the lowest,
Parameter IDT Stat. Diff.? followed by the values determined in compression. The com-
Comp. |t*| pliance values determined in tension are the highest. As dis-
Log (D0) -0.108 1.434 NO cussed earlier, the relatively low compliance values determined
Log (D1) -0.047 0.627 NO using the IDT test are probably the result of anisotropy and
M 0.029 1.436 NO
not, primarily, differences in air void, air void distribution,
d log a(T)/d T 0.008 2.140 YES
or both.
An important consideration in evaluating the three low-
temperature compliance tests is the variability in the resulting
100 seconds at all three test temperatures. The paired obser- data. To provide better estimates of variances, the data from all
vation test is constructed as follows (18): mixtures were combined into two sets having reasonably sim-
H0 : Y1 = Y2 ilar compliance values. The lower compliance set included
data from all mixtures for temperature 1 at 100 seconds
Ha : Y1 Y2 and temperature 2 at 10 seconds. The higher compliance set
If t t (1 - 2; n - 1) conclude H0 ; included data from all mixtures for temperature 2 at 100 sec-
onds and temperature 3 at 10 seconds. By combining the data
otherwise, conclude Ha in this way, 30 degrees of freedom were achieved in the vari-
t = (Y1 - Y2 ) s(Y1 - Y2 ) ance estimates. The resulting variances are shown in Table 17.
By calculating variance ratios for each pair of data, an
Where Y1 and Y2 are the two quantities being compared, for F-statistic was constructed and compared to a critical value
example, compliance at the lowest temperature and 100 sec- of F(1 - /2, n1 - 1, n2 - 1) = F(0.975, 30, 30) = 2.07 (18).
onds as determined using compression (Y1) and tension (Y2); At a significance level of 0.05, only the difference between
and s is the pooled standard deviation. From the results sum- the variances for the IDT test and the compression for the
marized in Table 11, it appears that the difference between lower compliance set is statistically significant. In general, it
compliance measurements made in compression and tension appears that the three test procedures produce data with sim-
is greater at short loading times than at long loading times, ilar variability. The pooled C.V. for the compliance values
although the compliance as determined in tension is always were 10 percent for uniaxial tension, 16 percent for uniaxial
greater than that determined in compression. Table 12 shows compression, and IDT for n = 1 replicate. For n = 2 replicates,
that several of the master curve parameters exhibit significant the C.V. values were 7 percent for uniaxial tension and 11 per-
differences. The master curve parameters included in Table 12 cent for uniaxial compression and IDT. The C.V. dropped
(and Tables 14 and 16) are D0, the glassy compliance; D1, the further for n = 3 replicates to 6 percent for uniaxial tension
location parameter; M, the limiting log-log slope of the com- and 9 percent for uniaxial compression and IDT.
pliance function; and the shift constant, d log a(T )/d(T ) (the
slope of the log of the shift factor with respect to temperature).
Tables 13 and 14 are the corresponding summary compar-
isons of compliance as measured in uniaxial tension and as TABLE 17 Estimated variances for compliance
measurements
determined using the IDT procedure. In this case, the differ-
ences appear even larger, with most compliance values and Lower Higher
Compliance Compliance
most master curve parameters showing statistically signifi-
Temp. 1, 100 s & Temp. 2, 100 s &
cant differences for the two procedures. Note that the differ- Test Temp. 2, 10 s Temp. 3, 10 s
ences in compliance values range from about 45 percent to Tension 7.53E-15 8.74E-14
over 100 percent, with the compliance in tension always much Compression 1.52E-14 8.16E-14
larger than that determined using the IDT test. IDT 6.95E-15 6.67E-14
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Comparison of Strength Test Procedures 800
Y = 285 + 0.336X
Direct Tension Strength, psi
R-Sq = 33 %
An important aspect of the IDT creep and strength test 700
procedure is the specific procedure required to perform the
600
IDT strength test. As currently written, the IDT strength test
in AASHTO T322 requires deformation to be monitored using 500
vertical and horizontal LVDTs mounted on the specimen.
400 Equality
The load for calculating strength is determined from the point Reg.
at which the vertical minus horizontal deformation is a maxi- 300
95% CI
95% PI
mum. Unfortunately, this procedure often results in damaged
or destroyed transducers. As a result, many laboratories now 400 500 600 700 800 900
run the IDT strength test without LVDTs and simply use the IDT Strength (Uncorrected), psi
maximum load to calculate the strength. One of the main Figure 16. Regression line with 95-percent confidence
objectives of the experimental plan was to evaluate the differ- and prediction intervals for relationship between
ences among the uncorrected IDT strength determined from uncorrected IDT strength and direct tension strength.
the maximum load, the corrected IDT strength determined
from the maximum difference in the vertical and horizontal
deformations, and the strength as measured in direct tension.
This approach should provide good estimates of actual tensile
Figure 15 shows the relationship between uncorrected and
strength without risking damage or destruction of expensive
corrected IDT strengths. The relationship is reasonably good,
with an R2 value of 74 percent. instrumentation during the IDT strength test.
An important, related question is whether or not the correct A simple, alternative approach to estimating tensile strength
strength actually provides tensile strength values similar to is to develop a regression equation based on mixture volumet-
those measured in direct tension. Figure 16 illustrates the rela- ric composition. Such a method might be useful, for instance,
tionship between uncorrected IDT strength and the direct ten- in quality control applications. The best such model found for
sion strength. Figure 17 is the corresponding plot for corrected the data generated in this project is shown in Figure 18, which
IDT strength and strength in the direct tension test. is a plot of direct tension strength as a function of VFA.
It is clear that the procedure in AASHTO T322 does in fact This relationship is better than that between IDT strength
provide a better estimate of the tensile strength measured in and tensile strength and similar in strength to that between
direct tension than using the maximum load in the IDT test to corrected IDT strength and tensile strength. However, in
calculate strength. However, the relationship is still not very examining this figure it was noticed that several of the out-
strong, with an R2 value of 49 percent. It should be remem- lying points were for mixtures made using a modified binder
bered that asphalt concrete stiffness is anisotropic and that (PG 76-22).
strength might also be so. Therefore, differences in IDT and A multiple regression model was developed which allowed
uniaxial tensile strength are not necessarily indicative of for a different slope for mixtures with unmodified and mod-
inaccuracies in either test procedure. Although the AASHTO ified binders by using an indicator variable for binder type
T322 procedure does appear to be reasonable, it is suggested, and including in the model the interaction term for indica-
because of practical problems with this approach, that tensile tor variable by VFA. The results of this regression model
strength be estimated from uncorrected IDT strength using are summarized in Table 18. It was found that if both a differ-
the equation given in Figure 15 (R2 = 74 %): ent intercept and slope were allowed for the modified binder,
neither term was significant. A different slope was allowed
Tensile Strength = (0.78 × IDT Strength) + 38 (8) in this case because it was believed to be a more reason-
800
900 Y = 256 + 0.452X
IDT Strength, Corrected, psi
Direct Tension Strength, psi
Y = 38 + 0.781X
800 R-Sq = 74 % 700 R-Sq = 49 %
700
600
600
500 500
400 Equality
Reg. 400 Reg.
300 95% CI 95% CI
200 95% PI 300 95% PI
400 500 600 700 800 900 400 500 600 700 800
IDT Strength, Uncorrected, psi Corrected IDT Strength, psi
Figure 15. Regression line with 95-percent confidence Figure 17. Regression line with 95-percent confidence
and prediction intervals for relationship between and prediction intervals for relationship between corrected
uncorrected and corrected IDT strength. IDT strength and direct tension strength.
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700 Y = -708 + 16.8X 750
Y = -738 + 16.9X
Direct Tension Strength, psi
Direct Tension Strength, psi
R-Sq = 51 % 700
R-Sq = 76 %
650
600
600
550
500
500
450
400
Reg. 400 Reg.
95% CI
350 95% CI
300 95% PI 95% PI
300
68 69 70 71 72 73 74 75 76 77
70 75 80
VFA, Vol. %
Modified VFA, Vol. %
Figure 18. Regression line with 95-percent confidence Figure 19. Regression line with 95-percent confidence
and prediction intervals for relationship between VFA and and prediction intervals for relationship between VFA
direct tension strength. (modified to account for effect of modified binder) and
direct tension strength.
able assumption. Based upon the results given in Table 18,
the regression equation for strength of mixtures using non- strengths estimated from VFA, using Equations 9 and 10 (or
modified binders is: improved versions of these relationships) are probably ade-
quate. Additional research should be performed to better
Strength = -739 + 16.9 VFA ( 9)
define the relationship between mixture volumetrics, binder
For mixtures made using modified binders, the equation type, and tensile strength.
becomes
Effect of Test Procedure on Estimated
Strength = -739 + 18.1 VFA (10) Cracking Temperature
As seen in Figure 19, this approach greatly improved the From the previous analyses and discussions, it is clear that
quality of the model. In this plot, modified VFA is simply there are differences in both creep compliance and strength,
VFA for mixtures with unmodified binders and 1.08 × VFA depending upon the specific test procedure used. Ultimately,
for mixtures made using modified binders--this adjustment the most important aspect of these differences is their effect
accounts for the difference in slopes for the two cases. Addi- on estimated critical cracking temperature. To evaluate the
tional research is needed to expand the data set underlying effect of the test procedure on critical cracking temperature, a
this model, especially with regard to additional modified thermo-viscoelastic analysis was performed using the three
binders. However, it is potentially a very useful method for different data sets, following Christensen's version (10) of
estimating tensile strength when measurements are impossi- Roque and Hiltunen's procedure (5). To limit the effect of dif-
ble or impractical. ferences in tensile strength, the direct tension tensile strength
Based on this analysis, the procedure included in AASHTO was used for each analysis. The results of these analyses are
T322 for determining the true point of failure in the IDT shown in Figures 20 through 22.
strength test produces significantly better estimates of the true In Figure 20, critical cracking temperature from compli-
tensile strength than simply using the maximum load devel- ance in uniaxial tension is compared to critical temperature
oped during the test. However, the AASHTO T322 procedure determined using compliance data in uniaxial compression.
is not highly accurate and can damage the LVDTs used to Included in this plot (and the following two) are two standard
monitor deformation during the test. It is therefore recom- deviation confidence intervals for the difference between
mended that the standard procedure for determining IDT two observations. The agreement in this case is reasonable,
strength should be to determine the maximum load, calculate except for two points (both Virginia limestone mixes), which
the uncorrected IDT strength, and then correct it using Equa- show much lower cracking temperatures using tension data
tion 8. For some applications, such as quality control testing, than those determined using compression data. The corre-
TABLE 18 Results of regression model for direct tension strength
with VFA and binder type as predictors
Standard Significance
Predictor Coefficient Deviation t-value Level
Constant -739.0 228.8 -3.23 0.007
VFA 16.939 3.171 5.34 0.000
Ind. Varb × VFA 1.1794 0.317 3.72 0.003
R2 = 76.3 %; R2 (adjusted for degrees of freedom) = 72.7 %
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24
-10 uniaxial compression compliance data is shown in Figure 22.
MD Diabase Again, the relationship is relatively weak.
PA Gravel It is somewhat puzzling that the overall differences in com-
-20
Tc (Tension), C
VA Granite pliance values for the three procedures do not seem to affect
VA Limestone the critical cracking temperatures. For example, because
-30 Equality
the compliance in uniaxial tension is in general significantly
higher than that determined from the IDT test, it would be
-40
expected that the critical cracking temperatures determined
using uniaxial tension compliance data would, in general, be
-50
lower than those determined from IDT data. However, this is
-50 -40 -30 -20 -10
not the case, as seen in the previous plots. Apparently, differ-
Tc (Compression), C ences in the shapes of the master curves and in the tempera-
Figure 20. Comparison of critical temperature ture dependence as determined using these procedures tend to
determined from creep compliance in uniaxial tension and offset the trends in differences in compliance. The overall
creep compliance in uniaxial compression (R2 = 55%). result is that all three methods produce critical cracking tem-
peratures in the same temperature range. However, the rela-
-10
tionships between critical temperatures are poor. This con-
MD Diabase firms that uniaxial compliance test data cannot be used as a
PA Gravel substitute for IDT compliance data.
-20
Tc (Tension), C
VA Granite
VA Limestone
-30 Equality Summary and Findings on Comparison
of Low-Temperature Creep Compliance Tests
-40 and Strength Tests
Based upon the results of low-temperature compliance and
-50
strength tests performed on 16 different mixtures using several
-50 -40 -30 -20 -10
different test procedures, a number of important findings are
Tc (IDT), C apparent. Perhaps most importantly, asphalt concrete spec-
Figure 21. Comparison of critical temperature imens prepared using a gyratory compactor are anisotropic--
determined from creep compliance in uniaxial tension and the compliance determined across the diameter is different
creep compliance from IDT test (R2 = 42%). from that measured along the length of the cylinder. In gen-
eral, it appears that the IDT creep compliance is slightly less
-10
than the uniaxial compliance in compression and substan-
MD Diabase tially less than the uniaxial compliance determined in tension.
PA Gravel Although laboratory compaction using the gyratory device
-20
VA Granite does not exactly replicate field compaction, it seems likely that
Tc (IDT), C
VA Limestone similar anisotropy exists in pavements. Therefore, caution
-30 Equality must be used when comparing compliance or modulus values
for asphalt concrete determined using different test geometries
-40 and using the resulting values in pavement design. Because of
this anisotropy, it is recommended at this time that the IDT
-50 creep test be retained as the standard method for measuring
-50 -40 -30 -20 -10 low-temperature creep compliance of asphalt concrete. There
Tc (Compression), C does not seem to be a similar degree of anisotropy in strength
test data. Tensile strengths determined in direct tension are
Figure 22. Comparison of cracking temperature similar to those determined using the corrected IDT strength
determined from IDT test and creep compliance in uniaxial test procedure in AASHTO T322. Furthermore, it appears
compression (R2 = 42%). that corrected IDT strength can be estimated fairly well from
uncorrected IDT strength using Equation 8. Therefore, the
sponding figure in which critical temperatures were determined overall recommendation from the experimental portion of this
using uniaxial tension compliance data and IDT compliance study is that the IDT creep and strength test be retained for use
data is shown in Figure 21. In this case, the agreement is in estimating the thermal cracking resistance of asphalt con-
poor--there does not appear to be a useful relationship crete but that IDT strengths obtained from the maximum load
between the results of these analyses. The comparison of crit- should be empirically adjusted to provide more realistic esti-
ical temperatures determined from IDT compliance data and mates of the actual tensile strengths of mixtures.
