Determination of Coefficient ofThermal Contraction of Asphalt Concrete Using Indirect Tensile Test Hardware

Yusuf A. Mehtal, Donald W. Chrislensen2 and Shelley M. Stoffels]

Draft Copy Submlffed fo r Acceptance by the Journal of Assoc/Q/lOn of Asphalt Paving Technologists December. J 998

1 Graduate Student, The Pennsylvania State University, Transportation Research Building, University Park, PA 16802. Ph.: (814) 863.8010, Fax: (8 14) 865.)039, email: \'aIII I.1i'pw.ed\I 1 Assistant Profmor . The Pennsylvania Stale University, Transportation Research Building, University Park, PA 16802 Ph.: (814) 86J·I903, Fax: (8 14) 865-3039, email: d .... ~ I '1lpru roll. 'Associate Proftssor, The Pennsylvania Stale University, Transportation Research Building, University Park, PA 16802 Ph._ (81 4) 865-4622, Fax: (814) 865.3039, email: poffdstap5U.edu,

ABSTRACT

The indirecl1ension (IDT) test, as developed during the Strategic Highway

Research Program (SHRP) is a tethnique for determining the creep compliance and

strength of asphalt concrete mixtures in tension. These data can be used in thermo­

viscoelastic analysis to evaluate the abili ty of the mixture to resist thermal cracking in a

given application. An essential piece of information in performing the calculation of

thermal stress using IDT cn:~p data is the coefficient of thermal contraction (a) of the

mixture. During SHRP, a mel hod was proposed for estimating a based upon the

volumetric propenics of the minure. Stoffels and Kwanda (I ) have shown (hal this

procedure is nOI accurate and proposed instead a method for measuring Cl using bonded

strain gages In tius paper, a similar technique is presented that uses linear variable

differential transformers (L VDTs) as are normally included in IDT hardware. With this

procedure, engineers and researchers can quickly and acwrately measure the coefficient of

thermal contraction of mixtures as pan of me standard IDT procedure_ The proposed

method was found \0 be only slightly more variable than that using strain-gages, and the

results for an aluminum reference standard and three asphalt concrete mixtures were found

\0 be in good agreement with values reported by Stoffels and Kwanda. Inclusion of

thermal contractJon measurement in the ITJT procedure will significantly improve the

accuracy of the resulting thermal stress calculatioos and low.temperature cracking

predictions.

Keywords Indirect tenSIon test, coefficient of thermal contraction, asphalt concrete.

L ... TRODUCTION

Asphalt concrete IS known to exhibit viscoelastic properties and is also a

thermorheologically simple material. tis physical propenies are largely dependent on

temperature To evaluate thermally induced strains and resulting stresses, the coefficient

of thermal contraction value must be known (2). The a -value is an impOn8nt parameter in

thermal cracking performance model used in Superpave and for low-temperature stress

calculation of asphalt concrete (3) Recently, Stoffels and Kwanda (I) obtained accurate

and repeatable a-values of asphalt concrete by using electrical resistance bonded stram

gages. In this study, !DT hardware was used to measure the a-value of the SHRP A- OOS

asphalt concrete samples instead of strain gages, and the feasibility of the lOT hardware m

measuring the coeffi cient of contraction of asphalt conmte was evaluated. The lOT

hardware is consistent with the Superpave equipment, is easy 10 use, and is inexpensive.

considering that many specimens can be tested before the linear variable differential

transducer (L VOT) may need to be replaced The purpose of this paper is to describe the

process of calibration of lOT hardware and 10 discuss the accuracy and repeatabi lity of the

IDT bardware in measuring the coefficient of thermal contraction of asphalt concrete

The scope of the work presented in the paper includes a review of the present

techniques, explanation of procedures including detennination of the II-value of L VOTs

and the a -value of the refmnce aluminum beam., and comparison of the measured II-value

of asphalt concrele from strain gage and ITom IDT hardware.

BACKGROUND

Coefficient of Thermal Contraction

The coefficient of thermal contraction is defined as the change in length or volume

of a material resulting from temperature change. The linear coefficient of thermal

contraction is given by

where:

6, , a=--or

a '" linear coefficient of thermal contraction (IrC)

ru:r '" change in thermal strain

t.T '" change in temperature eC)

(I)

For a homogenous and isotropIc material, the !lnw coefficient oflhennaJ

contraction is one-third of the volumetric coefficient of thermal contraction. Asphalt

concrete is usually considered 10 be a homogenous and isotropic material, and in the past

linear coeffi cients of thermal contract Lon have been calculated from volumetric

measurements (1,2,3)

Techniques of Mtasuring Cotfficien, of Thmnm COlltrtu:ri0 1l

Researchers have used different types of strain gages 10 determine the coefficient

of thermal contl1l.ction for measuring the a-value of aspb.aJt concrete. Hooks and Goetz

found thai these gages were difficuh 10 accurately calibrate and showed inconsis tencies in

readings due to the effect of temperature on the gages (4,5), They used Wimmore strain

gages, which were n01 affected by temperature and gave reasonable readings, but were

difficuh 10 use Lillle6eld (6) and Jones (2) used an eJClenscmeter 10 measure Ihe Ihermal

contraction of asphalt concrete. This apparatus consisted of a piece of steel rod equipped

with IWO brackets fixed to each end Burgess (7) used a dilatometer to perform his

measurements, and Osterkamp et al (8) used a linear voltage displacement transformer

and preCISion push-rod type dilatometer Hooks and GoelZ (4) also used a diJatometer,

along with a dual microscope technique to measure the coefficient of lhermal contraction.

Recently, Stoffels and Kwanda (I) used electrical resistance strain gages to measure

coefficients of thermal contraction This technique worked well, but tbe cost of tbe strain

gages IS higb. The metllod described In this paper is based upon Stoffels and Kwanda's

work, but lVDTs were used rather Iban strain gages.

Thumal Erpansion-Conrraction Characleristics of Asphalt Concrete

Hooks and Goetz (4) studied the effecu of certain mixture variables sucb as type

ofaggregate, grade, and asphalt cement content on coefficient oflbennaJ comraclion.

The}' found that the coeffiCient for the mixtures varied approximately in proportion 10 the

thermal comraction coeffiCients and Ihe volume of the respective component materials (4).

l

Jones (2) developed an equation to calculate the coefficient of thennal contraction of the

mix from its individual components

,

_ !(V~(' B,/C +Vj(i(1 · 8 1(0 ) a lV " -. 3 Vrom

(2)

where ..... B.o.oo :::

B",

linear coefficient of thermal contraction of asphalt mixture (Ir e)

volumetriC coefficient of thermal contraction of aggregate (I f' e)

volumetric coefficient of thermal contraction of the asphalt

cemenl in Ihe solid Slale

asphalt content of mixture (volume %)

aggregate content of mi~ure (volume %)

100 'I.

Lytton et aJ (3) modified the above equation \0 account for the effect of air·voids.

The modified equation is.

(J)

where"

V II1R air content of mixture (volume %)

In the study conducted by Stoffel s and Kwanda ( I), the coefficient of (henna!

C(Inlraction was measured in the range o[O·C and -25 ·C. Since the pUfllOse CrlmS

study was to compare Ihe coefficient of thermal contraction values measured using the

lOT LVDTs and the strain gages, the temperature range ortesling in this study was also in

the range oro O( and -25 °c.

'ndirtrl Tf!1LJilf! Tut Hardwon

The indirect tensile lest hardware used in this project was developed during SHRP

l

(J) Two LVOTs are attached to each face oflhe specimen at right angles. The LVOT

hardware includes the L VOT core, the housing material made of AI51 400 series magnetic

stainless sleel, the aluminum casing, the brass pins, and the copper wires. A voltage

proponional 10 the displacement IS generated when the core is moved imo the housing

material. The L VOT is connected to the data acquisition board through a signal

conditioner. A schemati= of the L VOT is shown in fi gure L

Copper Wires

Core Housing ~ Material

~ -,

f.ll! • '" ,,','_1. ,

Gage Length

Screws

1-+ Aluminum Casing

B rass Pins

L. Specimen

Figure l. Schematic orIDT LVDTs.

EXPERIMENTAL DESIGN

A titanium silicate plale was used for determination of the coefficient of thermal

contraction of the L VOl s A reference aluminum beam of known a-value was also used

for verifying whether lOT L VDTs can accurately measure coefficient of [hennal

contraction. The coefficient of thermal contraction values of an aluminum reference

spe<:imen were calculated from seven LVDTs were compared . Two replicate

measurements were obtained from each L VOT. The experimental design is shown in table

The a-value of asphalt concrete specimen obtained using!DT hardware was

compared with the coefficient of thermal contraction value from strain gages, Four

replicate measurements were obtained using l VOT and two replicate measurements were

,

obtained using a st rain gage fo r each mix The sta tistical design for comparison of a-value

of asphalt concrete from the two Itst methods is shown in table 2

Table L Exprrimenlal DtSign for Comparison of a-Value of Aluminum Bum from All Senn LVDTs.

Resoonse Van'able' CoeffJOent of Thermal Contraction of Aluminum Beam Factor levels DeQrees of Freedom LVOTs 7 6 Error 2 reDlicales 7 Tolal 13

Table 2. Experimental Design for Comparison onesl Methods.

Response Variable: Coefficient of Thermal Contraction of ASllhalt Concrete

Factor level Degrees of Freedom

Mix 3 2 Method (lVOT and Strain Gage) 2 1

Error (No. of measurements using lVDTs = 4) 12 11 No. of measurements usina strain aaees = 21

Total 17 16

MATERIALS

Three mixes from the SHRP A-OOS projet\ were evaluated in this study. A single

specimen from each of the mixes was tested in this study Tbe coefficient oftherma1

contraction value of each of the specimens of these mixes was previously measured using

strain gages (!). These mixes were selected so as to cover a broad range of thermal

contraction values A specimen from each of these three mixes was tested so that the

coefficient oftherma! contract ion between IDT hardware and the strain gage method

could be compared. The physical characteristics of asphalt concrete specimens tested in

this study are shown in table 3 (I). The coefficient of th~mal conuaction of aspbalt

cement was assumed as J 45 x I O~1 °C (3 ).

, , ,

7

Table 3. Physical CharaCltriuics of Asphalt Conmle Spttimens (I).

PTI Asphalt Aggregate linear Volumetric Code Content Type Aggregate Air Asphalt Aggregate

(%) Coefficient (%) (%) (") (Weight) (10' f C)

N1 5.2 Sandstone 0.97 D.B 12.7 86.4 N13 4.7 Gramte 0.95 2.2 11 .0 86.B N2B 5.0 Dolomite 0.B2 B.9 11.5 79.6

PROCEDURES

Calibration of mT Hardware

The lOT hardware was calibrated to verify the accuracy of the L VDTs in

measuring the coefficiem of thermal contraction and 10 identify problems with the L VOTs.

The calibration oftbe IDT hardware consisted oftbe following two steps: (I)

delemunalion of the coefficient of thermal contraction of the !DT hardware, and (2)

determination of the coeffimnt of thermal contraction of the reference steel beam using

the IDT hardware. Each of the steps is explained in the following sections.

Determination of Coefficient of Thumal Contraction of /Dr Hardware

In order to measure (he a-value of asphalt concrete specimens, the coefficient of

thermal contraction of the L "'DTs must he measured. However, the complex

configuration of the L VOT makes it difficult to calculate the a-value of the L VOT from

the a-values of the individual components. Thus it is necessary to measure the coefficient

of thermal cOnTraction of the L'lOTs To perform this measurement, the L VOTs were

first attached to a titanium Slhcate specimen manufactured by Meto-Measurements, Inc

( I). This plate has an a-value of 0 00) ± 0.00) x. JO.! re, which is negl igible compared

to the range of a-values oi asphalt concrete and the L VOTs. Thus, any obselVed change

,

in tbe L VOT readings is due [0 the contraction or expansion of the L VOT itself. The

dimensions oflhe plate are 152.3 mm x 25 ] mm x 6 J mm Two LVDTs were attached

on either side of a titanium SIlicate plate The platt was then clamped to the IDT platen

using a C-clamp The gage length orlhe L VDT was 38 nun. Figure 2 shows a schematic

diagram for this experimental setup

f1-.g====!" IDT Hardware H (LVDTsl

Titanium Silicate Plate

C-Clamp

IDT-Platen

Figure 2. Elperimental Stt·Up for Determination of Coefficient of Thnmal Contraction of lOT Hardware.

The titanium silicate plate and the L VDTs were allowed to equilibrate at 0 °C for 1

hour, after which the L VOl readings were zeroed and then the data acquisition was

started. The L VOT traces were acquired every second. The dala Wefe acquired for 500

seconds and the traces were observed. If the traces did not stabilize, the data acquisition

was stopped and the L VDT and the titanium silicate plate were conditioned for a longer

time before repeating the test. If the traces had stabilized, the chamber was sel aI-25°C

and the test was allowed to run for! hour or until the traces stabilized at tlUs lower

temperature. During the change in temperature, the chamber typically cooled at about I 5

DC/min. A typical trace of the L VDTs on a titanium silicate specimen is sho"''JI in figure J.

Two independent tests were conducted on each of the L VDTs. Table 4 shows the

replicate measurements and the average values of the coefficient of thermal contraction of

all seven L VOTs.

E E -o • E • u • C. • i5

,

O.lll -------------------,

0.025 .

0.02 I '. ~ '--'-;;,;;7"-'-' ............ -- -' . ~ .. -' ..........

/ 0.D15

, / / 1 ' I V 1 I

/ I 1 ' ,,'

I: I' I

iJ' 0 1~~L-------~~~~--~--~--~ o 11XX1 1500 lIllI

Tine, sa::

Figure 3. Typical Traces of l VDTs on a Titanium Silicate Specimen Dllring Thtrmal Contraction from 0 °C to _25 °C.

The coefficient of contraction values of l VDTs was used to measure the

coefficll~nl of thermal comraC\lon of the reference aluminum beams. The standard

deViation for coefficiem of thermal comraction ofLVDTs was 0 J4 x 10'! I °C

10

Table 4. Coemcient ofTh erma' Conlrlclion of LVDTs.

Coefficient of Thermaf Contraction of LVDTs, x 10" I "C LVOr Replicate 1 Replicate 2 Average RH1 2.24 1.79 2.01 LH1 1.89 1.73 1.81 RV1 1.84 2.08 1.00 LV1 1.89 2.37 2.13 RH2 1.92 2.05 1.99 LH2 1.71 1.73 1 72 RV2 245 141 1.93

Ddtrmination 0/ Coefficient a/ Thermal Contraction of Aluminum Beams

To verify the proper functioning of the IDT hardware, the coefficient of thermal

contraction of an aluminum beam (ALCOA 3003 H14) was determined. The dimensions

of this beam were 3.2 mm x 25.4 mm x 152.3 mm. The standard value of the coefficient

of thermal contraction specified in the Handbook of Chemistry and Physics (9) is 2 32 x

1O"I"C, which is similar to typical values for asphalt concrete. Stoffels and Kwanda, using

the same aluminum sample, mUSlJred an average coefficient of thermal contraction value

of2.18 x 10,Ire (I) The coefficient of thermal contraction of the aluminum beam was

determined in the temperature range of 0 °c and - 25 °C using all seven L VOT s Two

replicate determinations were made using each L VOT The aluminum beam was clamped

in the same way as the titanium silicate beam (see figure 2), and the same testing

procedure was used.

During this test, the contraction of the aluminum beam caused the L VOT core to

move into the housing material, which was the value obtained ITom the data acquisit ion

software. The apparent coefficient of tbermal contraction was this observed reading

divided by the gage length. However, the contraction of the L VOT hardware itself caused

the core to move out of the housing material. Hence, to calculate the coefficient of

thennal contraction of aluminum, the coefficient of thermal contraction of the hardware

must be added 10 Ihe observed coefficient oftherm.al contraction. Table 5 shows an

example calculation for the coefficient of thermal contraction of an aluminum beam.

II

Table 5. Example Calculat ion orThermal CoeffidtOI ofConlractioD of Aluminum Beam Using lOT Hardware.

Step LVDT RHl

1 LVDT Readmg at 0 °C 0 2 LVDT Reading 81-25"C x 10~. mrn 38.0 3 Observed Deformation x 10-.4, mm = (2) - (1) 38.0 4 Gage Length (mm) 38.0 5 Observed Strain x 10'4, (mm/mm) = (3)1{4) 1.0 6 Observed Coefficient of Thermal Contraction x lO,5rC = (5)125 0.40 7 eoeff. Of Contraction of l VDT x 10-5rC (From Table 2) 2.01 8 Actual Coefficient of Contraction x 10-5/"C =

Observed Coeff. (6) , Cooff. o( Contraction 0( LVDT (7) 2.41

Table 6 shows the measured values for the coeffi cient of thermal contraction of the

aluminum beam using the lDT hardware. A statistical analysis was done 10 verify whether

the coefficients oftherma! contraction of aluminum measured using each of the L VDrs

were the same. A one-way analysis of variance was conducted considering L VOT as a

factor, a p-value of 0 186 was obtained Since the p-vaJue was greater than 0.05, the

difference in the coefficiem of thermal contraction for the aluminum beam obtained from

each of tbe L VDTs were Slatlstically insignificant at a 95 percent confidence level (10).

The overall mean for the coefficient ofthennai contraction of the aluminum beam was

2 44 x IO"I"C, with a standard deviation of 0.19 x IO.II"C. This is very close to the

standard value of 2 32 x 10·lr C Thus, this experiment verified tbatthe procedure using

the L VDTs was working wen

The contraction of the L VDr contributes up [0 80 percent oftbe contraction of

the aluminum beam Even though the contraction of the L VDT is required to calculate

the contraction of the alurrunum beam, the contraction of the aluminum is physically

independent of the contracl!on of the L VDr An accurate value of the contraction of the

aluminum beam can be obtained if the contraction oh lle L VDr is measured accurately.

LVl 0

30.5 30.5 38.0 0.8 0.32 2.13

2.45

12

Determination of Coefficient or Therm al Contractio n of Asphal! Concrele

The three asphalt caRmie specimens tested in lhis phase of the work were ISO

mm in diameter and SO mm in thickness Four L VOl s were attached to the asphalt

concrete sj}ecimen prior 10 testing. Four replicate measurements were taken on each

specimen. Each replicate measurement included dismounting of the hardware and

removing of the brass clips and then fe-mounting or lhe L VDTs al the previous localion

rable 6. Coefficient ofThermal Contraction of Aluminum Bu m Measured Using All Seven LVOTs.

Coefficient of Thermal Contraction of Aluminum Beam, x 1a~ 1"(; LVDT Replic ate 1 Replicate 2 Average RH1 2.41 2.60 2.50 LH1 2.69 2.37 2.53 RV1 2.17 2.12 2.15 LV1 2.45 2.48 2.47 RH2 2.55 2.95 2.75 LH2 2.39 2.25 2.32 RV2 2.12 2.55 2.33

Tbe study by Kwanda indicated that the position orlhe strain gages on the

specimen did nOl affect the result (I I). Figure <I shows the position of me L VDT s with

respect 10 strain gages. The lOT hardware was placed on either location I or location 2,

as shown in figure <I, depending on the space available on the specimen_

Position of IDT Hardware

6-inch.diameler specimen

Position of Strlin Gages from Study by Stoffels and Kwanda (I)

Figure 4. Position of LVOTs on Each Fact of Specimen.

Il

All three samples were tested in the temperature range 0(0 DC to -25°C and the

testing procedure was the same as used in the testing oflhe aluminum beams, as described

earlier The specimen was simply placed on the plalen instead of being clamped to the

platen like the titanium silicate and the aluminum beam. Once again the rate of change in

temperature was not controlled during testing, as the study by Kwanda showed that the

rale of change in temperature did not affect the value of coefficient of [hennal contraction

beiwetn 0 °C and - 25°C (II ) A dummy specimen with a thennocouple in the center

was used 10 determine whether the Itst specimen had reached the desired temperature.

The specimen look about one hour 10 reach O·C and stabilized at -25°C after lDout 2

hours The IOlal testing lime, including mounting the L VOTs, was J 112 hours. A typical

plot on l VOT during thermal contraction of aD asphalt concrete specimen is shown in

figure 5

In figure 5, the traces initially moved in the positive and then in the negative

dirtction This is because the L VOT contracted firSt, followed by contraction of the

asphalt concrete specimen due to higher thermal conductivity of the L VOT as compared

to asphalt concrete. If the coefficient of thermal contraction of asphalt concrete were less

than the L VOT the traces would be positive, as bappened for asphalt concrete used in the

this study

RES ULTS AND ANALYSIS

Coefficient of ThermQI Con frQcrion VQlua of Asphalt Concrete Meosured Using IDT

Hardware

A coefficient of thermal contraction value of asphalt concrete was calculated from

each of the fou r L VDT readings Four such replicate measurements were taken and the

overall average was then calculated by averaging these four determinations. Table 7

shows the coefficient of thermal contraction values of asphalt coacrete obtained !Tom each

L VOT on a replicate measurement

" aas I

aOOl '

aooz l \ , .. ~\ .',':.. .. ~

•

\ 0

E E .. -0.001 . < - lllERT • E

\ • u • -0.001 C. • is

-O.as IMRT .. -, .-. , ..

-O.1XlI • \ .. \'\_ .... ,--_._--_ .... _-.

-0.01

-O.0I2 L---------~----~----------------~ o

Figure S, A Typical Trace ofLVDTs During Thermal Contradion or Asphalt Concrete from 0 °C to - 2S 0c.

A statistical analysis was done to compare the replicate measurement of a-values

of asphalt concrete. A p-vaJue 0(0.78 was obtained; since the p-value was grealer than

0.05, the replicate measurements of a-values were statistically the same at a 95 percent

confidence leveL

Ta ble 7. Coeffi cicnI ofThermal Contraction of Asphalt Concrete Samples Musured Using IDT Hardware.

a-value of Asphalt Concrete Using lOT Hardware x 10 I'C

I N1 I N13 N28 Replicate Measurement 1

Reading 1 2.32 2.89 1.74 Reading 2 1.99 2.72 1.20 Reading 3 1.30 2.87 1.69 Readino 4 1.93 3.09 1.78 Average 1.88 2.89 1.61

Replicate Measurement 2 Reading 1 2.57 2.12 1.10 Reading 2 2.29 1.77 1.33 Reading 3 2.57 2.04 1.67 Reading 4 2.56 2.77 1.70 Averaae 2.50 2.17 1.45

Replicate Measurement J Reading 1 2.25 2.60 1.70 Reading 2 1.80 2.65 1.61 Reading 3 2.70 2.23 1.37 Readino 4 2.82 1.49 1.44 Average 2.39 2.24 1.53

Replicate Measurement 4 Reading 1 2.17 1.54 1.75 Reading 2 2.36 2.49 1.37 Reading 3 2.94 2.46 1.84 Readina 4 2.69 2.50 1.97 Avera!)e 2.54 2.25 1.73

Overall Average 2.33 2.39 1.58

Compadson of Coefficient of Thermal Contraction Va/uu Obtained f rom Various

Methods

Il

Table 8 shows the a-values of asphalt concrete samples measured using strain

gages. The coefficient of thermal contraction values calculated using equation 3 for mixes

Nt , Nil, and N28 were 2 40 )( 10·j 1°C, 2,10 x 100j 1°C, and 3.01 )( looj 1°C,

respe<:l ively In the slUdy by Stoffel s and Kwanda ( I), tWO specimens for each mix were

tested A one-way analysis of variance was done to compare the a-value of asphalt

concrete between two specimens for a mix. A p-value 0(0 32 was obtained, indicating

that the a-value was stat istically the same for the IWO specimens of each of the three

rruxes

Table S. Coefficient of Thennal Contraction of Asphalt Concrtle Sa mples Musurtd Using Stra in Gages (II.

a-Value of Asphalt Concrete Using Strain Gages. x 10 I 'C Nl N13 N2B

Reading 1 1.86 2.B2 1.42 Reading 2 2.46 22B 1.49 Reading 3 2.44 2.97 1.50 Reading 4 1.9B 2.B5 1.59 Averaae 2.1B 2.73 1.50

16

A statistical analysis was done 10 compare the coefficient of thermal contraction

values measured using the IwO test methods according to the statistical design shown in

table 2. Analysis ofvanance was conducted considering mix and test method as a factor

The p-value orO.85 fo r the test method was obtained, indicating that the lest methods are

statistically the same at a 95 percent confidence level. The a-values for all the three mixes

obtained using lDT hardware, strain gages and those calculated using equation 3 are

shown in figure 6.

5,------------------------, C Calculaled

4 • Strain Gages

• LVOr, 3

2

1

a LL_

Nl N13

Mixture Code

N2B

Figure 6. Coefficient orrhemlll Contraction or Asphalt Concrde Using Different Methods.

17

The a-values for the three mixes obtained using IDT hardware were between 5

percent and 13 percent of the values oblailled by using strain gages and between] perten!

and 48 perctlll of predicted value using volumetric relationship Seddik and Haas (12)

also observed Jarge differ/met! between the measured and the Superpave volumetric

relationship, indicating that the volumetric relatioDship may be inaccurate.

Comparison 0/ Vllr;ability ill Coefficient o/ThtrmDi CoIlf1action Measuremenu Made

Using Strain Gage and /Dr Hardware

A statistical les\ was done \0 compare variances of coefficient of thermal

contraction of asphalt concrete measured using L VDTs and strain gages. In this study,

sixteen a-values of asphall concrete were calculated from each L VOT reading on a single

specimen for each of the three mixes. In the study by Kwanda and Stoffels (I) seven a·

values of asphalt concrete were obtained for mix NI, seven for mix N2 and eight for milt

N28. The a·values for the three mixes was pooled together for each oflhe lest methods.

Thus, a total of 48 measurements were obtained using L VOTs, and 22 measurements

were obtained using strain gages A F-Iesl was done to compare Ihe variances. The

hypmhesis for the F-Itst for comparison of variances (10) states that:

1-4 = the \'Inances are the same.

For which the tesl SlatJstic is

wllere

F' =E... s ' ,

The deciSIOn rule for le\'el of significance a is given by"

(4)

"

where VI and \II are the degrees of freedoms auociated with SI and SI respectively

The statistical analysis is shown in table 9 Since the ratio of variances (F' ) is 1m

than FUI!.noll. as shown in table 9, the hypothesis is proven and the variances are

stat istically the same at 9S percent confidence level.

Table 9. Slalistical Analysis for Compuison of VarianctS,

Comparison of Variances Method LVDT Strain Gage

Measurements 46 22 Degrees of Freedom 47 21 Variances 0.29 0.24 Ratio of Variances (F·) 1.19 Fa025 ~nl 1.32

Efftct on TIIermal Stuss

The observed discrepancies in calculated and measured values oflhe coefficient of

thennal contraction will significantly affect the ca1culation of thermal stresses generated in

the pavement during a low-temperature event. The thermal stress generated when a

pavement cools in the wintertime is in fact directly proportional to the value a (3, 13) To

demonstrate the effet:t of errors in the value of this parameter, surface thermal stresses

were calculated for the three mix~ used in this study_ The procedure used was a slight

modification of the method developed by Roque, Hiltunen and others during SHRP (3, 13 ,

14). The compliance values used in these analyses were those presented by Suular (I S)

and are given in table 10 The tensile stress values used were those measured during the

SHRP A-DOS projet:t at -10 °C 4.0 MPa for mixture Nl , 3 0 MPa for mixture NIJ , and

2.1 MPa for mixture N28 (J) For each of the three mixtures. three different values for 0-

were used: the value calculated using ~ualion J; the value found by Stoffels and Kwanda

using bonded resistance strain gages (1). and the value determined using L VDTs, as

discussed in this paper

Table 10. Crrep Compliance Valuts for Asphalt Concrete Miltures.

Creep compliance (j.JJ1I1/N) for mixture and temperature

N1 at N13.t N28 at

Time -20 DC _10 °C O· C ·20 °C _10 °C O·C -20 DC -10 DC O· c

S

1 17 23 38 38 90 59 29 61 81 2 18 24 43 41 105 83 30 58 94

5 19 27 46 47 127 117 30 63 104 10 20 30 54 52 151 141 30 61 120 20 20 32 64 57 175 167 31 67 134 50 22 35 74 65 225 231 33 85 170

100 24 36 87 75 276 299 34· 87 203 200 25 35 109 84 344 345 35 100 249

500 27 39 138 101 476 505 36 123 348 1000 29 47 178 117 609 701 38 140 464

I.

To illustrate the resuhs of the~ analyses, two figures have been prepared. In

figure 7, the criticaltcmper3ture al which the thermal stress reaches the tensile strength of

the mixtures is shown for each nuxture and each method of determining the coefficient of

thermal contraction The differences are small for mixture NI, and somewhat larger for

nllXlure N I) The calculated value of a for mixture N28, however, produces a critfcal

temperature about 6 °C higher than the critical temperatures found when the value for the

coefficiem of thermal comraclJon is measured using either experimemallechnique. Similar

results can be setn in figure 8. which shows the calculated thermal stress at - 10 °C for the

IlIIee mixtures, again uSing the various values for a. The differences for mixtures N I and

N I J appear mlall, whereas the thermal stress found using the calculated value of a is

almost twice that found uSing expenmentally determined values for the coefficient of

thermal contraction When thermal fatigue is considered, even the small differences for

mixtures N I and N 13 could lead to significantly different predictions in thermal cracking,

because of the exponential relationship betw~n rale of crack propagation and stress

magnitude (3)

Mixture Code

N1 N13 N28 u 0 • ,; -, ·10 ~ e • 0- ·20 E [] Calculated ~ ;;; ·30 • Strain Gages .!! ~

ILVOf, ·c -40 u

Figure 7. Critical Thennal Cracking Temperature Found Using a-Values Dtltrmined with Various Techniques.

4.00

• .. CCalcutaled :I; 3.00 .Strain Gages ,; I LVOfs • • - 2.00 ~

'" ;; E • 1.00

f' 0.00

N1 N13 N28

Mixture Code

Figure 8. Estimated Thermal Stress at Pavement Surfate at - to °C, Cakulated Using a.-Values Ddtrmined with VlriOUS Techniques.

10

II

CONCLUSIONS AND RECOMMENDATIONS

The following conclusions and recommendations are made based on the work summarized

in this paper.

Accurate values of coefficient of thermal coolfaction of asphalt concrete can be

obtained using the hardware in the Superpave IDT creep test.

Even though the IDT hardware has slightly higher variability as compared to strain

gages in measuring coefficient of thermal cootraction values, the results are more

reliable than using approximate volumetric relationships used in the Superpave. Since

the IDT hardware is currellIly being used for low-temperature characterization of

asphal! concrete, this hardware can also be used for obtaining coefficient ofthermaJ

contraction values of asphalt concrete.

Measurements of the coefficient ofthermaJ contraction coefficient should be made

when analyzing the potential thennal cracking of uphall concrete mixtures, as tile

Superpave equation for measuring the coefficient of thermal contraction is not

accurate

The coefficiem of thermal contraction of the L VDTs should be measured using a

material of negligible coefficient of thennal contraction value and then calibrated using

a reference material

At leasl three specimens should be tested or three independent replicate measurements

should be made

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I Stoffels. S M and Kwanda, D. F .• "Determination of the Coeffi cient of Thermal

Contraction of Asphalt Concrete Using Strain Gage Technique, " Proceedmgs of lhe

ASSOClatlon of Asphalr Paving Techn%glS/s, VoL 65, 1996, pp 73-93

2. Jones, G. M , Daner, M I , and Littlefield, G, "Thermal Expansion-Comraction of

Asphaltic Concrete," Proceedings of the AS$ociolion o[ Asphalt p{1\J/lIg

Teclmoiogisls, Vol. 36, 1968, pp 56-77

II

3. Lytton, R. L .• Uzan, J , Fernando, E. G, Roque.. R. , Hiltunen, D I and StoWels. S M,

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21

12 Seddik, H M K, and Haas, R , "Comparison of Superpave and other Models for

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13 Suutar, W G. and Roque, R., "Development and Evaluation of the Strategic

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