Investigation of shear stiffness and rutting inasphalt concrete mixes

Wael Bekheet, A.O. Abd El Halim, Said M. Easa, and Joseph Ponniah

Abstract: Field and laboratory testing programs were set up to evaluate the in-situ shear properties of asphalt concretemixes using the newly developed in-situ shear stiffness testing (InSiSST™) facility versus the laboratory evaluation us-ing the resilient modulus and torsion testing. The LTPP SPS-9A 870900 test site, which has six similar pavement sec-tions with different AC surface mix properties, was tested in the field using the InSiSST™ and core samples wereextracted from the site and tested in the laboratory. The results of the testing program were correlated with the ruttingof the test sections over a 4-year period. In this paper, the InSiSST™ facility is briefly introduced and the interpreta-tion of the data collected is presented. The experimental program and analysis procedures are then outlined. The analy-sis of variance was used to test the significance of the results, and a bivariate analysis was performed for correlatingrutting (as a criterion variable) and the different laboratory and field measured material properties (as predictor vari-ables). Finally, a regression analysis between the in-situ shear stiffness and pavement rutting is presented. The resultsof the study showed that the in-situ shear stiffness had the highest correlation coefficient with rutting rate, and thismight be a suitable measure to characterize the asphalt mixes and evaluate the rutting potential of asphalt pavements.This important result should be useful to the pavement engineers interested in the evaluation of rutting using a simplefield measure.

Key words: in-situ testing, laboratory testing, shear stiffness, shear properties, asphalt concrete, pavements, rutting,long-term performance.

Résumé : Des programmes d’essais sur le terrain et en laboratoire ont été élaborés pour évaluer les propriétés au ci-saillement in-situ des mélanges de béton bitumineux en utilisant l’équipement in-situ shear stiffness testing (InSiSST™)nouvellement développé par rapport à l’examen en laboratoire utilisant le module d’élasticité et l’essai en torsion. Lesite d’essai LTPP SPS-9A 870900, qui présente six sections de chaussée similaires avec différentes propriétés de la sur-face de béton bitumineux, a été mis à l’épreuve en utilisant l’InSiSST™; des carottes de sondage ont été extraites dusite puis testées en laboratoire. Les résultats du programme d’essai ont été corrélés à la formation d’ornières dans lessections à l’essai durant une période de quatre ans. Cet article présente l’InSiSST™ ainsi que l’interprétation des don-nées colligées. Le programme expérimental et les procédures d’analyse sont ensuite soulignées. L’analyse de la va-riance a été utilisée pour tester l’importance des résultats et une analyse bidimensionnelle a été effectuée pour lacorrélation de la formation d’ornières (en tant que variable critère) et les différentes propriétés des matériaux mesuréesen laboratoire et sur le terrain (en tant que variables explicatives). Finalement, une analyse de régression entre la rigi-dité au cisaillement in-situ et la formation d’ornières dans la chaussée est présentée. Les résultats de l’étude montrentque la rigidité au cisaillement in-situ possède le coefficient de corrélation le plus élevé avec le taux de formationd’ornières et qu’elle pourrait être une mesure appropriée pour caractériser les mélanges bitumineux et évaluer le poten-tiel de formation d’ornières des revêtements bitumineux. Ce résultat important devrait être utile aux ingénieurs des re-vêtements intéressés par l’évaluation de la formation d’ornières en utilisant une simple mesure sur le terrain.

Mots clés : essais in-situ, essai en laboratoire, rigidité au cisaillement, propriétés de cisaillement, béton bitumineux,chaussées, formation d’ornières, rendement à long terme.

[Traduit par la Rédaction] Bekheet et al. 262

Can. J. Civ. Eng. 31: 253–262 (2004) doi: 10.1139/L03-093 © 2004 NRC Canada

253

Received 30 May 2003. Revision accepted 24 October 2003. Published on the NRC Research Press Web site at http://cjce.nrc.ca on26 March 2004.

W. Bekheet,1,2 and A.O. Abd El Halim. Department of Civil and Environmental Engineering, Carleton University, Ottawa,ON K1S 5B6, Canada.S.M. Easa. Department of Civil Engineering, Ryerson University, Toronto, ON M5B 2K3, Canada.J. Ponniah. Ministry of Transportation, Toronto, ON M3M 1J8, Canada.

Written discussion of this article is welcomed and will be received by the Editor until 31 August 2004.

1Corresponding author (e-mail: wbekheet@stantec.com).2Present address: Stantec Consulting, 49 Frederick St., Kitchener, ON N2H 6M7, Canada.

Introduction

Permanent deformation of asphalt concrete (AC) surfaces,commonly known as rutting, is one of the widely observedsurface distresses in flexible pavements. Several studies haveshown that the shear properties of the AC mix are funda-mental in resisting rutting. Furthermore, the Strategic High-way Research Program (SHRP) has acknowledged theimportance of shear properties of both the binder and the ACmix and has incorporated them in the Superpave mix designmethods developed to improve long-term performance of as-phalt mixes in the field (Célard 1977; US-SHRP 1994).

Laboratory investigation showed that the shear stiffnesscorrelates best with rutting (Zahw 1995; Goodman et al.2002). Albeit laboratory investigation provide more controlover testing conditions, they might not represent actual fieldconditions, as a result of the difference in the boundary con-ditions and the inherent difference between the fabricatedlaboratory samples and the compacted field AC mat. Subse-quently, researchers at Carleton University, in cooperationwith the Ministry of Transportation Ontario (MTO) and theTransportation Research Board (TRB) innovations deservingexploratory analysis (IDEA) program, developed a testingfacility to measure the shear properties of asphalt pavementlayers in the field without the need for destructive coring. Itwas termed in-situ shear stiffness test (InSiSST™). In usingthis testing facility, the in-situ shear properties of AC mixesare evaluated through the application of a torsional momentto a circular area on the surface of the AC pavement, forcingit to rotate about an axis normal to the surface. The relation-ship between the angular displacement and the torsional mo-ment is then used to evaluate the shear properties of thesurface AC mixture.

An experimental program was set up with the objective ofcomparing the in-situ measured shear properties of the as-phalt pavements to the laboratory evaluated properties andevaluating the possible correlation between the in-situ shearproperties and rutting of the pavement sections. Field testingwas completed on test sections at the specific pavementstudies (SPS-9A) long-term pavement performance (LTPP)test site 870900 near Petawawa, Ontario. The SPS-9A studyis a specific study in the LTPP program for the validation ofthe SHRP asphalt specifications and mix design (Super-pave). The SPS-9A 870900 test site has six adjacent test sec-tions with similar pavement structures. However, the surfacelayer is designed using different mix design procedures.Laboratory testing was completed on core samples extractedfrom those sections.

The field and laboratory investigations included the use ofthe InSiSST™ facility to measure the in-situ shear propertiesof the AC mixes and the evaluation of the laboratory resil-ient modulus and shear properties of the mixes. In this pa-per, a brief description of the in-situ shear stiffness testingfacility is presented, followed by a detailed description ofthe experimental program. The analysis results and discus-sion are then presented, along with the study conclusions.

In-situ shear stiffness testing facility

The in-situ shear stiffness testing (InSiSST™) facility is atrailer-mounted testing equipment developed at Carleton

University to evaluate the in-situ shear properties of ACmixes. In testing the AC surface, the testing facility appliesa forced angular displacement to a circular area on the pave-ment surface through forcing a steel plate bonded to thepavement to rotate about an axis normal to the surface. Fig-ure 1 shows a photo of the InSiSST™, while Fig. 2 shows aschematic for the load application during in-situ testing.

The InSiSST™ is designed to provide loading at a con-stant strain and is equipped with a data acquisition system torecord the torque and the motor speed. The torque is mea-sured directly using a torque cell, while the angular displace-ment is calculated using the motor speed, assuming aconstant strain loading. Figure 3 shows a typical relationshipbetween the applied torque and the corresponding angulardisplacement resulting from in-situ testing. The shear prop-erties of the AC surface mixture are then evaluated usingthis relationship. More information about the developmentand background of this facility can be found elsewhere (AbdEl Halim 2001a, 2001b; Goodman et al. 2002; Bekheet et al.2001; Abd El Nabi 1995).

Mathematical backgroundThe problem of applying a torsional moment on the sur-

face of a half-space is known in the literature as Reissner–Sagoci problem. Reissner and Sagoci (1944) and Sneddon(1946) first addressed this problem in 1940s. They showedthat for an elastic, homogeneous, and isotropic material andby using the cylindrical coordinates (r, θ, z), the only non-vanishing stresses are the shear stresses τzθ and τrθ. Further-more, they proved that these stresses are functions of thecircumferencial displacement, ν, such that

[1] τ νθz G

z= ∂

∂and τ ν ν

θr Gr r

= ∂∂

−

where G is the shear modulus of the material. Figure 4shows the cylindrical coordinate system and the non-vanishing shear stresses.

Solving these equations, a general solution for the cir-cumferential displacement can be developed, and conse-quently an expression for the shear stresses τzθ and τrθ can bederived. The relationship between the applied torque, T, andthe resulting angular displacement is then derived by inte-grating τzθ over the loaded area, resulting in

[2] GTa

= 316 3Φ

where a is the radius of the loading plate and Φ is the angu-lar displacement in radians.

Test results interpretationThe torque and angular displacement relationship shown

in Fig. 3 are used to calculate a number of material proper-ties to characterize the AC mixes. These properties includethe initial shear stiffness, shear strain, and average shearstrength. The following subsections outline how each mate-rial property is calculated from the in-situ testing facility re-sults.

© 2004 NRC Canada

254 Can. J. Civ. Eng. Vol. 31, 2004

Initial shear stiffnessAccording to the mathematical model by Reissner and

Sagoci (1944), the relationship among T, Φ, and G for a lin-ear elastic material can be expressed using eq. [2]. Thisequation is used to calculate the shear modulus of the pave-ment material, or as better known in the pavement literature,the shear stiffness to imply that this value is not constant andis dependent upon test conditions such as the pavement tem-perature. The initial elastic shear stiffness is calculated usingthe relationship between the torque and the angular displace-ment at the early loading stages, after correcting the initialsection of the curve at the inflection point, as shown in

Fig. 3. This correction is carried out by shifting the verticalaxis to point O′, where the common tangent at the inflectionpoint intersects the X-axis, and adjusting all the angular dis-placement accordingly. This correction is performed to ac-count for initial irregularities during in-situ testing.

Maximum strainIn general, the failure of a sample could be defined in

terms of the maximum strain, Φmax, as a failure criterion.The maximum strain at failure is defined as the accumulatedangle of deformation from the start of the test up to failure.Consequently, the angular displacement at failure in radianscould be used as an index to evaluate the properties of theAC mix. The greater the angle corresponding to the maxi-mum torque, the higher the ductility of the mix. A ductilematerial would be more susceptible to rutting.

Average maximum shear stressAn average value of the maximum shear stress τ could be

calculated as the product of the shear stiffness and the maxi-mum strain, as shown in eq. [3]

[3] τ = G Φmax

The maximum shear stress value represents a uniformshear stress distributed over the total area of failure of thepavement sample, assuming the linear relationship betweenthe torsion and angular displacement is valid until failure.This assumption might not be valid, as the nonlinear plasticproperties of the AC mix are more prevalent near failure.However, the relationship represented by eq. [3] would be

© 2004 NRC Canada

Bekheet et al. 255

Fig. 1. In-situ shear stiffness testing (InSiSST™) facility.

Fig. 2. A schematic for the load application using theInSiSST™.

used to evaluate an average value of stress, representingboth the shear stiffness and the maximum strain sustained bythe AC mix.

Experimental program

The objective of the experimental program is to character-ize the AC mixes based on in-service pavement sections,where the construction and performance are known, usingboth in-situ and laboratory testing. Field testing was com-pleted on an SPS-9A LTPP test site 870900 near Petawawa,Ontario, and laboratory testing was performed on samplesrecovered from the site, as described in the following sub-sections.

Field testing programIn-situ testing was completed on the LTPP SPS-9A

870900 test site on highway 17 near Petawawa, Ontario insummer 2000. The LTPP SPS-9A study was designed withthe objective of validating the Superpave mix design. AnSPS-9A test site includes a number of test sections withidentical pavement structures but with different AC surfacemix properties. This configuration makes an SPS-9A site a

suitable candidate for testing using the InSiSST™ to evalu-ate the shear properties of the AC surface mixtures, as allother variables, with the exception of the surface mix prop-erties, are constant.

The 870900 site was constructed in April 1997 and iscomposed of three core sections, sections 870901 through870903, and three supplemental sections, sections 870960through 870962, for a total of six adjacent sections. Table 1shows the surface mix properties for the sections at the870900 site, while Table 2 shows the as-built properties ofthese mixes. The as-built data and the QC/QA data were ob-tained from the SPS-9A 870900 site construction report(ITX Stanley 1998). It is worth noting that these sections arepart of a controlled experiment and are constructed usinghigh quality materials. Consequently, given that the sectionsare relatively new, it is expected that the variation of the testresults might not be high.

Seven tests using the InSiSST™ were performed at eachsection, where five of the seven samples were located alongthe lane centerline, while the extra two samples were locatedeither in the wheel paths or on the shoulder. The results pre-sented in this paper are for the samples in the lane centerlineonly. Testing was carried out using 100 mm diameter steelplates.

The strain rate used during testing was 0.0233 rad/s. Theair temperature during the testing period ranged between 27and 32 °C, and the pavement temperature ranged between 33and 39 °C. Table 3 shows the average, standard deviationand coefficient of variation for the five samples completedon each of the tested sections. As can be noted from the ta-ble, the results were generally consistent with a coefficientof variation ranging between 6% and 20%, which is gener-ally acceptable in the pavement literature.

Laboratory testing programSamples were cored from each of the field sections for

testing in the laboratory. Laboratory testing included resil-

© 2004 NRC Canada

256 Can. J. Civ. Eng. Vol. 31, 2004

Fig. 3. Typical relationship between the torque and the angular displacement.

Fig. 4. Coordinate system and nonvanishing stresses.

ient modulus testing and torsion testing on AC core samplesrecovered from the field. The objectives of the laboratorytesting were: (a) to evaluate a fundamental material prop-erty, such as the resilient modulus, of the different mixes;(b) to determine laboratory shear properties of the mixes;and (c) to investigate the correlation between the laboratoryevaluated resilient modulus and shear properties of the ACmixes, and the field results and rutting of these mixes. Thecores were taken from the same locations within the sec-tions, where the in-situ testing was completed, along thelane centerline. Cores were 100 mm in diameter, with a totalthickness equal to the thickness of the surface layer.

The nondestructive resilient modulus testing was per-formed on three samples from each set, while direct torsiontesting was done on all five samples to determine the shearstrength and shear modulus of the mix. The torsion test isnot a standard ASTM test for AC pavements. However,Zahw (1995) used the torsion testing to test solid asphaltcylinders to determine the shear properties. Later, Goodmanet al. (2002) used these results and showed that there was ahigh correlation between the rutting resistance of the ACmix and its shear stiffness.

For a cylinder of height L and radius r, the maximumshear stress or the shear strength and the shear modulus canbe determined using the following equations (Higdon et al.1990):

[4] τmax = TrJ

[5] GT LJ

=Φ

where J is the polar moment of inertia. However, as theseequations assume a linear triangular distribution of the shearstress over the area of the circular cross sections of the cyl-inder with a zero value at the center and a maximum value atthe edge, an average shear stress can be calculated using

[6] τ τ= max

2

Torsion testing was carried out using the same gearbox-motor controller combination used in the field. Testing wascompleted at room temperature (20 °C), using a custom-

© 2004 NRC Canada

Bekheet et al. 257

Testsection

Surfacethickness (mm) Mix design Binder specifications

870901 72 HL3 Marshall design 85/100 penetration graded AC870902 59 Superpave 12.5-mm mix PG 58-40 (polymer modified)870903 67 Superpave 12.5-mm mix PG 58-34870960 67 Superpave 12.5-mm mix PG 58-28 (polymer modified)870961 64 Superpave 12.5-mm mix PG 58-40870962 69 HL3 Marshall design PG 58-40 (polymer modified)

Table 1. Petawawa SPS-9A LTPP test sections specification.

Testsection

BRD*(kg/m3)

MRD†

(kg/m3)Compaction(%)

Air voids(%)

Bindercontent (%)

Passing sieve4.75 mm (%)

870901 2348 2447 96.6 4.1 5.6 50.2870902 2378 2463 94.5 3.4 5.1 51.9870903 2368 2474 94.2 4.3 5.0 51.1870960 2391 2476 94.3 3.5 4.9 48.6870961 2384 2468 93.5 3.4 4.9 48.1870962 2347 2432 94.3 3.5 5.5 49.1

*Bulk relative density, based on construction QC/QA core data.†Maximum relative density, based on construction QC/QA core data.

Table 2. As-built properties of AC surface mixture for the 870900 sections.

Shear stiffness (MPa) Maximum strain (rad) Average shear strength (MPa)

Testsection

Pavementtemperature (°C) Mean SD CoV* Mean SD CoV* Mean SD CoV*

870901 33 16.7 1.5 8.9 0.078 0.005 6.5 1.34 0.17 12.7870902 35 13.9 2.0 14.2 0.078 0.009 10.9 0.99 0.16 16.2870903 36 15.9 2.3 14.4 0.074 0.003 3.9 1.15 0.23 20.0870960 39 14.0 1.5 10.9 0.064 0.009 13.6 0.89 0.17 19.1870961 37 12.1 0.7 6.0 0.055 0.009 17.1 0.67 0.14 20.9870962 38 14.8 1.0 6.7 0.063 0.011 18.1 0.92 0.12 13.0

Note: SD, standard deviation; CoV, coefficient of variation.*CoV = 100 (standard deviation)/mean.

Table 3. Summary of field testing results at the LTPP test sections.

made assembly. The gearbox, motor controller and the dataacquisition system from the InSiSST™ were assembled on afixed steel setup in the laboratory. Using the same gearboxand the motor control used in the in-situ testing for the labo-ratory testing ensured that the strain rate, which was 0.0233rad/s, and data acquisition for both the in-situ testing andlaboratory testing are similar.

Table 4 shows the results of the resilient modulus testingand the torsion testing completed on the AC samples. Itshould be noted that the temperature during laboratory test-ing was not equal to the temperature during field testing. Asa result, it will not be possible to directly compare the actualvalues of the measured parameters from the field and thelaboratory. Subsequently, these values will be evaluatedthrough a correlation analysis, as shown in the followingsubsections.

Rutting at the 870900 long-term pavement performancetest site

Rutting for the LTPP test sites is evaluated using thecross-sectional profile. The cross-sectional profile data arecollected for the 150-m section at 11 locations at a 30-mspacing. The SPS-9A test site at Petawawa was constructedin 1997, and since construction date rutting was measuredthree times:1997 (immediately after construction), 2000, and2001. The rutting data were available from the National In-formation Management System (NIMS), LTPP database, andMTO records. Figure 5 shows the rut depth for the differentpavement sections at the 870900 LTPP test site. It should benoted that the pavement sections are fairly new and in goodconditions. Consequently, the measured rut depths were gen-erally small.

On examining the rutting data, it was noticed that all sec-tions had some rutting in the 1997 survey, just after con-struction. This rutting cannot be attributed to traffic loadingbut rather to construction quality. Consequently, using theabsolute rutting values, 4 years after construction, as a per-formance indicator might be misleading. Furthermore, insome cases, rutting for a particular section at a given yearwas less than the previous year that was unexpected. Subse-quently, three rutting indices were suggested for use in theanalysis. The first index is the rutting rate in millimetres peryear. The rutting rate is the average annual rutting over timeassuming a linear relationship between rutting and time. It iscalculated as the slope of the best-fit straight line for theavailable data from each section. Thompson and Norman

(1993) used the rutting per load repetition rate to evaluatepavement performance. However, as traffic for all the test-ing sections is identical, it should be acceptable to use therutting rate as a function of time rather than traffic.

The second rutting index is the absolute accumulated rut-ting over the 4-year period of the life of the pavement sec-tions. The third rutting index is again the accumulatedrutting over the 4-year period of the life of the pavement,however, assuming the rutting would not decrease over time.Consequently, the rutting reading for 2001 for section870902 was discarded, as the rut depth for 2001 was lessthan that for 2000. The rutting values, rutting rate, and theaccumulated rutting for the different test sections are shownin Table 5.

Statistical analysis

The analysis of variance (ANOVA) was performed on thedata collected from both field and laboratory testing to testthe significance of the variation in the data. The bivariateanalysis technique is then used to identify the material prop-erty that correlates most with one of the rutting indices. Forthe material property selected through the bivariate analysis,a multiple t-test was carried out between each pair of sec-tions to identify the AC mix with significantly differentproperties. The selected material property was then used in aregression analysis with the selected rutting index to developa preliminary relationship between rutting of the AC mixand its shear properties.

© 2004 NRC Canada

258 Can. J. Civ. Eng. Vol. 31, 2004

Fig. 5. Rutting of the 870900 SPS-9A test sections.

Test section Resilient modulus (MPa) Shear stiffness (MPa) Maximum strain (Rad) Average shear strength (MPa)

Mean SD CoV* Mean SD CoV* Mean SD CoV* Mean SD CoV*

870901 1333 360 27.0 243 37 15.4 0.038 0.009 24.2 2.61 0.55 21.1870902 1444 308 21.3 165 41 25.1 0.028 0.005 19.2 1.38 0.94 68.1870903 2470 390 15.8 250 32 12.8 0.032 0.004 10.8 2.38 0.55 23.1870960 1288 452 35.1 271 44 16.2 0.030 0.004 12.3 1.84 0.73 39.7870961 1144 37 3.2 172 61 35.3 0.029 0.006 19.0 1.71 0.71 41.5870962 1249 582 46.6 147 32 21.7 0.033 0.011 34.5 1.26 0.52 41.3

Note: SD, standard deviation; CoV, coefficient of variation.*CoV = 100 (standard deviation)/mean.

Table 4. Summary of laboratory testing results for the LTPP test sections.

Analysis of varianceThe analysis of variance is performed to test the signifi-

cance of the difference in means of the collected data fromboth field and laboratory testing. The null hypothesis wasthat the difference in the means is not significant, such that aparticular property or calculated index is not able to differ-entiate among the different mixes. At a specific confidencelevel, 1-α, the null hypothesis is rejected if the calculated F-static is greater than the F-critical. F-critical is a statisticallimit calculated for a specific α, statistical degrees of free-dom, and the total error in the tests.

A confidence level of 95% was selected to test the nullhypothesis for the field and laboratory results. The results ofthe ANOVA analysis are shown in Table 6. As can be notedfrom the table, the null hypothesis was rejected for all thetest results, with the exception of the maximum strain for the

laboratory test results. This indicates that all the other mate-rial properties or indices are able to identify and differentiateamong different AC mixes.

Bivariate analysisThe bivariate analysis was performed to explore the corre-

lation between the rutting indices (as criterion variables) andthe different indices calculated from the field and the labora-tory (as predictor variables). The bivariate correlation coeffi-cients were computed for each pair of variables, includingthe correlation between the criterion variables and each pre-dictor variable as well as the inter-correlation between eachpair of the predictor variables. The correlation coefficient, R,which is the square root of coefficient of determination, R2,between any two particular variables, is a measure of the de-gree of linear association between those two variables,

© 2004 NRC Canada

Bekheet et al. 259

Rut depth (mm)

Test section Sept. 1997 Oct. 2000 Oct. 2001Rutting rate(mm/year)

Accumulatedrutting (mm)

Accumulatedrutting (mm)*

870901 1.4 1.4 1.4 0.01 0.07 0.07870902 0.9 1.6 1.3 0.14 0.47 0.69870903 0.7 0.9 1.2 0.12 0.52 0.52870960 1.4 1.8 1.9 0.12 0.50 0.50870961 1.4 2.3 2.6 0.30 1.24 1.24870962 0.7 0.6 0.9 0.05 0.28 0.28

*Rutting was assumed not to decrease, 2001 reading for 870902 was discarded.

Table 5. Rutting at the 870900 SPS-9A LTPP test sections.

Source ofvariation SS df MS F-static P-value F-critical

Nullhypothesis

In-situ testing resultsShear stiffness Section 65.0 5 12.99 6.285 0.0007 2.621 Rejected

Error 49.6 24 2.07Total 114.6 29

Maximum strain Section 0.0025 5 4.9×10–4 7.762 0.0002 2.621 RejectedError 0.0015 24 6.4×10–5

Total 0.0040 29Average strength Section 1.342 5 0.268 10.110 2.7×10–5 2.621 Rejected

Error 0.637 24 0.027Total 1.979 29

Laboratory testing resultsShear Section 69 741 5 13 948 7.751 0.0002 2.621 Rejectedstiffness Error 43 186 24 1 799

Total 112 927 29Maximum strain Section 0.0003 5 7.0×10–5 1.415 0.255 2.621 Accepted

Error 0.0012 24 4.9×10–5

Total 0.0015 29Average strength Section 7.19 5 1.44 12.353 5.3×10–6 2.621 Rejected

Error 2.80 24 0.12Total 9.99 29

Resilient modulus Section 3 615 126 5 723 025 4.713 0.013 3.106 RejectedError 1 840 919 12 153 410Total 5 456 045 17

Note: The null hypothesis is rejected if F-static > F-critical. SS, sum of squares; df, degrees of freedom; MS, mean square.

Table 6. The analysis of variation (ANOVA) results for field and laboratory testing results.

where R ranges from 0 to 1 (or –1) with a value of one indi-cating perfect correlation. A negative correlation coefficientwould indicate inverse correlation, and the strength of thiscorrelation depends on the absolute value of the coefficient.

Table 7 shows the correlation matrix between the differentfield and laboratory results for the six sections at the 870900SPS-9A LTPP test site and rutting at these sections. Asnoted, the linear inter-correlation between the rutting indicesis rather high, 99%, indicating that using any of them shouldyield the same results. Obviously, this is due to the ratherwell-behaved performance of the sections, with the excep-tion of section 870902, and the relatively small values of therutting. Subsequently, the rutting rate was selected as a crite-rion variable for further correlation with the pavement per-formance, as it is not affected by the rutting at construction.

The inter-correlation among the field-testing results showsthat, in general, the strain is least correlating with other cal-culated values. The correlation coefficients between theshear stiffness and the average maximum shear stress weregenerally high, indicating that either of them should be suffi-cient to represent the properties of the pavement. The inter-correlation among the laboratory testing results again showsthat the maximum strain least correlates with the other cal-culated values and that the correlation coefficients betweenthe shear stiffness and the average maximum shear stress aregenerally high. The correlation between the resilient modu-lus and the other laboratory shear variables ranged between0.35 and 0.49, indicating a rather weak correlation.

Rutting had higher correlation coefficients with the fieldtesting results than the laboratory testing results and theshear stiffness had highest correlation with all rutting param-eters. The correlation between the in-situ shear stiffness andrutting ranged between 0.85 and 0.88, while for the labora-tory shear stiffness results, the correlation coefficientsranged between 0.24 and 0.35. On the other hand, the resil-ient modulus showed very weak correlation with the ruttingof the sections, with a correlation coefficient ranging be-tween 0.11 and 0.14.

Based on the bivariate analysis, the in-situ shear stiffnesswas selected from the predictor variables to characterize theAC mixes because the in-situ shear stiffness had the highestcorrelation coefficient with the rutting rate and represents afundamental material property of the mixture.

Multiple t-test analysisThe results of the ANOVA showed that at least one of the

sections was significantly different, which indicates that theInSiSST™ facility has successfully identified the variationamong the sections. However, to identify the sections havingsignificantly different shear stiffness, a t-test was performedfor each pair of sections to statistically test the hypothesisthat the results are not significantly different. Table 8 showsthe multiple t-test analysis results, while Table 9 shows theacceptance of the hypothesis results based on these t-tests.The bold values in Table 9 show the sections that are notsignificantly different.

As can be noted from the results of section 870901, whichis designed using the Marshall mix design approach and thepenetration graded binder, the shear stiffness was signifi-cantly higher than for the other sections with the exceptionof 870903. Section 870961 had significantly lower shear

© 2004 NRC Canada

260 Can. J. Civ. Eng. Vol. 31, 2004

Rut

ting

Fie

ldte

stin

gre

sult

sL

abor

ator

yte

stin

gre

sult

s

Rut

ting

rate

Acc

umul

ated

rutt

ing

Acc

umul

ated

rutt

ing*

She

arst

iffn

ess

Max

imum

stra

inS

hear

stre

ngth

She

arst

iffn

ess

Max

imum

stra

inS

hear

stre

ngth

Res

ilie

ntm

odul

us

Rut

ting

Rut

ting

rate

1.00

0.99

0.99

–0.8

7–0

.59

–0.8

0–0

.25

–0.6

8–0

.28

–0.1

4A

ccum

ulat

edru

ttin

g1.

000.

98–0

.85

–0.6

6–0

.81

–0.2

4–0

.63

–0.2

6–0

.11

Acc

umul

ated

rutt

ing*

1.00

–0.8

8–0

.54

–0.8

0–0

.33

–0.7

2–0

.35

–0.1

2

Fie

ldte

stin

gre

sult

sS

hear

stif

fnes

s1.

000.

690.

950.

460.

810.

660.

49M

axim

umst

rain

1.00

0.83

0.25

0.35

0.40

0.44

She

arst

reng

th1.

000.

470.

780.

710.

44

Lab

orat

ory

test

ing

resu

lts

She

arst

iffn

ess

1.00

0.30

0.77

0.40

Max

imum

stra

in1.

000.

690.

09S

hear

stre

ngth

1.00

0.47

Res

ilie

ntm

odul

us1.

00

*Rut

ting

was

assu

med

not

tode

crea

se,

2001

read

ing

for

8709

02w

asdi

scar

ded.

Tab

le7.

Biv

aria

teco

rrel

atio

nm

atri

x.

stiffness than the other sections with the exception of section870902.

Regression analysisIn this study, six test sections at the 870900 LTPP site

were tested. A regression analysis to investigate the relation-ship between the in-situ shear stiffness and the rutting ratewas performed based on the results from these sections. Fig-ure 6 shows a plot of the data points for the shear stiffnessand the corresponding rutting rate for the six tested sections.It should be noted that each data point represents an averageof five samples and these data were shown in Table 3. Thesedata used in this regression analysis are limited, such that itwill not be possible to conclude a mathematical relationshipamong the variables. However, the data plot shows a possi-ble relationship between the rutting rate and the shear stiff-ness. Using logarithmic trend line for fitting, the followingrelationship between rutting rate (RR) and shear stiffness (G)was obtained:

[7] RR = –0.7803ln(G) + 2.2091

The coefficient of determination for this relationship was0.79. A linear trend line also resulted in a coefficient of de-termination of 0.76. These results show a high potential for

the in-situ shear testing to evaluate the rutting potential ofAC mixes.

Discussion

The results of the in-situ and laboratory investigation ofthe relationship between rutting in asphalt pavements andthe shear properties of the AC surface mix presented in thispaper showed that, generally, the in-situ testing resulted inmore consistent results than the laboratory testing. The coef-ficients of variation for the laboratory results were generallyhigher than that for the field results. Furthermore, the in-situtesting result had much higher correlation with rutting of thedifferent AC mixes. As an example, for the shear stiffnessmeasured in the field, the coefficient of variation for the sixsections varied between 6% and 15%, while for the labora-tory results the coefficient of variation in measuring theshear stiffness varied between 12% and 35%. In some cases,the coefficient of variation for the laboratory results reachedvalues up to 68%, as in the case of the laboratory averageshear stress for section 870902. This might be attributed tothe possible disturbance of the samples during coring andthe different boundary conditions between the field testedand laboratory tested samples.

It has also been noticed that there was a significant differ-ence in the values of the shear stiffness as calculated fromthe field testing and the laboratory testing. Two factorsmight have resulted in such a discrepancy. The first factor isthe temperature difference between the in-situ testing andlaboratory testing. While the temperature in the laboratorywas controlled at 20 °C, the temperature in the field wasmuch higher, and the tests were done on a hot sunny daywith air temperature reaching 32 °C and the pavement tem-perature reaching 39 °C.

The other factor that affected the results is the accuracy indetermining the actual angular displacement at failure duringtesting. As mentioned earlier, the angular displacement wascalculated assuming constant strain rate. However, furtherinvestigation has shown that depending on the condition ofthe AC mixture, the actual strain rate might not be constant

© 2004 NRC Canada

Bekheet et al. 261

870901 870903 870962 870960 870902 870961

870901 1 0.5102 0.0323 0.0176 0.0206 0.0001870903 1 0.2822 0.1236 0.1224 0.0039870962 1 0.3636 0.3478 0.0013870960 1 0.9249 0.0387870902 1 0.0667870961 1

Table 8. Multiple t-test results for the shear stiffness.

870901 870903 870962 870960 870902 870961

870901 1 Accept Reject Reject Reject Reject870903 1 Accept Accept Accept Reject870962 1 Accept Accept Reject870960 1 Accept Reject870902 1 Accept870961 1

Table 9. Hypothesis acceptance based on multiple t-test.

Fig. 6. Relationship between rutting rate and in-situ shear stiffness.

(Bekheet 2003). The actual angular displacement at failurewas, sometimes, significantly less than that calculated usingthe constant strain rate assumption. It was noted that usingthe constant strain loading assumption resulted in decreasedvalues of the shear stiffness and increased values of the an-gular displacement at failure. However, the actual strain ratedid not affect the ranking of the different AC mixture, asevaluated using the InSiSST™, because stiffer AC mixeshad higher shear stiffness values regardless of the strain ac-tual strain rate. Further modifications are still needed in theInSiSST™ facility to ensure more accurate results.

The analysis results show that rutting of the different sec-tions correlates more with the shear properties of the mixthan the resilient modulus. Furthermore, the results shown inTable 7 indicated that the in-situ testing results had highercorrelation coefficients with rutting than the laboratory test-ing. Rutting of the sections correlated well with the fieldmeasured shear stiffness, with R2 of 0.79.

Concluding remarks

The paper has presented an experimental program usingthe newly developed in-situ shear stiffness testing facility.The objective of the study was to use in-situ and laboratoryshear properties to characterize the AC mixes and to investi-gate possible correlation between rutting of the asphalt pave-ment and the in-situ shear stiffness of the AC mix. TheLTPP SPS-9A 870900 site, which has six adjacent test sec-tions, was tested in the field using the InSiSST™ and coresamples were extracted from the site and tested in the labo-ratory. The in-situ testing was completed using theInSiSST™, which was used to evaluate the shear propertiesof the AC surface mixture by applying a torsional moment toa circular area on the pavement surface through forcing asteel plate bonded to the pavement to rotate around an axisnormal to the surface. Rutting of the test sections over a 4-year period was evaluated using the monitored data availablefrom the NIMS.

Based on the results of the experimental program, the fol-lowing conclusions can be made:• The in-situ testing, in general, was more consistent than

laboratory testing, as shown through the lower coefficientsof variation for the sample sets.

• The in-situ testing results had higher correlation coeffi-cients with rutting compared with the laboratory results,indicating that the in-situ measurements better correlatewith rutting.

• The shear properties of the AC mixes had better correla-tion with rutting than the resilient modulus.

• The in-situ shear stiffness had the highest correlation co-efficient with rutting rate and might be a suitable measureto characterize the asphalt mixes and evaluate the ruttingpotential of asphalt pavements.The results presented in this paper suggest that a relation-

ship exist between the in-situ shear stiffness of the AC mixesand rutting of asphalt pavements. However, this relationshipwas developed based on limited amount of data and rela-

tively new pavement sections. Further monitoring of the testsections performance is required to lend more support tosuch a relationship.

Acknowledgements

The authors gratefully acknowledge the financial and in-kind support of the Ministry of Transportation Ontario(MTO), the Natural Sciences and Engineering ResearchCouncil of Canada (NSERC), and Carleton University tech-nical support staff.

References

Abd El Halim, A.O. 2001a. Design, development and validation ofan advanced in-situ shear stiffness test facility for asphalt con-crete pavements. National Cooperative Highway Research Pro-gram IDEA Report No. 55, Transportation Research Board,Washington D.C.

Abd El Halim, A.O. 2001b. Measurement of in-situ shear strengthof asphalt pavements. Report, Ontario Ministry of Transporta-tion, Toronto, Ont.

Abd El Nabi, R.M. 1995. Influence of highway geometry on dis-tress of asphalt concrete pavements. Ph.D. thesis, Zagazig Uni-versity, Egypt and Carleton University, Ottawa, Ont.

Bekheet, W. 2003. Investigation of in-situ shear properties of as-phalt concrete. Ph.D. thesis, Carleton University, Ottawa, Ont.

Bekheet, W., Hassan, Y., and Abd El Halim, A.O. 2001. Modellingin-situ shear strength testing of asphalt concrete pavements us-ing the finite element method. Canadian Journal of Civil Engi-neering, 28(3): 541–544.

Célard, B. 1977. Esso road design technology. Proceedings of the4th International Conference on the Structural Design of As-phalt Pavements, Ann Arbor, Mich., 22–26 August 1977. TheUniversity of Michigan, Ann Arbor, Mich. Vol. 2, pp. 76–77.

Goodman, S., Hassan, Y., and Abd El Halim, A.O. 2002. Shearproperties as viable measures for characterization of permanentdeformation of asphalt concrete mixtures. Transportation Re-search Record 1789, Transportation Research Board, NationalResearch Council, Washington, D.C. pp. 154–161.

Higdon, A., Ohlsen, E.H., Stiles, W.B., Weese, J.A., and Riley,W.F. 1990. Mechanics of materials (Fourth Edition). John Wiley& Sons Inc. New York, N.Y.

ITX Stanley Limited. 1998. Construction report on LTPP 870900,SPS-9A Project, Petawawa, Ont. Report No. FHWA-TS-98-87-02,Federal Highway Administration, LTPP Division, McLean, Va.

Reissner, E., and Sagoci, H. 1944. Forced torsional oscillation ofan elastic half space. Journal of Applied Physics, 15: 652–654.

Sneddon, N. 1946. Note on a boundary value problem by Reissnerand Sagoci. Journal of Applied Physics, 18: 130–132.

Thompson, M., and Norman, D. 1993. Rutting rate analyses of theAASHO road test flexible pavements. Transportation ResearchRecord 1384, Transportation Research Board, National ResearchCouncil, Washington, D.C. pp. 36–48.

US-SHRP. 1994. Permanent deformation response of asphalt-aggregate mixes. Report SHRP-A-415, United States StrategicHighway Research Program, National Research Council, Wash-ington, D.C.

Zahw, M.A. 1995. A. Development of testing framework for evalua-tion of rutting resistance of asphalt mixes. Ph.D. thesis, CarletonUniversity, Ottawa, Ont. and Al Azhar University, Cairo, Egypt.

© 2004 NRC Canada

262 Can. J. Civ. Eng. Vol. 31, 2004