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Implementation and verification of amechanistic permanent deformationmodel (shift model) to predict rutdepths of asphalt pavementYeong-Tae Choia & Y. Richard Kima

a Department of Civil, Construction, & Environmental Engineering,North Carolina State University, Raleigh, NC 27695-7908, USAPublished online: 19 Jun 2014.

To cite this article: Yeong-Tae Choi & Y. Richard Kim (2014) Implementation and verification of amechanistic permanent deformation model (shift model) to predict rut depths of asphalt pavement,Road Materials and Pavement Design, 15:sup1, 195-218, DOI: 10.1080/14680629.2014.927085

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Road Materials and Pavement Design, 2014Vol. 15, No. S1, 195–218, http://dx.doi.org/10.1080/14680629.2014.927085

Implementation and verification of a mechanistic permanent deformationmodel (shift model) to predict rut depths of asphalt pavement

Yeong-Tae Choi∗ and Y. Richard Kim

Department of Civil, Construction, & Environmental Engineering, North Carolina State University, Raleigh,NC 27695-7908, USA

(Received 2 August 2013; accepted 2 November 2013 )

The shift model is implemented in the layered viscoelastic asphalt pavement analysis forcritical distresses (LVECD) program to predict the rut depth of asphalt pavements. The rutdepth measurements taken at the National Center for Asphalt Technology (NCAT) test trackand the Federal Highway Administration Accelerated Facility (FHWA ALF) test sections areevaluated using the model. The model can successfully evaluate rut depth, which proves thecapability of the model implemented in the LVECD program. The slight over-prediction of theNCAT sections can be explained by ageing in the field that increases the pavement’s resistanceto rutting. The simulation results support the hypothesis that triaxial stress sweep tests withconfinement can represent the permanent deformation behaviour of asphalt concrete in thefield. In this regard, excessive shear flow may be the reason for the under-prediction of theFHWA ALF mixtures. For better predictions, a correction factor (i.e. a transfer function) issuggested, which is quantified via the ratio of shear stress to shear resistance. After applyingindividual transfer functions, the permanent deformation model in the LVECD can evaluatethe growth of the rut depth. Therefore, even though the shift model is a uniaxial model, themodel can predict the rut depth of asphalt concrete by employing the transfer function.

Keywords: permanent deformation model; rutting; shift model; shear flow; rut depthprediction

1. IntroductionPermanent deformation is one of the major distresses in asphalt pavements. Rutting, another namefor permanent deformation, causes serviceability problems such as water spray and hydroplan-ing. These problems are related to wet weather conditions and thus may be linked to seriousroad accidents. In this regard, rutting represents a significant performance factor and should becontrolled from pavement design to road maintenance. In order to control rutting, understandingits behaviour and mechanisms in the field is crucial.

It is generally known that densification and shear flow induce rutting. Densification refers toair void changes, i.e. volume contraction. Shear flow makes asphalt materials translate withouta change in volume, such as seen in the shear failure of soil under a foundation (Knappet &Craig, 2012). That is, the volume of asphalt concrete changes due to densification only. Severalresearchers (Coleri, Wu, Signore, & Harvey, 2012b; Gokhale, Choubane, Byron, & Tia, 2005;Harvey & Popescu, 2000) have tried to define the mechanisms that underlie rutting behaviourbased on the concepts of densification and shear flow. Shear flow creates humps on either side ofthe wheel path; thus, if densification does not occur, the volume under the wheel path should be

∗Corresponding author. Email: ychoi5@ncsu.edu

© 2014 Taylor & Francis

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equal to the volume of the hump. The volume difference between the hump and the wheel pathcan be assumed to be caused by densification.

Using this assumption, Harvey and Popescu (2000) and Gokhale et al. (2005) quantified theeffects of shear flow on rut depth. In their studies, they pointed out that the shear flow componentaccounts for 22% to 114% of the total rut depth at the end of accelerated pavement testing witha heavy vehicle simulator (HVS). The average contributions of the shear flow are 49% and 58%for the Harvey and Popescu study and Gokhale et al. study, respectively. Accordingly, theseresearchers concluded that shear flow plays a key role in rutting.

It is widely known to asphalt pavement engineers that permanent strain grows in three stages,the primary, secondary, and tertiary stages, and each stage has a corresponding mechanism. Inthe primary stage, permanent strain increases mainly due to densification. In the secondary stage,the strain increases constantly and is considered to be in the steady state. In the tertiary stage,shear flow starts and the strain increases dramatically and the sample reaches failure. That is, theprimary and secondary regions have negligible shear effects, and so the focus is on the tertiaryregion to represent the effects of shear flow. Triaxial lab testing would target the tertiary region,but such lab tests require a very long testing time, especially in the case of a confined triaxial test.

However, triaxial tests of soil indicate a shear type of failure. Based on this observation, thetriaxial test can represent shear-related behaviour to an extent, even though the triaxial test forasphalt material is limited to the secondary region. To address this issue, the triaxial stress sweep(TSS) test (Choi & Kim, 2013a) is suggested to characterise the shift model (Choi & Kim, 2013b),which is a permanent deformation model that accounts for the effects of temperature, load time,and deviatoric stress on permanent deformation. However, this assumption that laboratory triaxialtesting can represent shear-related effects on permanent strain has not yet been proved. Thispaper investigates this assumption and the capability of the shift model and the TSS protocolby comparing rut depth predictions obtained from the model with field-measured rut depths thatcontain different levels of shear flow contribution.

2. ObjectivesThis paper aims to suggest a relationship between laboratory triaxial test results and the fieldbehaviour of asphalt concrete in terms of permanent deformation. Moreover, this study seeksto verify this relationship. For this purpose, the viability of the shift model combined with theTSS test protocol is demonstrated via field rut depth measurements. Through this process, theunderstanding of the rutting behaviour of asphalt pavement in the field is improved, which isanother objective of this paper

3. Relationship between rutting behaviour in the lab and in the fieldThe mechanisms involved in rut depth development can be hypothesised using field observationsand via mechanical insights. Figure 1 describes the general configuration of rut depth developmentin asphalt pavement. Rut depth is defined as the distance between the lowest point in the wheel pathand the highest point of upheaval. The rut depth, sometimes referred to as total rut depth, is the sumof the downward rut depth measurement and the upheaving (upward) rut depth measurement. Thedownward rut depth includes the deformation of the asphalt layer, base layer, and subgrade layer,and is measured as the distance from the original pavement surface to the bottom of the wheelpath. Therefore, the base and subgrade layers may play a role in downward rut depth development.However, this study concentrates on the development of an asphalt concrete model; thus, the rutdepth of the base and subgrade layers is excluded, and hereafter, AC rut depth or rut depth refers

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Figure 1. Schematic diagram of mechanism of rut depth development.

to the downward rut depth of the asphalt layer only. Total rut depth is defined as the entire distancefrom the top of the hump to the bottom of the wheel path.

Permanent deformation is caused by the traffic load that is applied to the wheel path. The areaof the asphalt layer under the wheel path experiences compressive stress in the vertical direction;the compressive stress directly generates permanent deformation. Thus, this zone is referred toas the active zone, and either side of the active zone is referred to as the passive zone, as shownin Figure 1. The deformation of the passive zone originates from the deformation of the activezone; however, the passive zone also has an effect on the active zone.

When a vehicle load is applied to asphalt pavement, the active zone deforms vertically, and lat-eral deformation occurs due to Poisson’s effect. At the same time, horizontal stress, which behaveslike confining pressure against the active zone, also develops. In order to specify this phenomenon,two extreme cases can be assumed. The first case (Case I) is that the passive zone has sufficientresistance against lateral permanent deformation and thus confines the lateral deformation of theactive zone. The second case (Case II) is that the passive zone does not have any resistance againstlateral deformation For Case I, the applied stress can make the active zone deform only in thevertical direction due to the constraint of the passive zone. Instead of lateral deformation, hori-zontal stress develops. In this case, the volume change equals the vertical strain. Case II showsthe unconfined state; that is, the passive zone has no rutting resistance. An asphalt element inthe active zone deforms laterally as much as Poisson’s effect (νvpε

vpz ) allows. νvp is a viscoplas-

tic Poisson’s ratio that can be obtained through unconfined testing. It is obvious that the actualbehaviour of asphalt pavement in terms of permanent deformation falls somewhere between thatof Case I and Case II. In short, the applied load induces not only vertical permanent deformationbut also horizontal permanent deformation with confining pressure (horizontal stress).

Shear flow also plays an important role in rut depth evolution, as Harvey and Popescu (2000)and Gokhale et al. (2005) concluded. Shear flow usually is observed at high temperatures. Athigh temperatures, the passive zone has little resistance against rutting. That is, the state of theasphalt pavement is close to that of Case II (unconfined condition) whereby the asphalt pavementexperiences huge permanent deformation. Furthermore, shear flow can start and accelerate thepermanent deformation.

Gokhale et al. (2005) measured changes in air void content and changes in the thickness of thepavement in the wheel path and at the hump for asphalt pavements subjected to accelerated pave-ment testing using an HVS. These results are plotted in Figure 2(a) and 2(b). The line of equality(LOE) in these figures indicates that the downward deformation (i.e. rutting) is caused by densi-fication only. Under the wheel path, all the points show a reduction in air void content and mostpoints lie under the LOE, which implies that the downward deformation exceeds the volumetricchange due to densification. The mechanism that contributes to the downward deformation in thewheel path in addition to densification causes no volume change and is believed to be shear flow.

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Figure 2. Air void change and thickness change of asphalt pavement (a) at the wheel path and (b) at hump,and (c) shear stress distribution near the wheel path from layered viscoelastic analysis. ((a) and (b) fromGokhale et al. (2005)).

The downward deformation versus air void change relationship is quite different at the hump,as shown in Figure 2(b). Most of the data points for the top layer are positioned above theLOE, indicating the presence of a mechanism that expands the layer in the vertical directionand increases the air void content of the layer. This expansion is the reason that the Harvey andPopescu (2000) work reports a shear effect of over 100%. Most of the data points for the bottomlayer are positioned either along or slightly below the LOE, indicating that densification and asmall amount of shear flow are the governing mechanisms for the hump side of the bottom layer.

The expansion shown in the hump side of the top layer may be due to dilation caused byshear stress. The shear stress concentration shown in Figure 2(c) supports evidence of suchdilation. The stress distribution computed by the LVECD program indicates that the shear stressis concentrated at the edge of and beneath the wheel path. If the concentrated shear stress exceedsthe shear strength, then shear dilation takes place. Judging from the shear stress location and fieldobservations of air void content change, shear stress may create dilation and, moreover, may helpto generate a hump. Because the important deformation in the rutting analysis is the downwarddeformation in the wheel path, the deformation behaviour in the hump area caused by dilationmay not be of direct importance. However, the deformation behaviour in the hump area changesthe stress state in the passive zone, which in turn affects the permanent deformation behaviour ofthe active zone.

Coming back to the discussion of the passive and active zones, the behaviour of the passivezone relies on the active zone and, again, the passive zone affects the behaviour of the activezone. That is, both zones interact with each other, but the active zone governs the behaviour.

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The interaction of the active zone and the passive zone results in confining pressure and lateraldeformation in the passive zone. The confining pressure is an output in terms of stress, and thelateral deformation is a result of strain. Therefore, either one of these two variables can representthe behaviour of the passive zone.

Triaxial tests can be used to simulate field conditions in the laboratory because the conditionsfor triaxial testing are close to the stress state under the wheel. The confining pressure of the triaxialtest represents the effects of the passive zone on the active zone, as illustrated in Figure 1. Thedeviatoric stress represents the vehicle loading. If the confining pressure measured from the fieldis applied to laboratory testing, then field performance can be evaluated accurately. However,confining pressure continuously changes while a vehicle travels along the road surface. Evenif the exact history of the confining pressure in the field is known, laboratory simulations areimpractical due to the limitations of the currently used test device. Therefore, constant confiningpressure usually is applied.

Another output of the interaction between the active and the passive zones is viscoplastic strain.Poisson’s ratio calculated using permanent strain is specified as the effective Poisson’s ratio orviscoplastic Poisson’s ratio. The effective Poisson’s ratio in the field can be calculated usingthe relationship between axial strain and volumetric strain, as expressed in Equation (1) whichis same as elasticity. The change in air void content of the asphalt pavement corresponds to thevolumetric viscoplastic strain, and the change in thickness of the asphalt layer provides the verticalviscoplastic strain.

εvpvol

εvpz

= 1 − 2υvp for viscoplasticity, (1)

where εvpvol is the volumetric viscoplastic strain (= εx + εy + εz), ε

vpz the vertical (axial)

viscoplastic strain, and νvpeff the viscoplastic (effective) Poisson’s ratio.

In order to evaluate the reasonableness of the triaxial testing to simulate the field conditions,the strain concept is utilised. If the Poisson’s ratios measured in the lab and in the field are closeenough, the confining pressure that is used for lab testing may be acceptable as a representativestate of stress for rutting in the field. Coleri, Harvey, Yang, and Boone (2012a) measured rutdepths and changes in air void content from pavements subjected to HVS testing at 50◦C. Theratio of volumetric permanent strain to vertical permanent strain was about 0.39; thus, the effectivePoisson’s ratio of the PG64-28PM mixture (dense-graded and polymer-modified binder) in fieldis 0.39. The triaxial test results are not available to the authors for the Poisson’s ratio comparison.Therefore, the data from two mixtures with different aggregate gradations, asphalt contents, andbinder grades are used instead for this comparison. These mixtures are the Federal HighwayAdministration (FHWA) control mix composed of 12.5 mm nominal maximum aggregate size(NMAS) and 5.3% PG 70-22 binder and the 9.5 mm NY mixture (NY9.5B) with 6.1% PG 64-22(modified) binder. The target air void contents for the triaxial test specimens of the FHWA mixtureand NY9.5B mixture are 4% and 5.4%, respectively.

Figure 3 presents the viscoplastic Poisson’s ratios obtained from the triaxial repeated loadpermanent deformation (TRLPD) tests of these two mixtures. The viscoplastic Poisson’s ratiosfor the TRLPD tests at 54◦C range from 0.25 to 0.45 for the FHWA mix. Poisson’s ratios of theNY9.5B mix were measured at three different temperatures, and at 47◦C the Poisson’s ratio isbetween 0.3 and 0.55. The field-measured Poisson’s ratio (around 0.39) is within the range of thePoisson’s ratios obtained from lab testing. This finding implies that triaxial testing with confiningpressure between 10 and 20 psi can reasonably represent the effects of the passive confinementthat exists in the field pavements.

The findings from the SHRP A-003A project suggest that high shear stress induces shear defor-mation, which is the primary cause of rutting. Therefore, applying shear stress directly to asphalt

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Figure 3. Viscoplastic Poisson’s ratios obtained from TRLPD tests: (a) FHWA ALF control mix with20 psi confinement and (b) NY9.5B mixture with 10 psi confinement.

concrete specimens is believed to be the best way to determine the permanent deformation charac-teristics of asphalt mixtures. As a result, a repeated simple shear test-constant height (RSST-CH)test has been proposed. Harvey, Lee, Sousa, Pak, and Monismith (1994) successfully predicted rutdepths of field test sections via the RSST-CH test. Von Quintus, Mallela, Bonaquist, Schwartz,and Carvalho (2012) performed both RSST-CH and triaxial tests (i.e. flow number tests) andreported that it is difficult to determine which test better represents the field conditions.

Based on the observations made in this section, the triaxial test is selected as the permanentdeformation characterisation test for this study. Although the triaxial test does not assess the shearresistance of asphalt mixtures directly, the deformation behaviour in the triaxial test does offerinformation about the shear resistance of the mixture, as indicated by the shear failure of soilsin triaxial testing. The selection of the triaxial test also is based on the practical reason that itcan be performed in the Asphalt Mixture Performance Tester, which is gaining popularity amongstate highway agencies, without any major changes to the equipment. The wide availability ofthe Superpave gyratory compactor that can be used to produce triaxial test specimens is anotherstrong reason for this selection.

4. Overview of the shift model with the TSS test protocol and implementation4.1. Overview of shift model and TSS test protocolChoi and Kim (2013a) have suggested a permanent deformation model, the so-called shift model,and test protocol, the TSS test. The shift model calibrated by the TSS test predicts the permanentstrain for a random loading history well. The random loading history has the same loading historyas in the field, except for temperature. Therefore, this study focuses on the prediction of rut depthin the field via the shift model calibrated by the TSS test protocol.

The shift model (Choi & Kim, 2013b) is grounded on two superposition principles, time–temperature (t − T ) and time–stress (t − S), and is expressed here as Equation (2). Thesuperposition principles provide two shift functions, i.e. reduced load time shifting and devi-atoric stress shifting. A mastercurve is utilised as the reference for these shifts. It is noted thatthe shift model proposed by Choi and Kim (2013b) is based on deviatoric stress with a constantconfining pressure of 10 psi (69 kPa); therefore, the shift model is a uniaxial model. The imple-mentation of the uniaxial shift model into the LVECD program requires careful treatment of theeffects that the changing stress state along the pavement depth has on permanent deformation.Because the confining pressure changes along the depth of the pavement, the integration of thematerial-level shift model into the pavement analysis using deviatoric stress could be misleading.

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A fully three-dimensional material model is required in order to account correctly for the effectsof the stress state on the permanent deformation at different pavement depths. However, char-acterisation procedures that typically are required to develop a three-dimensional model are toocumbersome to be used in routine material testing for pavement design and analysis.

In this study, the deviatoric stress-based shift model is reformulated using vertical stress, whichis the sum of the deviatoric and confining stresses, in order to implement the stress shift functioninto the LVECD program. Vertical stress in the downward direction (i.e. depth) seems reasonableconsidering the assumption of the axisymmetric condition and constant confining pressure.

εvp = ε0Nred(NI +Nred)β

(mastercurve),{aξp = p1ξ

p2p + p3

aσv= d1σ

d2v + d3

(shift functions),(2)

where, ε0, NI , β is the coefficient of the incremental model (mastercurve), Nred the number ofcycles at the reference loading condition (N × 10atotal), N the physical number of cycles for acertain loading condition, atotal the total shift factor, which is the sum of the shift factors (aξp + aσv),aξp the reduced load time shift factor, aσv the vertical stress shift factor, ξp the reduced load time, σv

the vertical stress (sum of deviatoric stress and confining pressure), Pa the atmospheric pressurethat has the same unit as σv, and p1, p2, p3, d1, d2, d3 the regression parameters for the shiftfunctions.

The TSS test protocol includes a reference test and multiple stress sweep (MSS) tests. Thereference test, which is a general TRLPD test with haversine loading followed by a rest period,produces a reference permanent deformation growth curve. The MSS tests consist of three loadingblocks that have different deviatoric stress levels in increasing order (i.e. 70, 100, and 130 psi),and provide two shift functions by combining the mastercurve. The reference test is performedat a high temperature (TH). The MSS tests require three specimens, and each specimen is testedat the high (TH), intermediate (TI), and low (TL) temperatures. Detailed information, includingtesting temperature determination, can be found elsewhere (Choi & Kim, 2013a).

4.2. Implementation of the shift model into the finite element (LVECD) programThe North Carolina State University (NCSU) research team has developed the LVECD (LayeredViscoElastic Pavement Analysis for Critical Distresses) program that simulates damage growthusing moving vehicle data and pavement temperature data. The LVECD program simulates vari-ous types of axle loads as well as climate changes. The LVECD program combines the concepts ofFourier transform and finite element discretisation to reduce simulation time by orders of magni-tude shorter than those of conventional three-dimensional models (Eslaminia, Thirunavukkarasu,Guddati, & Kim, 2012). The LVECD program captures the effects of viscoelasticity and themoving nature of traffic loads with high efficiency. The entire procedure, from entering inputs toviewing outputs, is operated through a user-friendly graphic interface, shown in Figure 4, whichis similar to that found in the MEPDG software.

The LVECD program divides asphalt layer(s) into several sublayers and then calculates thepermanent strain using inputs of the shift model: vertical stress, load time (pulse times), and tem-perature. The maximum rut depth is calculated for the centre of the wheel path. The temperaturesare obtained directly from the LVECD program inputs. Then, the remaining inputs are the loadtimes.

Load time is defined as the duration that vertical stress is applied to an element. In order toobtain the load time, the vertical stress from the LVECD simulation is fitted with a haversineshape. The fitted haversine shape accommodates the load time, which can be calculated from the

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Figure 4. Screen shot of LVECD program input window.

y

R

x

Figure 5. Load time (pulse time) and normalised load time for various conditions: (a) load time for vehiclespeed, (b) normalised load time for vehicle speed, (c) load time for various conditions at 60 mph, and (d)linear fitting.

period of the fitted function. Figure 5(a) presents the load time changes in terms of pavementdepth. The normalised load times, i.e. the ratio of load times at certain depths to the load timesat the surface of the pavement, collapse onto one another, as shown in Figure 5(b). Because theeffect of vehicle speed on load time disappears after normalisation, one speed, 60 mph, is appliedfor the analysis. Figure 5(c) includes various temperature gradients, pavement properties andstructures, and illustrates that those factors have little effect on the load time. The normalised

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load time increases linearly in terms of pavement depth. This finding matches the well-knownfact that vertical stress spreads and decreases linearly with depth. One linear equation in termsof normalised load time, expressed here as Equation (3), can represent the load time at a certaindepth

tptsurfacep

= 0.151 × pavement depth + 1.0, (3)

where tsurfacep is the pulse time at the surface of an asphalt pavement and is calculated from the

vehicle speed and tyre contact area. Instead of fitting all the vertical stress levels to obtain theload time, Equation (3) is implemented into the LVECD analysis for computational efficiency.

5. Materials and TSS testsIn order to verify the shift model implemented in the LVECD program, full-scale test resultsobtained from the National Center for Asphalt Technology (NCAT) test track and Federal High-way Administration Accelerated Facility (FHWA ALF) test sections are utilised. In this paper,the mixtures from two sites are tested following the TSS protocol, and the rut depths are predictedby the shift model in combination with the LVECD program. All the lab tests and predictions forNCAT mixtures have been performed by LaCroix (2012).

5.1. Test conditions in the fieldGibson et al. (2012) evaluated the effects of modified binders on both fatigue and rutting throughlaboratory testing and full-scale testing and proposed a new binder purchase specification thatconsiders the features of the modified binders. Therefore, all the mixtures of the FHWA ALFsections have the same aggregate gradation and volumetric properties but different binders. Thefunction of the NCAT test track (West et al., 2012) is to evaluate the performance of warmmix asphalt (WMA) and reclaimed asphalt pavement (RAP) mixtures; therefore, the test trackpavements have the same structure but different mixtures. Table 1 provides a summary of therelevant test conditions for both (NCAT and FHWA ALF) full-scale tests.

Table 1. Summary of testing condition of full-scale testing.

Conditions FHWA ALF NCAT

Loading method HVS, axle load (689 kPa/44.48 kN) Tractor-trailer, relatively constantloading

Temperature Constant, 74◦C, 64◦C, 45◦C EnvironmentalWandering Channelised WanderingStructure Asphalt One layer, one mixture, two

thicknesses (100, 150 mm)Surface (32 mm), intermediate

(70 mm), base (76 mm)Basea Crushed agg. base (100 mm) Dense graded (140 mm)SGa AASHTO A-4 Dense graded

Mixtures Control, SBS-LG, CR-TB,Terpolymer

C, O, FW, AW, R, RWb

Comments Same aggregate gradation butdifferent binder

Same structure but different mixturesfor each section

aUnbounded layer: base and subgrade (SG) layers.bC-Control, O-Open graded friction course (OGFC), FW-Foam type WMA, AW-Advera additive WMA, R-50% RAP,RW-50% RAP with foam type WMA.

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Figure 6. Schematic diagram of cross-sections and lanes at FHWA ALF test site.

Table 2. Description of NCAT test track sections (LaCroix, 2012).

Label Description Section number

C Control S9O OGFC surface with control intermediate/base S8FW Control mixtures using foamed asphalt WMA S10AW Control mixtures using Advera additive WMA S11R 50% RAP mixture N10RW 50% RAP mixture using foamed asphalt WMA N11

As shown in Figure 6, the FHWA ALF sections have thin (100 mm) and thick (150 mm)pavement structures constructed for each mixture. Each lane has four sites: two for rutting andtwo for fatigue. Rut depth is measured in both the rutting and fatigue lanes. A layer deformationmeasurement assembly (LDMA) device is used to measure the rut depth of the asphalt pavementlayer only. The total rut depth at the centre of the wheel path also is measured. Figure 6 illustratesthe lanes that correspond to the four NCSU test mixtures: Lane 2 (Control), Lane 4 (SBS-LG),Lane 5 (CR-TB), and Lane 12 (Terpolymer). Also, the NCSU research team has 6 sections outof the 46 sections in the NCAT test track. Table 2 presents the basic information for the sixcorresponding mixtures. Each pavement consists of three different layers.

5.2. Lab testing conditions and materialsFor the four FHWA ALF mixtures, the Control mix contains unmodified binder and is PG 70-22,and the SBS-LG, CR-TB, and Terpolymer mixes contain polymer-modified binders. The SBS-LG mix has a normal styrene–butadiene–styrene (SBS)-modified binder with approximately 3%linearly grafted SBS polymer by weight. The crumb rubber terminal-blended (CR-TB) modifiedasphalt binder is produced in a process that blends recycled tyre crumb rubber (5.5%) with newSBS rubber (1.8%) at asphalt terminals. The Terpolymer binder utilises 2.2% reactive Terpoly-mer or three copolymers (Dupont™ Elvaloy®). Additional relevant information can be found

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elsewhere (Gibson et al., 2012). All four mixtures are tested using the proposed test protocol, i.e.the TSS tests. Two replicates are applied, and the averaged permanent strain levels are applied tothe analysis and characterisation of the shift model.

As shown in Figure 6, each lane is composed of two lifts of asphalt concrete; the top lifthas a higher air void content than the bottom lift, except for the Control mixture (Lane 2). Foraccurate predictions, specimens are fabricated with two different air void contents. The high airvoid content, AVH, is equivalent to that in the top lift, and the low air void content, AVL, isequivalent to that in the bottom lift. Figure 7 shows the TSS test results and the effect of air voidcontent on permanent strain. The left-hand graphs show higher permanent strain levels than theright-hand side because of the higher air void content. It can be concluded that densification isone of the determining factors of permanent deformation.

The TSS test results indicate that the mixes with polymer-modified binders have a strongerresistance to rutting than the Control mixture. The reference tests at the high temperature present aclear ranking for rutting resistance: CR-TB, Terpolymer, SBS-LG, and Control, in order from bestto worst resistance to rutting. This order conforms to that of the full-scale test results. Therefore,the reference test is a candidate test method to evaluate the rutting resistance of asphalt mixturesin terms of ranking.

After the TSS tests are completed in the lab, the results are used to characterise the shift model.Table 3 presents the calibrated coefficients of the FHWA ALF mixtures. The coefficients for theNCAT test track mixtures can be found in LaCroix (2012). These coefficients are used as inputsfor LVECD analysis in order to predict rut depths of asphalt pavements.

6. Rut depth prediction of full-scale testing sectionsIn this section, rut depths from the selected NCAT test track pavements and FHWA ALF pavementsare predicted using the TSS test results, the shift model, and the LVECD program.

The rut depths of the NCAT test track were measured after two years of trafficking. Figure 8depicts the test track measurements and predicted rut depths using the LVECD program withEnhanced Integrated Climate Model (EICM) climate information for that site. Two different rutdepth predictions are shown in Figure 8. The rut depth denoted as “Prediction” is determined basedon the channelised loading assumption in that all the truck loadings applied on the NCAT test trackare used in the LVECD simulations without accounting for the effects of vehicle wandering onthe rutting performance. The other prediction, denoted as “Prediction (Wandering)”, is made byaccounting for the wandering of truck traffic on the test track using the approach employed in theNCHRP 1-37A Mechanistic-Empirical Pavement Design method. NCHRP 1-37A (the MEPDGmanual) assumes 10 in to be the standard deviation for truck traffic wander and adjusts the numberof axle load applications over an evaluation point in order to account for vehicle wandering. Thisassumption leads to about a 20% reduction of the total ESAL (LaCroix, 2012). This 20% reductiondecreases the predicted rut depth by about 9%, as shown in Figure 8, and brings the predictionscloser to the measurements.

In general, Figure 8 demonstrates that the predicted rankings match well with the field obser-vations; the difference is within a few millimetres without applying any correction factor. Thepredicted rut depth value, however, is always higher than the measured one. This outcome isaffected by the fact that ageing (which had occurred in the test track pavements for two years andreduced the amount of permanent deformation) is not included in the LVECD simulations.

In summary, the NCAT test track test conditions are the same as in-service asphalt pavementconditions, except for the relatively constant loading of tractor-trailers. That is to say, the test tracksimulates traffic loading, wandering, actual climate change, actual pavement structure (including

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Figure 7. TSS test results of FHWA ALF mixtures: AVH is equivalent to top lift and AVL is equivalentto bottom lift (for air void content).Note: “Refer” means a reference test, and TH, TI, and TL are the high, intermediate, and low temperatures.

base layer and subgrade), ageing effects, and so on. The LVECD analysis is found to predict rutdepth under these realistic field conditions. This finding verifies that the prediction methodologyused in this study, that is, the TSS test as the material characterisation test, the shift model for thematerial permanent deformation model, and the LVECD program for the pavement analysis, hasthe capacity to predict rut depth in the field reasonably. For future study, the inclusion of ageingand wandering would improve the predictability of the model.

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Table 3. Calibrated coefficients of the shift model for FHWA mixtures.

SBS-LG CR-TB Terpolymer

Functions Control AVH AVL AVH AVL AVH AVL

Master β 0.7460 0.8238 0.8268 0.8173 0.8178 0.8177 0.8274ε0 0.0057 0.0060 0.0041 0.0041 0.0033 0.0048 0.0028NI 2.2214 2.9400 3.1756 2.7493 2.6352 3.5230 3.6011

Load time p1 5.7658 31.3185 −0.7412 6.7500 4.9682 4.3547 37.3018p2 0.0785 0.0074 −0.1349 0.0478 0.0849 0.0872 0.0074p3 −5.5171 −31.3940 0.9334 −6.4869 −4.6533 −4.0045 −36.6557

Vertical stress d1 0.0067 0.0047 0.0050 0.0048 0.0156 0.0066 0.0154d2 2.2822 2.4538 2.3816 2.4932 2.0405 2.4172 2.0687d3 −0.6635 −0.6567 −0.6038 −0.7298 −0.9458 −0.8621 −0.9918

Figure 8. Measured versus predicted rut depths for NCAT test sections after two years (LaCroix, 2012).

Table 4. Comparison of predicted rut depths and measurements at 50,000 passes from the FHWA ALFpavements.

Predicted Field-measured

Mix 100 mm–64◦C 100 mm–74◦C 150 mm–45◦C 150 mm–64◦C Ranking 100 mm–64◦C 150 mm–64◦C

CR-TB 1.963 2.433 1.826 2.906 1 1 9.06 –Terpoly. 2.042 2.416 1.996 2.987 2 2 – 11.15SBS-LG 2.560 2.888 2.670 3.731 3 3 12.80 12.63Control 5.446 8.120 3.586 8.059 4 4 13.72 14.11

Note: The bold letters indicates ranking (good performance to bad performance).

For the FHWA ALF pavements, LVECD analysis is performed for four cases: 100 mm thickpavement at 64◦C and 74◦C, and 150 mm thick pavement at 45◦C and 64◦C. The results are shownin Table 4 at 50,000 passes for each loading condition, and the entire rut depth evolutions areplotted in Figure 9. The higher temperatures and thicker structures produce the greater rut depthmeasurements. The dashed lines in Figure 9 represent the predicted rut depths, and the solid linesand symbols represent the measured downward rut depths. The polymer-modified mixtures showsimilar rut depths, which are smaller than the rut depth measurements of the unmodified (Control)mixture.

Table 4 indicates that the CR-TB mixture exhibits the best rutting resistance and the Control mixis the worst for all conditions. This ranking stays constant regardless of the loading conditions and

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Figure 9. Comparison between field measurements and predictions of asphalt concrete rut depth: (a)Control, (b) SBS-LG, (c) CR-TB, and (d) Terpolymer mixtures.Note: Solid symbols and lines are measurements and hollow symbols and dotted lines are predictions.

agrees with that predicted from the LVECD program. This finding suggests that the permanentdeformation model and test protocol employed in this study have the ability to assess ruttingresistance in terms of ranking.

However, even though the order of magnitude is the same for asphalt rut depth, the predictionis always smaller than the measured one for all loading conditions. The difference increasesas the number of wheel passes increases. Investigation into the mechanism that induces thedifference between the predictions and the measurements would provide further understandingabout permanent deformation of the field. The constant ratio of measured rut depth to predictedrut depth, regardless of the number of wheel passes, also would provide a clue. This ratio canserve as a correction factor to improve the predictability of the model implemented in the LVECDprogram. In the next section, the correction factor (i.e. ratio) is investigated to determine thecharacteristics of permanent deformation behaviour in the field.

7. Evaluation of full-scale test results7.1. Effect of shear flow on rut depthThe shift model predicts the rut depth measurements for the NCAT test track within just a fewmillimetres; however, it does over-predict them slightly. This over-prediction can be explainedby ageing. Judging from the test conditions, especially vehicle wandering, shear flow is minimalat the NCAT test track. Therefore, the good predictions for asphalt concrete rut depths appear toindicate that the model and test protocol with constant confining pressure reflect field performancereasonably well.

On the other hand, the rut depths of the FHWA ALF test sections are under-predicted. The errorof the FHWA mixtures is larger than that of the NCAT mixtures. The under-prediction may be

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caused by the excessive shear flow that is observed in the FHWA ALF full-scale testing lanes butnot in the NCAT pavements. The shear flow would expedite the rut depth development more thanis expected from TSS testing. Even though the shear flow effect is included in the data from thetriaxial tests, 10 psi confining pressure seems to constrain the lateral deformation. Therefore, thecontribution of shear flow in the triaxial test is not sufficient to predict the rutting performance inthe FHWA ALF pavements. The slight over-prediction of the rut depth for the NCAT conditionsand the more severe under-prediction for the FHWA ALF conditions seem to suggest that theTSS test works well when the shear flow is relatively minor, as is the case at the NCAT test track.When the shear flow is quite significant, as is the case with the FHWA ALF pavements due tochannelised loading and very high temperatures, adjustments are needed in order for the predictedrut depth to match the measured rut depth.

In order to verify this hypothesis with regard to triaxial testing, results of work performed atthe University of California, Davis (UC-Davis) (Coleri et al., 2012a, 2012b) are applied to theanalysis because there are no field measurements of volumetric strain for the NCAT mixturesand FHWA ALF mixtures. The UC-Davis mixture (PG64-28PM) is a densely graded polymer-modified mixture. The asphalt layer is paved on top of concrete pavement. Coleri et al. conductedfull-scale tests on two different thicknesses, 64 and 114 mm, which are denoted as thin andthick, respectively. The test temperature was 50◦C with channelised loading. Due to the lack ofmixture properties for the PG64-28PM mix, the properties of the FHWA mixtures are entered intothe LVECD program. The LVECD program uses the same structure as the UC-Davis mixtures.Figure 10 presents the prediction results.

The downward rut depth measurements obtained from the full-scale testing of the UC-Davismixtures are used for this comparison. The downward rut depth does not include the upheavalportion, and the asphalt layer is on top of the concrete pavement; thus, the downward rut depthcan be considered as the change in thickness of the asphalt layer. The measured rut depths fallsomewhere between the predicted rut depths using the Control mixture properties and the SBS

Figure 10. Rut depth prediction for the UC-Davis pavements without correction factors: (a) using prop-erties from the FHWA Control mixture, (b) using properties from the FHWA SBS mixture, and (c) usingproperties from the FHWA CR-TB mixture.

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mixture properties. The binder used in the PM64-28PM mixture is polymer-modified and isgraded as PG 64-28. The binder for the FHWA polymer-modified mixture is PG 70-28 and forthe unmodified (Control) mixture is PG 70-22. The high-temperature performance grade (PG) isassociated with rutting resistance. The FHWA mixtures have a high PG; accordingly, the predictedasphalt concrete rut depth measurements of the FHWA polymer-modified mixtures are lower thanthe measured rut depths. If the PG64-28PM mix is tested and used for the shift model calibration,the predicted rut depths would be closer to the field measurements than what is shown in Figure 10.The full-scale tests show humps, which are believed to be the result of shear flow. Even whenapplying the predicted rut depth values derived from the properties of the FHWA ALF modifiedmixtures to the UC-Davis work, the underestimation becomes less than for the FHWA mixtures.This observation appears to indicate that the shift model can evaluate rutting performance betterunder the less excessive shear flow condition, that is, the lower testing temperature used in theUC-Davis tests.

In addition to a direct comparison of rut depth measurements, the effective Poisson’s ratioserves as additional evidence to support the hypothesis. The hypothesis claims that if the effectivePoisson’s ratio in the field is the same as that used in the lab tests, the lab test results can representthe behaviour in the field. The effective Poisson’s ratio for the PG64-28PM mix is about 0.39,which is calculated using the relationship between the volumetric strain and vertical strain (seeEquation (1)). The averaged viscoplastic Poisson’s ratios obtained from the TSS tests of the FHWAALF mixtures are 0.29, 0.32, and 0.35 for the SBS-LG, CR-TB, and Control mixes, respectively.The averaged viscoplastic Poisson’s ratios are smaller than the effective Poisson’s ratio of the field.Again, the smaller viscoplastic Poisson’s ratio is due to the higher PG of the FHWA mixtures. Ifthe PG64-28PM UC-Davis mix is tested, the viscoplastic Poisson’s ratio would be similar to thatof the FHWA mixes.

These observations would support that excessive shear flow makes asphalt pavement deformmore than usual, thereby increasing the error of the shift model predictions. Accordingly, correc-tion is required to evaluate rutting performance accurately under severe loading conditions thatcause excessive shear flow.

7.2. Correction factorThe most fundamental way to address the effects of shear flow in the different field cases shown inthis paper is to employ a three-dimensional material model. The model should explain the effect ofconfining pressure on the active zone; simultaneously, it should simulate the interaction betweenthe active zone and the passive zone. However, the development of a three-dimensional model isa task that requires a significant amount of effort and numerous tests. Also, the implementation ofa three-dimensional model by state highway agencies would be difficult due to the complexitiesand time involved in the testing.

A simpler way to obtain better predictions is to develop a correction factor (or function). Theratio of measured rut depth to predicted rut depth obtained by the LVECD program, defined asEquation (4), represents the correction factor. A correction factor that is greater than unity (one)indicates that rutting has been expedited due to excessive shear flow. A correction factor that isless than one indicates that the rut depth is under-predicted

Correction Factor = AC Rut Depth|measured

AC Rut Depth|predicted. (4)

The correction factors are calculated for each of the three field studies presented in the paper.Figures 11 and 12 present comparisons of the recalculated asphalt concrete rut depth predictionsthat were obtained by applying correction factors versus the measurements. In Figures 11 and

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Figure 11. Recalculated asphalt concrete rut depth in the UC-Davis pavements by applying individualcorrection factors using properties from FHWA mixtures: (a) Control, (b) SBS, and (c) CR-TB.

12, the solid symbols on the solid lines are the measurements, and the hollow symbols on thedotted lines are the recalculated predicted asphalt concrete rut depths with the correction factors.All the curves for the predicted asphalt concrete rut depths obtained from both the UC-Davis andFHWA ALF full-scale tests collapse onto the curves for the measured rut depths from the primaryregion to the secondary region. The slope of the secondary region is very similar to that of themeasured one. The good agreement for all conditions and for the whole range of test conditionsafter correction verifies that shear flow expedites asphalt concrete rut depth growth, but the overalltrend of the growth is similar to that from the triaxial test.

The MEPDG (NCHRP 1-37A, 2004) program requires a depth correction function and a transferfunction. The transfer function can be included via a local calibration process whereby the lab testresults are matched to the field measurements. In addition, the depth correction factor is utilisedin order to correct the permanent deformation that is predicted by the MEPDG. The idea of thedepth correction factor is to match the confining pressure at different depths, as shown in theexample given in Figure 13. The depth correction factor adjusts the predicted depth according tothe well-known observation that rutting usually occurs within the top four inches of the pavement.

In summary, when shear flow plays an insignificant role, the correction factor and/or transferfunction would not be necessary to predict rut depth accurately. Even in the case where excessiveshear flow is significant, the LVECD program with the shift model requires only one constantcorrection factor per loading condition to predict field rut depths, whereas the MEPDG utilisesthe depth correction factor and/or a transfer function. If the correction factor can be estimated forsevere shear flow loading conditions, the shift model with the LVECD program will predict rutdepth for all conditions.

Figure 14 presents the correction factors for the three test sections; the NCAT test track, UC-Davis, and FHWA ALF sections are listed in order of correction factor ranking. Consideringtest conditions such as temperature, wandering, and ageing, the severity of the loading conditionfollows the ranking order of the NCAT, UC-Davis, and FHWA tests, which is the same as the

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Figure 12. Recalculated asphalt concrete rut depth for the FHWA ALF sections by applying individualcorrection factors.Note: Solid symbols and lines are measurements and hollow symbols and dotted lines are predictions.

Figure 13. Example of depth correction factors.

ranking order of the correction factors. The NCAT track allows for wandering and the averagepavement temperature is 21◦C, whereas the UC-Davis and FHWA ALF sections use channelisedloading and the temperatures are maintained as a constant of 50◦C for the UC-Davis sections and74◦C and 64◦C for the FHWA ALF sections.

The FHWA ALF mixtures graphed in Figure 14(c) also support the observation that loadingconditions seem to be related to the correction factor. The lanes at 74◦C and 45◦C are tested at twoyears and three years, respectively, after the 64◦C lanes are tested. Two or three years of ageingwill stiffen the asphalt concrete, and thus, these lanes show more rutting resistance than the other

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Figure 14. Correction factors to match AC rut depth in full-scale test sections.

lanes. The low temperature (45◦C) lanes exhibit the strongest rutting resistance because theyexperience the longest period of ageing and their temperature is also the lowest. Therefore, theorder of the loading conditions in the horizontal axis of Figure 14(c) also represents the rankingof rutting resistance. As the rutting resistance increases, the correction factor decreases.

These observations reinforce the idea that correction factors are associated with loading condi-tions or shear resistance. In cases where the amount of shear resistance is enough that the asphaltpavement does not deform due to shear flow, then the asphalt pavement deforms similar to theNCAT test sections. For this condition, the shift model implemented in the LVECD program canpredict rut depth well. Ageing and vehicle wandering tend to make the predictions deviate fromthe measurements. These two factors should be considered for better predictions; however, theyare out of the scope of this study.

In the case of UC-Davis full-scale testing where some shear flow affects permanent deformationbut not significantly, the correction factor is slightly greater than one. If a certain level of error isacceptable in the prediction, the correction factor can be considered as one. For better predictions,the effect of shear flow should be considered. When the shear resistance is low or the load levelis severe, as in the FHWA ALF test sections, the asphalt pavement has a tendency to deformsignificantly due to shear flow. This case requires a correction factor to adjust for predicted strain.

In summary, in the case of insignificant shear-related behaviour, other effects such as ageingand wandering become more dominant so other approaches would be considered to improvethe asphalt concrete rut depth predictions. However, a correction factor is required when shearflow plays a significant role in permanent deformation. The correction factor due to shear flow isreferred to as the shear correction factor.

7.3. Estimation of shear correction factorShear flow may initiate when the shear stress exceeds the shear strength in an asphalt pavementstructure. Shear stress is a result of loading conditions (i.e. vehicle load, temperature, structure

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y

y

Figure 15. Shear strength mastercurve of FHWA control mix (Tresca yield criterion).

of the asphalt pavement, etc.), whereas shear strength is a material property. If both the shearstress and the shear strength are known, then it is possible to estimate when the shear flow willstart and/or the significance of its effect on rutting. The ratio of shear stress to shear strength mayat least indicate the severity of the shear flow and, thus, this ratio would be related to the shearcorrection factor.

The shear strength value can be obtained by monotonic testing based on the Tresca yieldcriterion. The shear strength is defined as half of the deviatoric stress at failure, as expressed inEquation (5)

τ = 12 (σ1 − σ3) = 1

2σd. (5)

Yun (2008) performed monotonic tests under various loading conditions, such as several differentstrain rates and temperatures. The FHWA ALF Control mix was tested at two different confiningpressures: unconfined (0 kPa) and confined (500 kPa). The peak stress, which is assumed to bethe uniaxial strength, was determined, and then the shear strength was calculated based on theTresca yield criterion. The shear strength is plotted in Figure 15 according to the reduced strainrate under the assumption that the time–temperature superposition (t–TS) principle is valid, evenat failure. Figure 15 provides one representative curve, which is referred to as the shear strengthmastercurve. The shear strength mastercurve demonstrates that the t-TS principle is viable evenat failure and describes the strength as a function of both strain rate and temperature; thus, theshear strength can be evaluated by this strength mastercurve. The power form fits the mastercurvewell for both 0 and 500 kPa confining pressure.

In order to determine the shear strength via the shear strength mastercurve, the reduced strainrate, i.e. the strain rate and temperature, should be known. The LVECD simulation results canyield the shear strain rate. Maximum shear stress takes place at the edges of and beneath the wheelpath. This area is called the shear bulb and is where the shear stress is concentrated, as shownin Figure 2(c). The shear stress and strain levels are determined at the maximum shear stresspoint. The shear strain rate is calculated using the shear strain history. The average slope near thepeak shear strain of the strain history is considered to be the shear strain rate. The shear strainrate and temperature can determine the shear strength using the shear strength mastercurve. Theshear strain rate is obtained from viscoelastic analysis (i.e. the LVECD program); therefore, theshear strain rate is adjusted to evaluate permanent deformation behaviour. One constant adjustedvalue is applied to the shear strain rates of all the other loading conditions of all the mixtures. The

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applied adjusted value is 2.0×10−3, which is determined by comparing the measured correctionfactor (refer to Figure 14) at 100 mm–64◦C for the Control mix.

The ratio expressed in Equation (6) is designated as the estimated correction factor. Theassumption of Equation (6) is that shear flow starts and expedites the rutting process when theshear stress exceeds the shear strength

Estimated Correction Factor = Max. Shear Stress

Shear Strength. (6)

Due to the lack of shear strength test results for the polymer-modified mixtures of the FHWA ALFsections, the shear strength mastercurve of the Control mix is utilised for the polymer-modifiedmixtures. The estimated shear correction factors shown in Figure 16(a) can explain the effectsof temperature and thickness of the asphalt layer on shear-related permanent deformation; here,the estimation does not include the ageing effect. The high-temperature simulation condition(100 mm–74◦C) requires larger correction factors. The thin layer (100 mm–64◦C) requires largercorrection factors than the thick layer (150 mm–64◦C). The relatively less severe loading condi-tion, 150 mm–45◦C, produces less than two for all the mixtures. This observation agrees with thegeneral accepted understanding of shear flow.

The estimated shear correction factors obtained via the prediction process are compared againstthe measured correction factors obtained by the ratios of field-measured rut depths to LVECDrut depth predictions, which are shown in Figure 16(b)–(d). Here, the shear strength mastercurveof the Control mix is applied to all other estimations. The estimated correction factors seem tomatch well overall with the measured ones in spite of some differences. For the full-scale testing,the 100 mm–74◦C and 150 mm–45◦C lanes experienced two and three years of more ageing thanthe 64◦C lanes, respectively. The more aged lanes show higher estimated values because it doesnot deform as much as unaged asphalt concrete. If the full-scale tests are performed under unagedconditions, the estimated values become similar to the measured values. However, the relativelyless severe condition, 150 mm–45◦C, requires similar correction factors between the estimationsand the measurements in spite of three-year ageing. This finding may indicate that ageing has a lesssignificant effect on rutting under general or less severe conditions than under severe conditions;however, this assumption is made under limited observations, such as few mixtures without theirown shear strength test results. Therefore, more experiments need to be performed in order toprove the assumption.

Figure 17 presents the estimated shear correction factors with the measured ones for the UC-Davis study. The shear strength mastercurve of the Control mix is applied again to the estimation.When a polymer-modified mixture, CR-TB or SBS-LG, is applied for the prediction, the estimatedshear correction factors coincide with the measured correction factors obtained via the asphaltconcrete rut depth prediction procedure. Because the Control mix is an unmodified mixture but theUC-Davis full-scale tests use polymer-modified mixtures, the estimated shear correction factor forthe Control mix deviates from the measured one. The relevant estimation would be for polymer-modified mixtures, and the estimated shear correction factor can also improve asphalt concreterut depth predictions when moderate shear flow is expected.

The shear stress and strength concepts that are used to estimate the shear correction factors alsocan express the effect of shear flow according to loading conditions and materials. However, allthe estimations of the shear correction factor in this study utilise the shear strength mastercurveof the Control mixture (unmodified binder mixture) only. In order to verify the reasonableness ofthis approach, the modified mixtures should be subjected to monotonic testing, and then, a shearstrength mastercurve can be developed to estimate the shear correction factors for the modifiedmixtures.

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Figure 16. Comparison of estimated and measured shear correction factors of FHWA ALF mixtures: (a)estimated factors only and (b) to (d) comparisons.

Figure 17. Comparison of shear correction factors for UC-Davis study when applying each property ofFHWA ALF mixtures.

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8. ConclusionsA summary of this study’s findings and the conclusions that can be drawn from this study are asfollows.

• The shift model is implemented in the LVECD program developed by the NCSU researchteam to evaluate rut depths in the asphalt pavement for realistic loading and environmentalconditions.

• The shift model implemented in the LVECD program predicts the rut depths of NCAT testtrack sections and FHWA ALF test sections.

• The LVECD model slightly over-predicts rut depth for the NCAT test track sections. Thisoutcome is due to the fact that ageing occurs in the NCAT test track pavements, but theLVECD program does not account for the effects of ageing. Thus, the measured rut depthsare lower than the predicted ones.

• The LVECD program with the shift model assesses the rut depths of the FHWA ALFsections within the same ranking order, but over-predicts them. This over-prediction is dueto excessive shear flow existed in the pavements due to channelised loading and high testtemperatures.

• Rut depth predictions obtained from the UC-Davis full-scale test results support the hypoth-esis that the TSS test protocol can represent field conditions, i.e. the shear effect on rutting,at least to some extent.

• A shear correction factor is suggested in order to include the effect of shear flow undersevere loading conditions. The shear correction factor is defined as the ratio of the maximumshear stress to the shear strength. The shear strength is calculated from the shear strengthmastercurve that can be constructed via monotonic tests at various loading conditions, suchas different temperatures and strain rates.

This study shows that the shift model implemented in the LVECD program predicts rut depthsof asphalt concrete well for ordinary loading conditions such as those found for typical in-serviceasphalt paved roads. The predictions prove the potential of the proposed combined shift modeland TSS test protocol. However, the model requires a correction factor to predict rut depthsaccurately in cases where shear flow governs permanent deformation. The ratio of shear stress toshear strength provides a good estimated shear correction factor; therefore, the shift model canpredict rut depths even under severe shear flow conditions. However, this verification is limitedto the FHWA ALF Control mixture. Additional testing is required to verify the concept of theshear correction factor.

AcknowledgementsThe authors gratefully acknowledge the support of the FHWA.

FundingThis research is sponsored by the Federal Highway Administration under project No. DTFH61-08-H-00005.

ReferencesChoi, Y., & Kim, Y. R. (2013a). Development of calibration testing protocol for the permanent deformation

model of asphalt. In Transportation research record: Journal of the transportation research board, no.2373 (Vol. 4, pp. 34–43). Washington, DC: Transportation Research Board of the National Academies.

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Choi, Y., & Kim, Y. R. (2013b). Development of characterisation models for incremental permanent defor-mation model for asphalt concrete in confined compression. Road Materials and Pavement Design, 14,266–288.

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