Rutting Prediction of Asphalt Pavement Layer Using C-ϕ Model

ixrmittingss design.nt design.

uation forhthee rut depth

Dow

nloa

ded

from

asc

elib

rary

.org

by

MA

RR

IOT

T L

IB-U

NIV

OF

UT

on

12/0

2/14

. Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

Rutting Prediction of Asphalt Pavement LayerUsing C – f Model

T. F. Fwa1; S. A. Tan2; and L. Y. Zhu3

Abstract: Past research has shown that the concept ofC–f ~cohesion and angle of friction! can be applied for asphalt paving mdesign. It has also been established that theC–f model is able to analyze the behavior of asphalt pavement under load, thereby pethe incorporation of mechanistic or semimechanistic distress models into asphalt mix design as well as pavement thickneTherefore theC–f concept offers a useful basis for an integrated procedure for asphalt paving mix design and asphalt pavemeThis paper further illustrates the usefulness of theC–f based approach by developing a rutting prediction model based on theC–fmodel. The proposed rutting prediction model employs the widely adopted expression of power relationship as the basic eqprediction of cumulative damage. The basic expression is modified by incorporating the following effects:~1! the effect of load througa stress ratio computed using theC–f concept,~2! the effect of temperature, and~3! the effect of loading speed. The applicability ofmodel is demonstrated using laboratory wheel tracking tests on three different mix types. A proposed procedure of applying thprediction model for estimation of rut depths in in-service pavements is also outlined.

DOI: 10.1061/~ASCE!0733-947X~2004!130:5~675!

CE Database subject headings: Asphalt pavements; Friction; Bearing capacity; Predictions.

, es-picalRut-

atedari-on innsibleave-phaltroce-P

n

ixrchers

51;con-xialthe

withturesmu-ons inad-

toolsmental-ment

t8,

ratedr-pastria. Itheg theodelssign.tedment

ctioniontion-age.ingted

CivilSin-

pt. ofent,

pt. ofent,

sionste bygingpos-2003.

4/5-

Introduction

Rutting is a major distress form found in asphalt pavementspecially when the ambient temperature is high as in a hot troclimate or during the summer months of temperate countries.ting is caused by the accumulation of irreversible~or permanent!deformation in all pavement layers under the action of repetraffic loading. Among the contributions of rut depth by the vous pavement layers, the cumulative permanent deformatithe surface course of asphalt pavement is known to be respofor a major portion of the final rut depth measured on the pment surface. Therefore rutting resistance of a paving asmixture is one of the important considerations in standard pdures for asphalt mix design~Asphalt Institute 1997; SHR1994!. This paper describes an approach that employs theC–f~cohesion and angle of friction! concept for rut depth predictioin an asphalt paving layer.

The idea of applying theC–f concept to asphalt paving mdesign was actively pursued by a number of pavement resea

1Professor, Center for Transportation Research, Dept. ofEngineering, National Univ. of Singapore, 10 Kent Ridge Crescent,gapore 119260, Republic of Singapore~corresponding author!. E-mail:[email protected]

2Associate Professor, Center for Transportation Research, DeCivil Engineering, National Univ. of Singapore, 10 Kent Ridge CrescSingapore 119260, Republic of Singapore.

3Research Engineer, Center for Transportation Research, DeCivil Engineering, National Univ. of Singapore, 10 Kent Ridge CrescSingapore 119260, Republic of Singapore.

Note. Discussion open until February 1, 2005. Separate discusmust be submitted for individual papers. To extend the closing daone month, a written request must be filed with the ASCE ManaEditor. The manuscript for this paper was submitted for review andsible publication on January 14, 2003; approved on November 24,This paper is part of theJournal of Transportation Engineering, Vol.130, No. 5, September 1, 2004. ©ASCE, ISSN 0733-947X/200
675–683/$18.00.
JOURNAL OF TRANSPORTA

J. Transp. Eng. 2004.

in the early 1950s~McLeod 1950; Endersby 1951; Goetz 19Smith 1951!. Research in this direction subsequently was distinued due probably to the complexity of the laboratory triatests which are time consuming and the difficulties in relatingtest results to field behavior of paving mixtures. However,modern test equipment, triaxial testing of asphalt paving mixis no longer prohibitive. The ability of this test procedure to silate different stress states has led to its widespread applicatigeotechnical engineering. Furthermore, the availability ofvanced theories and powerful computational and analyticalmeans that researchers can now make better use of fundamaterial properties like cohesionC, angle of frictionf, and elastic modulus for the purpose of asphalt mix design and pavestructural design.

The writers started the research on the use of theC–f concepfor asphalt paving mix design in 1992~Fwa et al. 1995, 1992001!. These earlier research efforts have proposed aC–f basedanalytical asphalt paving mix design concept. It was demonstthat the proposedC–f model could analytically derive the Mashall test results, hence offering a useful tool for analyzingpavements that were designed on the basis of Marshall critewas also established that theC–f model was able to analyze tbehavior of asphalt pavement under load, thereby permittinincorporation of mechanistic or semimechanistic distress minto asphalt mix design as well as pavement thickness deTherefore theC–f concept offers a useful basis for an integraprocedure for asphalt paving mix design and asphalt pavedesign.

This paper presents the results of a new phase of theC–fresearch program which is aimed to develop a rutting predimodel using theC–f concept. The proposed rutting predictmodel employs the widely adopted expression of power relaship as the basic equation for prediction of cumulative damThe basic expression is modified by incorporating the followeffects: ~1! the effect of load through a stress ratio compu
using theC–f concept,~2! the effect of temperature, and~3! the
TION ENGINEERING © ASCE / SEPTEMBER/OCTOBER 2004 / 675

130:675-683.

on-rent

ctorsse of

ema-werh willon the, ther rut

h arevicetionlop-

re ofl ap-couldhavel. Bysider

goodmentd in

ithinearchtion-. Tothe

rma-by a

ri-ingphaltnderanism9;

wasn thisent-r andearlie

-.

f

om-drload

-givenpeed

ng ofpliedy, the

of

-

es-

theadbeen

ristics

of atandfunc-lingnaly-lasticyieldacityre byier

byovidewingload-rack-g forphaltf the

Dow

nloa

ded

from

asc

elib

rary

.org

by

MA

RR

IOT

T L

IB-U

NIV

OF

UT

on

12/0

2/14

. Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

effect of loading speed. The applicability of the model is demstrated using laboratory wheel tracking tests on three diffemix types.

Proposed Form of Prediction Model

Identification of Model Parameters

Past research has identified the following as the important fahaving major effects on rut development in the surface couran asphalt pavement~Finn 1967; Ameri-Gaznon 1989!: ~1! mag-nitude of traffic loads,~2! loading speed,~3! number of loadrepetitions,~4! pavement temperature, and~5! rutting resistancof asphalt mixture. In general, for a given asphalt pavementterial, a deeper rut will develop under heavier traffic loads, lotraffic speeds, and higher pavement temperature. Rut deptalso increase as more and more load repetitions are appliedpavement. When different asphalt mixtures are consideredasphalt mix with lower rutting resistance will develop a deepewhen all other conditions are equal.

Since the five factors identified in the preceding paragrapvariables governing the operation conditions of any in-serpavement, it is desirable for any practical rut depth predicmodel to include their respective effects in the rut depth devement analysis. A prediction model that excludes one or mothese factors will severely restrict its usefulness for practicaplications. For example, a model that ignores loading speedonly be applied for analysis of pavement rutting in roads thattraffic speeds similar to those used in developing the modethe same argument, any prediction model that does not conasphalt mixture properties and its rutting resistance is onlyfor studying rut development in one particular asphalt pavetype. It is for these reasons that all five factors were includethe model development described in this study.

Basis of Prediction Model

This study focuses on load-induced deformation occurring wthe asphalt paving layer. Since early 1960s, considerable reseffort has been directed towards deriving mechanistic relaships to describe the development of rut under traffic loadingdate, however, no single universally accepted model ofmechanistic relationship for traffic-induced permanent defotion has emerged from the literature. One theory advancednumber of researchers~Finn 1967; Van de Loo 1974; AmeGaznon 1989; Leahy 1989! states that the concept of load bearstability is applicable for estimating the resistance of an aspavement layer to rutting under repeated traffic loading. Uthis theory, shear deformation is regarded as a major mechleading to rutting~Hofstra and Klomp 1972; Ameri-Gaznon 198Fwa and Tan 1992!.

The concept of bearing stability and shear deformationadopted in the analysis of rut depth development described ipaper. TheC–f model for asphalt mix design and pavembehavior analysis presented by Fwa et al.~2001! was the analytical tool for computing the bearing capacity of an asphalt layeits structural responses under load. Readers are referred toworks of the writers for details of the following:~1! laboratorydetermination of cohesionC, angle of frictionf, and the corresponding modulus of elasticity of an asphalt mixture~Fwa et al1995, 1998!, ~2! C–f approach for asphalt mix design~Fwaet al. 2001!, and~3! finite elementC–f model for the analysis o
structural responses of asphalt layers~Fwa et al. 1995, 2001!.
676 / JOURNAL OF TRANSPORTATION ENGINEERING © ASCE / SEPTEM


r

The proposed rut depth prediction model follows the cmonly adopted basic power equation form~Majidzadeh anKhedr 1979; SHRP 1993; Qi and Witczak 1998! to account fothe cumulative development of rut depth with the number ofapplications, as shown by the general expression of Eq.~1!

R5k•~N!a (1)

whereR5rut depth afterN number of load repetitions;a5modelconstant; andk5model coefficient. Eq.~1! is applicable for computing the rut depth of a known pavement structure under aapplied load and fixed loading conditions such as loading sand pavement temperature.

To expand the scope of coverage of the model of Eq.~1!, themodel coefficient can be represented by a function consistithe effects of pavement layer properties, magnitude of apload, loading speed, and pavement temperature. In this studk function is defined as follows:

k5~L !b•~T!c

•~ t !d with L5P/B (2)

whereL5load ratio of the magnitude of the repeated loadP to themaximum allowable loadB that defines the bearing capacitythe asphalt pavement layer;T5pavement temperature;t5loadingduration of each load application; andb, c, and d5model constants.

Substituting Eq.~2! into Eq. ~1! presents the complete exprsion for the proposed model of this study

R5~N!a•~L !b

•~T!c•~ t !d (3)

It is noted that the effects of the applied loadP and the loadbearing capacityB of the asphalt layer are accounted for byload ratioL. Though not exactly identical to the concept of loratio adopted here, some other forms of stress ratio haveused by researchers in analyzing the deformation characteof asphalt mixtures~Huschek 1977; Hopman et al. 1992!.

The load bearing capacity of the asphalt surface layerpavement structure is the maximum applied load it can withsbefore shear failure in the asphalt layer takes place. It is ation of the geometric properties~layer thickness! and structuraproperties~C andf! of the asphalt layer as well as the underlypavement layers. It is computed by means of finite element asis. The asphalt mixture was idealized as elastic perfectly pand the Mohr–Coulomb yield criterion was adopted as thefunction. Examples on the computation of load bearing capof an asphalt surface layer in a multilayer pavement structumeans of the finite elementC–f model can be found in an earlpaper by Fwa et al.~2001!.

Laboratory Experimental Program for ModelCalibration

Scope of Experimental Program

The proposed model of Eq.~3! was verified and calibratedmeans of a laboratory experimental program designed to prmeasurement data covering suitable ranges of the follomodel parameters: magnitude of applied load, number ofapplications, speed of loading~or loading duration!, and test temperature. A laboratory rutting test conducted using a wheel ting machine was adopted to provide the needed data, allowinvariations in the mentioned model parameters. For a given asmix type, the main experimental and analytical components o
model calibration program consisted of the following:
BER/OCTOBER 2004

130:675-683.

e rute of

ohe-st

ysis:thermine

Theg

imen-

resalsoed, ae rut-

theof rueremix

adedsingTypelightgre-

de ofslag

gatee C

bindegre-

ifiedused

testpara

free-twowide,ckser ofntact

pthm wasin thee rutm rutmous

ased

mmcov-cip-theheeles per

t

t

Dow

nloa

ded

from

asc

elib

rary

.org

by

MA

RR

IOT

T L

IB-U

NIV

OF

UT

on

12/0

2/14

. Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

1. Wheel tracking test: This test was conducted to producdepth development data covering the required rangmodel parameters;

2. Triaxial test: This test was performed to determine the csion C, angle of frictionf, and elastic modulus of the temix;

3. Bearing capacity determination by finite element analBased on theC–f approach, a finite element model ofwheel tracking test was developed and analyzed to detethe bearing capacity of the asphalt layer tested; and

4. Model calibration by statistical regression analysis:model coefficients of Eq.~3! were determined by performinstatistical regression analysis on the data derived expertally and analytically from steps 1–3.

It is known that different mix compositions of asphalt mixtuwill give rise to different rutting resistance responses. It isknown that even when the mix composition remains unchangchange of the type of aggregate or binder would change thting characteristics of the asphalt mixture. To illustrate thatproposed model could be used to represent the developmentfor different asphalt mix types, three different asphalt mixes wincluded in the experimental program. Table 1 shows thecompositions of the three mixes. Mix Type A was a dense-grasphalt mix commonly used in Singapore. It was prepared ugranite aggregate and penetration grade 60/70 asphalt. MixB was a steel-slag mix which was used at some busy trafficintersections in Singapore to reduce rutting. It had similar aggate gradation to that of Mix Type A and used the same graasphalt, but the granite aggregate was replaced by steelThese two mix types offer a comparison of the effect of aggreon the test results. To examine the effect of binder, Mix Typwas added by replacing the penetration grade 60/70 asphaltby a polymer modified asphalt binder, while keeping the aggate gradation and mix proportion unchanged.

Laboratory Wheel Tracking Test

The wheel tracking test machine used in this study was modfrom a three-wheel immersion-tracking machine commonlyin the United Kingdom~Road Research Laboratory 1962!. Themachine allowed control of the following test parameters:temperature, wheel speed, and wheel load. The modified aptus consisted of two parallel sets of loading wheels with arotating solid rubber tire each. This allowed for the testing ofspecimens simultaneously. The rubber tire measured 45 mmwith a diameter of 200 mm. Loads in the form of metal blowere applied to the wheels through a loading arm. The numbmetal blocks could be selected to fix the tire-specimen co

Table 1. Composition of Test Mixes

Mixtype

Aggregate gradation~percent pa

19.0~mm!

13.2~mm!

6.3~mm!

3.2~mm!

2.4~mm!

1.2~mm! ~

A 100 90 63 45 — 26

B 100 85 — — 51 —

C 100 90 63 45 — 26

pressure at a level within the range of 420–690 kPa.



t

.

r

-

A major modification to the original machine was the rut demeasurement method where an automated electronic systeinstalled to replace the chart drum and pen recorder systemoriginal apparatus. A laser sensor was installed to record thdepth at the midlength of each specimen, where the maximuoccurred. The signal of the laser sensor was fed to an autonodata acquisition unit which would log the progressively increrut depth with time to an accuracy of 0.01 mm.

For each test, two prismatic specimens measuring 4073138 mm390 mm were prepared. Each rubber tired wheelered a path of 254 mm longitudinally on a specimen in a rerocating motion. Each cycle of the reciprocating motion ofwheel produced two passes for all the points in the two wtracks. A constant test speed within the range of 0–80 pass

Fig. 1. Finite element mesh for laboratory wheel tracking tes

Aggregatetype Binder type

Binderconten

~%!300

~mm!212

~mm!75

~mm!

14 — 6 Granite Penetrationgrade 60/70

5.0

— 13 8.5 Steel slag Penetrationgrade 60/70

5.0

14 — 6 Granite Polymermodifiedasphalt

5.0

ssing!

600mm!

—

21

—


130:675-683.

ievedpeed

bathle totest

wateroomtatthe

di-tures at

g toaterre. At the

di-ssion

foundtch-

nter byarriedfining

dy byhat

spexature,. Theratureboutand

ouslyed by

0 toa forltpeci-

se re-iven

tion

astiche

Dow

nloa

ded

from

asc

elib

rary

.org

by

MA

RR

IOT

T L

IB-U

NIV

OF

UT

on

12/0

2/14

. Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

min could be selected. The control of wheel speed was achby a constant torque gauged motor equipped with electronic scontrol.

Test temperature was maintained by means of a waterheated with an electric heating element. This made it possibkeep the temperature at the top, bottom, and midpoint ofspecimens within 1°C of the desired test temperatures. Thebath temperature could be adjusted within a range from rtemperature~about 28°C! to 70°C by an electronic thermoswith a differential setting of 0.2°C. An adjustable weir keptwater level at the top surface of the test specimens.

Triaxial Test for C –f Determination

The apparatus used was modified from a conventional 6-in.~152-mm! diameter triaxial cell meant for soil testing. The major mofication required to the triaxial cell was to provide temperacontrol to cater to the need to test asphalt paving mixturedifferent temperatures. A perspex water bath sufficiently bicontain the triaxial cell was introduced. The water in the wbath was maintained at 2 to 3°C above the test temperatuthermal reservoir was employed to provide heated water adesired temperature.

The test specimens measured 102 mm~4 in.! in diameter an200 mm~approximately 8 in.! in height. The 200 mm tall specmens were compacted by means of double-plunger compreunder a static pressure of 25 kPa for 20 min. This has beeneffective to produce uniform density distributions closely ma

Fig. 2. Rut depths of M

ing those in Marshall specimens compacted by the standard drop-



hammer compaction method~Fwa et al. 1993!. The test specimewas placed between the loading platens and sealed from wameans of an impervious rubber membrane. Each test was cout at a selected constant temperature, strain rate, and conpressure. The loading rate as established in an earlier stuFwa et al.~1995, 1998, 2001! was 50.8 mm/min, the same as tadopted in the standard Marshall test.

During testing, the entire cell was immersed in the perwater bath. The main test parameters included test temperspeed of loading, and the magnitude of confining pressuretime required to heat up a specimen to a uniform test tempevaried from about 20 min for a test temperature of 40°C to a60 min for a test temperature of 60°C. The applied loadvertical displacement of the specimen were recorded continuthroughout the test. The vertical displacement was measurmeans of an LVDT.

Tests at four or more confining pressures ranging from400 kPa~58 psi! were performed to provide the necessary datdetermining the cohesionC and angle of frictionf of an asphamixture at a given test temperature and strain rate. Three smens were tested for each confining temperature. From thesults, Mohr circles were drawn to define a failure envelope gby a line tangent to the Mohr circles. The cohesionC is theintercept of the line with the vertical axis, and the angle of fricf is equal to the angle of inclination of the line.

For the triaxial test associated with each Mohr circle, an elmodulusEp was computed from the initial linear portion of t

e A in wheel tracking tests
ix Typ
deviator stress versus strain curve of the test. Based on the strain

BER/OCTOBER 2004

130:675-683.

nt of

t theren. Itpro-gree-

-

d ofitable

inerack-axi-

egli-ntlyacityuntil

ithinun-

e asodel

ture

threelevelskPa,

nd 60iallyratureepths000ths of

, andMixat

. Thebe

ngfuld forvels

Dow

nloa

ded

from

asc

elib

rary

.org

by

MA

RR

IOT

T L

IB-U

NIV

OF

UT

on

12/0

2/14

. Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

calculated from the total vertical displacement measuremethe triaxial test, earlier works by Fwa et al.~1995, 1998! haveconfirmed findings by past research of other researchers thawas a well-defined linear relationship up to about 1% straiwas also found that elastic modulus determined this wayduced results by finite element analysis which are in good ament with experimental measurements of the triaxial test~Fwaet al. 1995! and Marshall test~Fwa et al. 1998!, asphalt mix design ~Fwa et al. 2001!, and bearing capacity determination~Fwaet al. 2001!. These earlier works have shown that the methodetermining elastic modulus is a practical approach and is sufor the present study.

Finite Element Analysis of Bearing Capacity

An axisymmetric finite element model was applied to determthe bearing capacity of the asphalt layer tested in the wheel ting test. Fig. 1 depicts the finite element mesh adopted. Thesymmetric vertical boundary imposed was found to have ngible effect on the analysis and the model was sufficieaccurate for bearing capacity computation. The bearing capwas determined by increasing the applied load incrementallyshear failure took place.

It should be noted that the development of shear failure wthe asphalt surface layer is influenced by the property of thederlying layer. In the event of a multilayer pavement structuris found in the case of an actual pavement, a finite element m

Fig. 3. Rut depths of Mi

for the multilayer pavement structure should be used. Examples



of C–f finite element analysis of multilayer pavement struccan be found in Fwa et al.~2001!.

Development of Prediction Models

Test Results

Wheel Tracking TestsWheel tracking tests were conducted for three applied loads,wheel speeds, and three test temperatures. The three loadselected produced contact pressures of 420, 560, and 690respectively. The three wheel speeds applied were 20, 40, awheel passes per min. All three asphalt mix types were inittested under the following three temperatures: room tempeof 28, 40, and 60°C. Figs. 2 and 3 show the measured rut dfor Mix Types A and B, respectively. In general, after 3,passes of wheel loads, these two mix types produced rut depthe order of about 10 mm at 60°C, about 1 to 2 mm at 40°C0.3 mm at 28°C. Much smaller rut depths were recorded forType C~see Fig. 4!, with rut depths of the order of about 2 mm60°C, about 0.8 mm at 40°C, and less than 0.05 mm at 28°Crut depth readings for Mix Type C at 28°C were too small tomeasured reliably and could not be used for any meanianalysis. Therefore additional tests at 70°C were conducteMix Type C to produce the required data at three different le

e B in wheel tracking tests
x Typ
of test temperature.


130:675-683.

rived

uredeinderith asion

westnally

ixag-

ckinginderecamder

pen-0 andiese

ameand

tem-

l,t de-uggestcon-ixn, thealtMix

steel

es s

Dow

nloa

ded

from

asc

elib

rary

.org

by

MA

RR

IOT

T L

IB-U

NIV

OF

UT

on

12/0

2/14

. Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

Triaxial TestsFor each of the three test mixtures, the material properties defrom the triaxial tests were cohesionC, angle of frictionf, andelastic modulesEp . Table 2 presents the results of the meascohesion values. The cohesionC varied with temperature. ThcohesionC decreased with test temperature because the bbecame less viscous at higher temperature. Mix Type C wmodified polymer binder was found to have the largest coheat a given test temperature. Overall, Mix Type B had the locohesion value, although at 28°C its cohesion was margihigher than that of Mix Type A. The difference between MTypes A and B was presumably caused by the difference ingregate gradation and the types of aggregate used.

Table 3 shows that larger values of angle of frictionf weremeasured at higher temperatures, due probably to better paand interlocking among the individual aggregates when the bwas less viscous. The results suggest that when the binder bsufficiently fluid, say at 40°C or higher, the effect of the bin

Fig. 4. Rut depths of Mi

Table 2. Cohesion Values of Test Mixes at Different Temperatur

Temperature~°C!

Cohesion~kPa!

Mix Type A Mix Type B Mix Type C

28 1,768.8 1,820.1 —40 616.4 341.1 692.060 290.0 249.6 392.670 — — 209.3



e

tended to diminish and the measured angle of friction was dedent more on the properties of aggregate. For example, at 460°C, Mix Types A and C~having identical aggregate propertand gradation, but different binder type! had practically the samangle of friction. On the other hand, Mix Type B had the sbinder type as Mix Type A, but different aggregate typesgradations produced different angles of friction at the twoperatures.

Table 4 reveals that the measured elastic modulusEp variedwith both test temperature and confining pressure. In generaEp

increased with the magnitude of the confining pressure, bucreased as the test temperature was raised. The results sthat both the cohesion and angle of friction of the mixturestributed to the values ofEp measured. For instance, while MTypes C and A had the same aggregate type and gradatioformer produced higherEp because its polymer modified asphwas a stronger binder. Mix Type B had the same binder asType A. Its higher elastic modulus was contributed by theslag aggregate.

e C in wheel tracking tests

Table 3. Friction Angles of Test Mixes at Different Temperature

Temperature~°C!

Angle of friction ~deg!

Mix Type A Mix Type B Mix Type C

28 15.1 13.1 —40 33.4 36.9 33.860 36.0 40.5 36.470 — — 37.1

x Typ

BER/OCTOBER 2004

130:675-683.

putedn beuringpera-th ancom-gyperinge.

sec-r thea-

ed inplied

od-

of.98,cor-

f the

tive,t rut

-

.ents,the

ounttual

willence. Aent

testtualn ad-e.for

thegt tem-

tion.d forbetruc-

e.

n thef as-formd byrack-

4.59.5

ack-Dow

nloa

ded

from

asc

elib

rary

.org

by

MA

RR

IOT

T L

IB-U

NIV

OF

UT

on

12/0

2/14

. Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

Computation of Bearing CapacityThe bearing capacity of each wheel tracking specimen comby means of finite element analysis is found in Table 5. It caseen from the table that the bearing capacity of a specimen dthe wheel tracking test was highly dependent on the test temture. The bearing capacity decreased rather significantly wiincrease in temperature within the range of 28 to 70°C. Theputed results suggest that bothC andf contributed to the bearincapacity. Mix Type C had higher bearing capacity than Mix TA due to its stronger binder, while Mix Type B had higher beacapacity than Mix Type A because of its steel slag aggregat

Prediction Model by Regression Analysis

With the test results obtained as described in the precedingtion, a multiple linear regression analysis was conducted fomodel of Eq.~3! by considering the logarithmic form of the eqution as follows:

log~R!5a log~N!1b log~L !1c log~T!1d log~ t ! (4)

The input values of rut depthR and load repetitionsN are ob-tained from test results of Figs. 4–6. The load ratiosL for differ-ent test temperatures and applied load levels are summarizTable 6. The loading time under each loading speed and apload level is also given in the table.

By means of statistical analysis, the rut depth prediction mels for the three mix types were obtained as follows:

Mix type A: R5~N!0.45•~L !2.02

•~T!0.53•~ t !0.40 (5)

Mix type B: R5~N!0.50•~L !2.27

•~T!0.51•~ t !0.16 (6)

Mix type C: R5~N!0.28•~L !1.22

•~T!0.29•~ t !0.28 (7)

In the above equations, rut depthR is in mm, load ratioL innumerical value, temperatureT in °C, and loading durationt in s.All three models are highly significant, with very high valuesstatistical coefficients of multiple determination equal to 00.95, and 0.95, respectively, for mix types A, B, and C. The

Table 4. Elastic Moduli of Test Mixes at Different Temperatures

Temperature~°C!

Confining pressure0 ~kPa!

Mix A Mix B Mix C Mix A

28 271.1 463.6 — 86040 126.2 166.4 188.2 20860 55.4 78.5 97.7 13570 — — 57.3 —

Table 5. Computed Bearing Capacity of Specimens in Wheel Tring Tests

Temperature~°C!

Maximum allowable applied load~kPa!

Mix Type A~kPa!

Mix Type B~kPa!

Mix Type C~kPa!

28 7,560 7,840 —40 4,860 5,400 5,60060 1,920 2,600 2,90070 — — 2,080



responding numbers of observations used in the derivation othree models were 344, 308, and 383.

All the power coefficients in the three models are posireflecting the relationships identified in the test results thadepth increased with the following variables:~1! number of loadapplications,~2! magnitude of applied load,~3! pavement temperature, and~4! loading duration.

Potential Application for Predicting Rut Depthof Pavements

The proposed form of rut depth prediction model given by Eq~3!can be applied for estimating rut depth of in-service pavemprovided that proper calibration is performed to determinepower coefficients. Adjustments will have to be made to accfor the following variations of input parameters for an acpavement:1. Wander effect of wheel applications. Not all wheel loads

be applied on exactly the same location in a lane. Hsome form of adjustment factor will have to be appliedconcept similar to the correction factor for runway pavemmay be used.

2. Effect of mixed traffic stream. Unlike a wheel trackingin the laboratory, the wheel loading received by an acpavement has varied wheel loads and loading speed. Idition, the load ratioL will vary with pavement temperatur

As a first approximation, the following revised procedurerut depth estimation may be adopted:

R5C(i 51

n

@~Ni !a•~Li !

b•~Ti !

c•~ t i !

d# (8)

whereC5adjustment factor for the traffic wander effect, andtotal number of traffic loading is divided inton groups accordinto the magnitude of wheel load, travel speed, and pavemenperature. An implicit assumption of adopting Eq.~8! is that theprinciple of superposition is applicable in rut depth computaIt should be noted that to obtain the bearing capacity needethe computation of load ratioL, a finite element analysis mustperformed taking into consideration the complete pavement sture of surface course, base course, subbase, and subgrad

Conclusions

A rut depth prediction model has been proposed based oconsideration of shear deformation and bearing capacity ophalt mixtures. The final expression of the model was of theof a power equation, and the power coefficients were derivemeans of statistical regression analysis of laboratory wheel t

r Different Confining Pressures

ic modulus in MPa

fining pressure400 ~kPa!

Confining pressure800 ~kPa!

Mix B Mix C Mix A Mix B Mix C

1,034.1 — 2,884.8 5,570.8 —240.0 273.5 224.7 293.0 42210.7 228.5 146.4 224.8 35

— 118.4 — — 200.6

unde

Elast

Con

.7.4.2

ing test results. The analysis presented in this paper has demon-


130:675-683.

e rutoce-s haseingstmenuting

alt’ PhD

s

nd

ls,

entam,ton,

ltfile.’’

fld

gonhia,

Dow

nloa

ded

from

asc

elib

rary

.org

by

MA

RR

IOT

T L

IB-U

NIV

OF

UT

on

12/0

2/14

. Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

strated that the proposed model could closely estimate thdepth development in laboratory wheel tracking tests. A prdure for estimating rut depths in inservice asphalt pavementalso been proposed. A field demonstration project is bplanned as the next phase of research to determine the adjufactors needed to be incorporated into the model for comprut depths in actual pavements.

References

Ameri-Gaznon, M.~1989!. ‘‘Permanent deformation potential in asphconcrete overlays over Portland cement concrete pavements.’thesis, Texas A&M University, College Station, Tex.

Asphalt Institute.~1997!. Mix design methods for asphalt, Manual SerieNo. 2, 6th Ed., Lexington, Ky.

Endersby, V. A.~1951!. ‘‘The history and theory of triaxial testing, a

Table 6. Values of Parameters in Wheel Tracking Tests

Temperature~°C!

Appliedload ~kPa!

Load ratio~3100%!

Mix A Mix B

420 5.4 5.6

28 560 7.1 7.4

690 8.8 9.1

420 8.6 7.8

40 560 11.5 10.4

690 14.7 12.8

420 21.9 16.2

60 560 29.2 21.5

690 35.9 26.5

420 — —

70 560 — —

690 — —

aLoad moving speed was measured for each wheel speed at the m

the preparation of realistic test specimens.’’Special Technical Publi-



t

cation STP No. 106, American Society for Testing and MateriaPhiladelphia, 112–137.

Finn, F. N.~1967!. ‘‘Factors Involved in the design of asphalt pavemsurfaces.’’The National Co-operative Highway Research ProgrNCHRP Rep. No. 39, Transportation Research Board, WashingD.C.

Fwa, T. F., Low, B. H., and Tan, S. A.~1993!. ‘‘Compaction of asphamixtures for laboratory testing—Evaluation based on density proJ. Test. Eval.,21~5!, 414–421.

Fwa, T. F., Low, B. H., and Tan, S. A.~1995!. ‘‘Behavior analysis oasphaltic materials using triaxial test-determined properties.’’SpeciaTechnical Publications STP 1265, American Society for Testing anMaterials, Philadelphia, 97–111.

Fwa, T. F., and Tan, S. A.~1992!. ‘‘Laboratory evaluation of ruttinpotential of asphalt mixtures.’’ASTM Special Technical PublicatiSTP 1147, American Society for Testing and Materials, Philadelp211–224.

Wheel speed~passes/min!

Load movingspeeda ~cm/s!

Loading time(1023 s)C

20 8.6 33840 18.4 159

60 34.3 8820 8.6 338

40 18.4 15960 34.3 8820 8.6 33840 18.4 159

60 34.3 88

20 8.6 338.5 40 18.4 159

60 34.3 8820 8.6 338

0.0 40 18.4 15960 34.3 8820 8.6 338

2.3 40 18.4 15960 34.3 88

20 8.6 3384.5 40 18.4 159

60 34.3 8820 8.6 338

9.3 40 18.4 15960 34.3 8820 8.6 338

3.8 40 18.4 15960 34.3 88

20 8.6 338.2 40 18.4 159

60 34.3 8820 8.6 338

.9 40 18.4 15960 34.3 8820 8.6 338

.2 40 18.4 15960 34.3 88

t of the length of wheel path.

Mix

—

—

—

7

1

1

1

1

2

20

26

33

idpoin

Fwa, T. F., Tan, S. A., and Low, B. H.~1998!. ‘‘Relating triaxial test

BER/OCTOBER 2004

130:675-683.

Mar-

.s.’’

le

,

andr-e-

altalt

halt.r-

us.e-h

n-

--

ttionsl

eprac-

ngh

Dow

nloa

ded

from

asc

elib

rary

.org

by

MA

RR

IOT

T L

IB-U

NIV

OF

UT

on

12/0

2/14

. Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

properties of asphalt mixtures to mix parameters determined byshall stability test.’’J. Test. Eval.,25~5!, 471–479.

Fwa, T. F., Tan, S. A., and Zhu, L. Y.~2001!. ‘‘ReexaminingC–f con-cept for asphalt paving mix design.’’J. Transp. Eng.,127~1!, 67–73

Geotz, W. H.~1951!. ‘‘Comparison of triaxial and marshall test resultProc., Assoc. Asphalt Paving Technol.,20, 200–245.

Hofstra, A., and Klomp, A.~1972!. ‘‘Permanent deformation of flexibpavements under simulated road traffic conditions.’’Proc., 3rd Int.Conf. on the Structural Design of Asphalt Pavements, London, Vol. 1613–621.

Hopman, P. C., Pronk, A. C., Kunst, P. A., Molenaar, A. A. A.,Molenaar, J. M. M.~1992!. ‘‘Application of the visco-elastic propeties of asphalt concrete.’’Proc., 7th Int. Conf. on the Structural Dsign of Asphalt Pavements, Nottingham, U.K., Vol. 1, 693–705.

Huschek, S.~1977!. ‘‘Evaluation of rutting due to viscous flow in asphpavements.’’Proc., 4th Int. Conf. on the Structural Design of AsphPavements, Ann Arbor, Mich., Vol. 1, 497–508.

Leahy, R. B.~1989!. ‘‘Permanent deformation characteristics of aspconcrete.’’ PhD thesis, University of Maryland, College Park, Md

Majidzadeh, K., and Khedr, S.~1979!. ‘‘Evaluation of permanent defo
mation in asphalt concrete pavements.’’Transportation Research


Record 715, Transportation Research Board, Washington, D.C.McLeod, N. W.~1950!. ‘‘A rational approach to the design of bitumino

paving mixtures.’’Proc., Assoc. Asphalt Paving Technol.,19, 82–87Qi, X. C., and Witczak, M. W.~1998!. ‘‘Time-dependent permanent d

formation models for asphalt mixtures.’’Transportation ResearcRecord 1639, Transportation Research Board, Washington, D.C.

Road Research Laboratory.~1962!. Bituminous materials in road costruction, Her Majesty’s Stationery Office, London.

Smith, V. R.~1951!. ‘‘Application of the triaxial test to bituminous mixtures.’’ ASTM Special Technical Publication STP 106, American Society for Testing and Materials, Philadelphia, 55–78.

Strategic Highway Research Program~SHRP!. ~1993!. ‘‘Developmenand validation of performance prediction models and specificafor asphalt binders and paving mixes.’’Rep. No. SHRP-A-379, FederaHighway Administration, Washington, D.C.

Strategic Highway Research Program~SHRP!. ~1994!. The superpavmix design system manual of specifications, test methods andtices, Federal Highway Administration, Washington, D.C.

Van de Loo, P. J.~1974!. ‘‘Practical approach to the prediction of ruttiin asphalt pavements: The shell method.’’Transportation Researc
Record 616, Transportation Research Board, Washington, D.C.

130:675-683.

Documents

Rutting Prediction of Asphalt Pavement Layer Using C-ϕ Model