Development of a Mechanistic-Empirical Model to Characterize Rutting in Flexible Pavements

e Taiwanand pavingnges in theddition, athe ruttinglayer, and

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Development of a Mechanistic-Empirical Model toCharacterize Rutting in Flexible PavementsJian-Shiuh Chen, P.E.1; Chih-Hsien Lin2; Erwin Stein3; and Jurgen Hothan4

Abstract: Dramatic increases in the number and weight of vehicles have resulted in severe rutting on highways in Taiwan. ThArea National Freeway Bureau constructed an in-service test road in 1996 to investigate the effect of pavement structuresmaterials on pavement performance. A mechanistic-empirical rutting model was developed to account for material property chaprogression of rutting over time and the cumulated compressive plastic strains of all layers on the basis of traffic loading. In athree-dimensional, dynamic finite-element simulation was established to calculate pavement responses that were input intomodel for predicting permanent deformation. Traffic speed showed significant impact on vertical strains at the top of the surfaceits influence was consistent with those measured by other researchers. The rutting parameters in the model were calibrated usiobtained from the field test, and the validation outcome showed that their predictions were in good agreement with measuredresults of this paper demonstrate that incorporating the mechanistic-empirical approach in the prediction of rutting is viable anvaluable information on the contribution of each layer to permanent deformation in flexible pavements.

DOI: 10.1061/~ASCE!0733-947X~2004!130:4~519!

CE Database subject headings: Pavement design; Flexible pavements; Simulation models.

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Introduction

Data collected from toll stations in Taiwan indicated that theerage tandem axle weight of heavy vehicles reaches 100which is much higher than the allowable weight of 80 kN~Chenet al. 2001!. Rutting, the load-induced permanent deformatiopaving materials, is becoming the major distress in flexible pments. Approximately one-third of flexible pavements need trehabilitated annually, which costs about 70% of the maintenbudget in Taiwan~MOTC 1998!. Pavement engineers have btrying for years to control the rutting trend. The rut depth ocon a pavement surface due to mixture densification, plastic dmation, shoving, and other factors. This paper is primarilycused on plastic deformation observed on flexible pavemNewer materials such as polymer-modified asphalt concretecomposites used to reduce rutting demand more fundamentsign principles. Highway agencies feel that there is an urgentto better design the pavement structure in light of heavier lohigher traffic volume, and newer materials. The cornerstonpavement design is the ability to predict the behavior of pamaterials by rational methods.

1Professor, Dept. of Civil Engineering, National Cheng Kung UnTainan 701, Taiwan.

2PhD Candidate., Dept. of Civil Engineering, National Cheng KUniv., Tainan 701, Taiwan.

3Professor, Institute of Structure and Numerical Mechanics, HannUniv., Hannover 30167, Germany.

4Professor, Institute of Transportation Engineering and PlanHannover Univ., Hannover 30167, Germany.

Note. Discussion open until December 1, 2004. Separate discumust 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 June 13, 2002; approved on April 23, 2003.paper is part of theJournal of Transportation Engineering, Vol. 130,
No. 4, July 1, 2004. ©ASCE, ISSN 0733-947X/2004/4-519–525/$18.00.
JOURNAL OF TRA

J. Transp. Eng. 2004.

Two basic approaches have been used in the pavementto analyze the rutting behavior in flexible pavements. Theapproach is to statistically relate rutting to pavement condisuch as material properties, loading, and environmental feaSeveral methods use indices such as the soil classification aCalifornia bearing ratio to estimate pavement performance~AI1961; Peatti et al. 1962; Shook and Finn 1962!. These empiricamethods are only applied to a given set of environmental, mrial, and loading conditions. The second approach is to formthe rutting mechanism and associate the hypothesis withment responses. The Asphalt Institute~1982! model and the She~1978! model are the typical example, which assume that mothe rutting is due to permanent deformation within the subglayer. This approach is based on the mechanistic concept,more realistically characterizes in-service pavements andproves the reliability of designs. Data from various reports, hever, indicate that the subgrade contributes only parts of therutting, and the surface, base, and subbase layers contribumajor portion of the total rutting~Krutz and Stroup-Gardin1990; Collop et al. 1995; Ramsamooj et al. 1998; ArchillaMadanat 2001; White et al. 2002!. In addition, these subgradstrain-based rutting methods do not account for the hardeffect of paving materials during pavement service time.

Nevertheless, the mechanical responses of pavements aquired for pavement performance models and can be analytevaluated. Previously the mechanistic method was not wused because of the difficulty in obtaining comprehensive chterizations for the various paving materials and mechanicasponses under traffic loading. With the recent advancemecomputing technology, the dynamic finite-element programbeen successfully used to calculate the pavement response~Zafiret al. 1994; Chen et al. 1995; Siddharthan et al. 2002!. Because othe gaps that exist in the knowledge base, the mechanistic dmethod needs to be supported by empirical relationshipsforthcomingAASHTO 2002 Guide for Design of Pavement St
tures also relies heavily on the mechanistic as well as empirical
NSPORTATION ENGINEERING © ASCE / JULY/AUGUST 2004 / 519

130:519-525.

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principles. Issues relating to the mechanistic-empirical apprneed to be better defined before practical and realistic dprocedures can be developed and put into use. This paper adeveloping a mechanistic-empirical model to characterizecontributions of the rutting behavior from all layers in flexipavements using data obtained from an in-service test road

Mechanistic-Empirical Rutting Model

It is well known that rutting increases at an increasing rate duthe initial years of operation, and then stabilizes with time~Mo-nismith and Tayebali 1988; Roberts et al. 1996!. Research hashown that the pavement response under traffic loading coof both recovery and irrecovery components~Perl et al. 1983Sousa and Weissman 1994; Uzan 1996!. The recovery part ielastic in nature, while the permanent part is related to plastIn general, elastic strain remains constant, while plastic sdecreases with increasing load application numbers.

Assume that we havel loading types and that each loadtype i is associated with a vertical elastic compressive strain (« i , j

e )in a pavement layerj. The permanent deformation in each layesummarized as the product of the compression strains resfrom traffic loading. Because the elastic compressive straindependent of the loading repetitions, the ratio of plastic totic components of the materials evaluated can be expressfollows:

« i , jp

« i , je

5m j3~N!2a j→« i , jp 5« i , j

e 3m j3~N!2a j (1)

In Eq. ~1!, « i , jp 5plastic or permanent strain at theNth applica-

tion; m j5permanent deformation parameter representing theportion between plastic and elastic strains for layerj;2a j5negative exponent indicating the rate of permanent dmation decreases with increasing load applications, i.e., reflethe hardening effect of layerj with repetitive loading; anN5repetition number. The coefficients for each layer can betermined from laboratory testing, or by using numerical optzation. This model is also incorporated in the VESYS pavemdesign and analysis procedure~Kenis 1978! and has been wideused in flexible pavement performance modeling for all matlayers.

Fig. 1. Accumulated plastic strain upon pavement surface ucontinuous traffic loading

Fig. 1 represents the accumulated plastic strain in layerj; in

520 / JOURNAL OF TRANSPORTATION ENGINEERING © ASCE / JULY/AU


t

each loading typei, the amount of plastic strain differs from otype to the next, while the elastic strain (« i , j

e ) is constant for thloading type. The first group causes more plastic strain thasecond one because of the hardening effect. The total pstrain in layerj due to the first load type after repetitions (n1,j) iscalculated by

«1,jp 5E

0

n1,j

«1,je 3m j3N2a jdN5

«1,je 3m j3~n1,j !

12a j

12a j(2)

The repetition numbern1,j can be rewritten as follows:

n1,j5F «1,jp 3~12a j !

«1,je 3m j

G 1/12a j

(3)

The total plastic strain subjected to the second load typerepetitions is then found to be as follows:

«2,jp 5E

n1,jeq,2

n1,jeq,2

1n2,j«2,j

e 3m j3N2a jdN

5«2,j

e 3m j

12a j@~n1,j

eq,21n2,j !12a j2~n1,j

eq,2!12aj# (4)

wheren1,jeq,25load equivalent number between the first load

and the second load type. A load equivalence factor~LEF! is theratio of between unit damages under two different load repetito failure in the layerj, such asNd2,j andNd1 j . Thus, the following equation is derived to calculate LEF2,j to convert the effect othe second load type to the first one:

LEF2,j5Nd2,j

Nd1,j5

n1,jeq,2

n1,j→n1,j

eq,25n1,j3LEF2,j (5)

According to Eq.~2!, we can calculate the critical plastic strto cause failure (« f , j

p ) in layer j by load repetitionsNd1,j

« f , jp 5

«1,je 3m j3~Nd1,j !

12a j

12a j(6)

The load repetitions to cause failure can be rearranged as fo

Nd1,j5F « f , jp 3~12a j !

«1,je 3m j

G 1/12a j

(7)

Nd2,j5F « f , jp 3~12a j !

«2,je 3m j

G 1/12a j

(8)

The following equation can be used to calculate LEF2 j based onEqs.~7! and ~8!:

LEF2,j5n1,j

eq,2

n1,j5

Nd2,j

Nd1,j5F «1,j

e

«2,je G 1/12a j

→n1,jeq,25n1,j3F «1,j

e

«2,je G 1/12a j

(9)

Substituting Eq.~9! into Eq. ~4!, we obtain

«2,jp 5

«2,je 3m j

12a jH S n1,j3F «1,j

e

«2,je G 1/12a j

1nx, j D 12a j

2S n1,j3F «1,je

«e G 1/12a j D 12a jJ
2,j
GUST 2004

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or «2,jp 5

«2,je 3m j

12a j@~n1,j3LEF2,j1n2,j !

12a j

2~n1,j3LEF2,j !12a j# (10)

In other words, the cumulative plastic strain («x, jp ) in layer j due

to thexth load type after applicationsnx, j can be expressed by

«x, jp 5

«x, je 3m j

12a jH S (

i 51

x

ni , j3F «x, je

« i , je G 1/12a j

1nx, j D 12a j

2S (i 51

x

ni , j3F «x, je

« i , je G 1/12a j D 12a jJ (11)

The preceding equation describes the equivalent number oapplications of all previous load types in thex load type. Thecumulative plastic strain (« j

p) for variousl load types in the layej is calculated as follows:

« jp5(

i 51

l« i , j

e 3m j

12a j@~ni , j3LEFi , j1n2,j !

12a j2~ni , j3LEFi , j !12a j#

(12)

The total plastic deformation (rp) for differentk layers, each witthicknesst j , is obtained by

rp5(j 51

k

t j3« jp5(

j 51

kt j3m j

12a j3(

i 51

l

« i , je

3@~ni , j3LEFi , j1n2,j !12a j2~ni , j3LEFi , j !

12a j# (13)

Convertingl load types to an equivalent number of the first t(n1,j

all ), we obtain

n1,jall 5n1,j3LEF1,j1n2,j3LEF2,j1...1n1,j3LEF1,j

5(i 51

l

ni , j3LEFi , j5(i 51

l

ni , j3F «1,je

« i , je G 1/12a j

(14)

The cumulative plastic strain (« jp) in layer j corresponding t

repetitions (n1,jall ) is equal to

« jp5

«1,je 3m j

12a j3~n1,j

all !12a j (15)

The total plastic strain from allk layers is found to be as follow

«p5(j 51

k«1,j

e 3m j

12a j3~n1,j

all !12a j (16)

Multiplying the plastic strain of each layer by the layer thickn(t j) to obtain the permanent deformation, and substitutingn1,j

all

from Eq. ~14!, we obtain

rp5(j 51

k t j3«1,je 3m j

12a j3~n1,j

all !12a j

5(j 51

kt j3m j

12a j3F(

i 51

l

ni , j~« i , je !1/12a jG12a j

(17)

Note that the preceding equation is not applicable to thetiary failure region, where large permanent deformations oquickly under few traffic repetitions. The rutting model propoin this study defines only the primary and secondary phas
material deformation.
JOURNAL OF TRA


In-Service Test Road

The Taiwan Area National Freeway Bureau~TANFB! began aresearch program in 1996 to investigate the effects of vapavement structures and paving materials on rut depth. Thsections on this six-lane highway represent typical traffic andvironmental conditions that pavements experience in Taiwanpavement system was built as a four-layer system, includinasphalt concrete course over a bitumen-treated base coursea granular subbase, and a subgrade, from top to down, sepa~Tsai and Chen 2001!. This test road was built with a singaggregate gradation with four binders, resulting in two contional asphalt concretes~AC! and two modified asphalt concre~MAC!, i.e., AC60/70, AC40/50, MAC1, and MAC2. Extenslaboratory tests and field surveys were conducted, and dataanalyzed and compared. The data included pavement strutraffic loading, travel speed, pavement temperature, maproperty, and performance survey. A database administeredTANFB was employed in this study for the model calibrationvalidation. This study proposes Eq.~17! to account for the contributions of all layers to rutting in flexible pavements. In eperiod of loading, the vertical compressive elastic strain at thof each layer is computed through the dynamic simulation. Urepeated traffic loading, the cumulative vertical compressivetic strains under periods of loading are calculated; then, thdepth~RD! is determined according to Eq.~18!

RD5tAC3mAC

12aAC3F(

i 51

l

ni ,AC~« i ,ACe !1/12aACG12aAC

1tbase3mbase

12abase

3F(i 51

l

ni ,base~« i ,basee !1/12abaseG12abase

1tsubbase3msubbase

12asubbase

3F(i 51

l

ni ,subbase~« i ,subbasee !1/12asubbaseG12asubbase

1tsubgrade3msubgrade

12asubgrade

3F(i 51

l

ni ,subgrade~« i ,subgradee !1/12asubgradeG12asubgrade

(18)

Dynamic Simulation

The ABAQUS program is a three-dimensional, dynamic finelement~3D-DFEM! program that has the capacity to simuactual vehicle loading conditions and estimate the structurasponse for flexible pavements. This program has been sufully used by other researchers~Zaghloul and White 1993; Cheet al. 1995; Cho et al. 1996!; thus, ABAQUS was employedthis study to analyze the response of flexible pavementstraffic loading. ABAQUS solves the dynamic analysis of traloading by using the eigenmodes of the system as a bascalculating the response. The traffic flow is separated intolevels of service~LOS! dependent on the travel speed, i.e., LOat 90 kph, LOS B at 60 kph, LOS C at 45 kph, and LOS D akph ~MOTC 1998!. The D level of service indicates high densbut stable traffic flow.

A time-dependent loading is presented in Fig. 2. To simutruck load moving at different speeds, the load cycle begins
a load magnitude equal to zero at time A in Fig. 2. After time A,

130:519-525.

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the load is increased linearly to a maximum value at time B.load magnitude remains constant during the time segmenafter which the load is decreased linearly to zero at time D.segment AB represents the approaching of the wheel, the seBC is the duration time calculated by contacted length divtraffic speed, and the segment CD shows the departure owheel. The time segment is a function of speed and the lengthe contact area. This process is repeated for the differenments in the wheel path at different times, depending on thefic speed. In 3D-DFEM, the load-time history on the loaded avaries as a function of the velocity of the moving vehicle.segments AB and CD are assumed to be 1025 s as micro-time(Dt) when a wheel just gets on the starting node or away fromterminal node.

In the 3D-DFEM analysis, paving materials were dividedtwo groups: asphalt mixtures and granular material. Resmodulus experiments were conducted for each group, anactual material behavior was taken into account. Asphalt mixwere modeled as a viscoelastic material that is time-temperature-dependent. The time-dependent properties werresented by instantaneous and long-term shear moduli. Theperature effect was considered through the changes inmodulus values at different temperatures. Granular matewhich consist of base, subbase, and subgrade, were mousing the Drucker-Prager model. This is an elastic-plastic min which granular materials are assumed to behave as elastterials for low stress levels. When the stress level reachestain yield stress, the materials will start to behave as an elaplastic material.

The 3D-DFEM model was developed to represent the pment structure using brick elements, as shown in Fig. 3. Becof symmetry, one-half of the wheelpath, together with one sidthe surrounding region, was used. The finite-element meshsists of a fine mesh close to the load and a coarse mesh fathe load. Mesh dimensions in the vertical direction were seleto match the pavement thickness. A 5.28-m-long wheelpathhalf-infinite elements on both sides was used to reduce theeffect. Both the asphalt concrete surface and base coursesmodeled as a double-element layer. The subbase course waeled as a single-element layer, whereas the subgrade was musing half-infinite elements. The appropriate boundary condiwere used. The mesh dimensions were constrained to satisappropriate aspect ratio to have the loaded area required aachieve the desired degree of detail.

A 20-m-long wheelpath with two 12.2 m unloaded endsboth sides was used to reduce the end effect. The contin

Fig. 2. Load amplitude function

moving loading on a pavement is simulated as shown in Fig. 4.



t

-

-

e-d

This is to simulate the effect of a vehicle on the pavemensponse. Load cycle application in the 3D-DFEM analysis coners that no load is applied at a point~k! on a pavement before timA. After time A, the load cycle is applied at pointk and to subsequent points at increments of time equal to the distance bethe axles. The use of a 3D-DFEM program as modeled inmanner is to analyze the structure of a representative pavemclosely as possible. Pavement responses of each layer wereputed for the evaluation of rutting on pavements.

Pavement Responses

The preceding dynamic simulation has been used to genedatabase of pavement responses under a variety of pavstructures and loading scenarios. Computed time historsponses of vertical elastic strain are shown in Fig. 5 for vaspeeds under a traffic load of 80 kN. The layer configuratiothis figure consisted of a 15 cm AC course and a 20bituminous-treated base placed on a 30 cm subbase and asubgrade. The tensile strains~represented by a ‘‘1’’ sign! and thecompressive strains~represented by a ‘‘2’’ sign! are calculatedirectly at the top of the AC layer. The two strain peaks cospond to the presence of two loaded areas traversing baback, representing a tandem axle. There is a significant increstrain magnitude as the vehicle speed decreases. The macompressive strain increases from 15031026 to 30031026 when

Fig. 3. Finite-element mesh

Fig. 4. Dynamic simulation under loading groups

GUST 2004

130:519-525.

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the speed of the vehicle decreases from 90 to 20 kph. Thecompressive strain implies that more rutting might occur wthe traffic travels at a lower speed, i.e., at the congested levFig. 5, negative strain indicates compression and positive srepresents tension. With increasing traffic speed, the portiopositive strain increases, thus sometimes moving to the teregion. Lower speeds primarily result in compressive strwhereas higher speeds cause tensile and compressive straternately. The characteristics of the computed strain historsimilar to those recorded in the field test by other researc~Sebaaly and Tabatabaee 1993; FHWA 1997!.

Parameter Determination

The parameters~a andm! in the rutting model are determinedeach layer using numerical optimization. To perform this taskvertical compressive strain of the middepth of each layer mucalculated according to pavement dynamic simulation. Finthe set parametersa and m involves solving the following optmizing problem:

Minimize F(s51

n

~RDspred2RDs

meas!2G (19)

where RDspred5predicted rut depth; RDs

meas5field measuremenandn5all sections being evaluated.

The vertical elastic compressive strain on the top of eachis calculated and input to Eq.~18! to obtain predicted rut dep(RDs

pred) for a sections. Field measurements (RDsmeas) for this

particular section were compared with the calculated onesrut depth was measured using the 3 m straight-edge method. Trut depth was averaged over 12 cross-profile measurementsalong each section. The process is to minimize the differenpredicted and measured rut depths for all sectionsn.

The results of this minimizing process are a set of aveparametersa andm values for each layer of the pavement. If oset of a and m values produces a good fit, the model and

Fig. 5. Effects of travel speeds moving on pavement AC60/7temperature 60°C

Table 1. Parameters ofa andm

Parameter

Surface

AC60/70 AC40/50 MAC1

a 0.20 0.24 0.17m 9.2031023 4.6031023 5.1231023

JOURNAL OF TRA


l-

coefficients are used to estimate rutting. A total of 69 secwere used to calibrate the model. Vertical elastic comprestrains were calculated for each layer. The calibrated reslisted in Table 1.

The sum of the squared error is 40.3 mm2. The standard erroof estimate is 3.04 mm; this is slightly larger than the stanerror in measuring the rut depth, i.e., 2.86 mm. The ratio betthe standard error of estimate of the model and the standaviation of observed rutting is 0.83; therefore, the model provimproved prediction over the mean measured rut depth. Nota and m values are site-related; each test section may havunique parameters. The availability of historical traffic as wetime-series distress is essential to perform proper calibration.collected at later times in the test road were used to validatmechanistic-empirical model.

Model Validation

To validate the model’s adequacy, the preceding calibrated mis used to predict rut depths obtained from later surveys. Figa plot of the predicted versus observed rutting values. The ovations are distributed around the equality line, indicating a gfit between the model and the data. The Wilcoxon Matchedtest is performed to test the hypothesis that the observedpredicted rutting values are drawn from the same distributionsignificant level of test is at 0.05~5%!. The test shows that thp-value is 0.698, which is much higher than the significance lTherefore, the observed and predicted rut depths are conclube from the same distribution.

Fig. 7 shows the rut depth for the AC60/70 pavement9,340,772 repetitions. Traffic loading within the regulated 14causes much less rutting than the overloaded 22.5 t. As theweight is overloaded, the surface layer tends to be subjectmore rutting because of stress concentration, which leads tting at the top of the pavement structure. Note thatbituminous-treated base shows good resistance to rutting agranular subbase is susceptible to more rut depths under hloads. All layers contribute to the overall rut depth as show

Base Subbase SubgraMAC2

0.145.0331023 1.0331024 1.173 7.631023

Fig. 6. Comparison between predicted and observed rut dep


130:519-525.

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Fig. 7. The contribution of each layer to rutting depends on trloading, material properties, and pavement structure.

Conclusions

Based on the analyses presented in this paper, the followingclusions were made:• A mechanistic-empirical model was developed to predict

ting depth as a function of pavement responses, materialerties, and traffic characteristics. This model estimateddepth in each finite layer as the product of the compresstrain in that layer and the material permanent deformationassociated with that layer.

• A dynamic simulation was established to calculate paveresponses of all layers subject to different speeds. All tpavement responses were input into the mechanistic-empmodel to calibrate the rutting parametersa and m. The cali-brated model reasonably fit the data points, with a stanerror lower than the measurement error of rut depth.

• The maximum vertical compressive strain at the top ofsurface layer corresponding to a travel speed of 20 kphtwo times greater than that of 90 kph. Traffic loading aspeed of 20 kph primarily resulted in compressive strain onsurface, whereas, for traffic loading at 90 kph, the strain vafrom compression to tension alternately.

• The mechanistic-empirical rutting model was validated usidifferent set of data obtained at different times from the stest sections of the in-service test road. The results showreasonable agreement between predicted and observedepths. Estimation of the rutting parametersa andm could beenhanced by calibrating each material layer to specific mrial types and site conditions.

Acknowledgments

The writers are very grateful to the National Science Cou~NSC91-2211-E-006-098! and the Ministry of Transportation aCommunication for providing financial support and field astance. The second writer is indebted to the National SciCouncil for providing a fellowship during his research in Gmany. Special thanks are extended to the anonymous revifor providing valuable comments.

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Fig. 7. Layer contribution to rut depth

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Documents

Development of a Mechanistic-Empirical Model to Characterize Rutting in Flexible Pavements