Construction and Building Materials 23 (2009) 3398–3405

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Construction and Building Materials

journal homepage: www.elsevier .com/locate /conbui ldmat

A simple stepwise method to determine and evaluate the initiation of tertiaryflow for asphalt mixtures under dynamic creep test

Shu Wei Goh 1, Zhanping You *

Department of Civil and Environmental Engineering, Michigan Technological University, 1400 Townsend Drive, Houghton, MI 49931-1295, United States

a r t i c l e i n f o a b s t r a c t

Article history:Received 18 November 2008Received in revised form 10 June 2009Accepted 18 June 2009Available online 19 July 2009

Keywords:Flow numberTertiary flowDynamic creepRepeated loadStepwiseSimple performance testAsphalt mixtureDeformation rate

0950-0618/$ - see front matter � 2009 Elsevier Ltd. Adoi:10.1016/j.conbuildmat.2009.06.020

* Corresponding author. Tel.: +1 906 487 1059; faxE-mail addresses: sgoh@mtu.edu (S.W. Goh), zyou

1 Fax: +1 906 487 1620.

A number of research studies have focused on the linkage between material properties and pavementperformance. Part of the efforts in this research was the development of Superpave simple performancetests (SPT). One of the Superpave SPT is the repeated loading or dynamic creep test. The output of this testis the flow number, which is the initiation of tertiary flow. A common method in examining the flownumber is to locate the lowest point in the strain rate versus cycle number curve, or the minimum valueof the strain rate. However, this method may provide confusion due to the variation in the test data.Researchers have been trying to discover new effective methods for determining flow number. Theirefforts have led to the development of several excellent approaches. However, these methods need tobe more refined in order to improve the user-friendliness to engineers, researchers, and even students.A new simple stepwise method was developed and evaluated in this paper. In this process, it wasassumed that the strain would only be maintained at the same point or increased over the load cyclenumber. Then, the flow number at the minimum point of new strain rate versus cycle number was deter-mined. The flow number results from this new method are simpler and more practical compared to othermethods for determining the flow number. In addition, the rate of deformation at the secondary stagewas correlated well with the flow number using this method.

� 2009 Elsevier Ltd. All rights reserved.

1. Background

The flow number is not a new concept for asphalt paving mate-rials. It has been widely used to determine the rutting distress aswell as permanent deformation characteristics since the mid1970s [1,2]. Brown and Snaith [3] performed experiments to inves-tigate the response of an asphalt mixture due to a repeated load.The failure of the asphalt mixture was defined as the cycle numberwhen a marked deformation occurred. Brown and Cooper [4] indi-cated that the penetration grade of asphalt slightly affected thedevelopment of permanent shear strain in the FN test. Additionally,the gradation of the mixture affected the shear strain significantlyand higher shear strain was found under fewer load cycles for gap-graded mixtures.

The development of a SPT has been the focus of considerable re-search efforts in the past several years. In fact, some aspects of thetests have been available for decades, such as the dynamic modu-lus (|E*|) and flow number (FN) tests of asphalt mixtures. Thesetests were found to have a good correlation with field performance

ll rights reserved.

: +1 906 487 1620.@mtu.edu (Z. You).

[5–7]. When comparing |E*| with FN, Zhou and Scullion [8] indi-cated that FN can be better for differentiating the performanceand quality of asphalt mixtures [8,9]. Faheem et al. [10] showedthat FN is an important mixture property and has a strong correla-tion to the Traffic Force Index (TFI), which represents densificationloading by the traffic during its service life [10]. More recently, astudy conducted by Witczak [11] demonstrated that a good corre-lation exists between the FN and field rutting performance.

2. Flow number testing

The flow number test is based on the results from repeatedloading and unloading of a Hot Mix Asphalt (HMA) specimenwhere the permanent deformation of the specimen is recorded asa function of load cycles. Normally, a 0.1 s loading followed by a0.9 s rest time is applied to the specimen as shown in Fig. 1a[12–14]. In addition, an effective temperature, often referred toas rutting temperature, is used in this test [5,15].

There are three stages of flow that occurred during the test de-fined as: primary, secondary and tertiary flow [13]. Under primaryflow, there is a decrease in the strain rate with time. Then, withcontinuous repeated load application, the next phase is the second-ary flow state, which is characterized by a relatively constant strain

0.1s loading

Time (Second)

Stre

ss (

kPa)

0.9s rest period

Fig. 1a. Loading and unloading of flow number test.

S.W. Goh, Z. You / Construction and Building Materials 23 (2009) 3398–3405 3399

rate. The material enters tertiary flow when the strain rate beginsto increase dramatically as the test progresses [7]. Tertiary flowindicates that the specimen begins to deform significantly andthe individual aggregates that make up the skeleton of the mixmove past each other [16–18].

The point or cycle number at which pure plastic shear deforma-tion occurs is referred to as the ‘‘flow number”. Fig. 1b illustrates atypical relationship between the total accumulative plastic strainand number of load cycles. Flow number is based on the initiationof tertiary flow or the minimum point of the strain rate curve [5] asshown in Fig. 1c. Also, the flow number has been recommended asa rutting indicator for asphalt mixtures [1,7,11,13].

3. Existing methods and approaches to determine flow number

The traditional method locates the minimum strain rate valuein the curve of strain rate versus cycle number directly from themeasured data as the flow number [12,19,20]. However, one lowdeceptive value of strain rate could result in a misleading flownumber value [21]. Fig. 2 shows the results from one flow number

Primary

Secondary

Tertiary

Perm

anen

t Str

ain

Cycle Number

Flow Number

Fig. 1b. Typical flow number test result.

Flow Number: Minimum point of strain rate

Cycle Number

Stra

in R

ate

Fig. 1c. Strain rate versus cycle number from flow number test.

test. It is observed that several minimum values from the strainrate were found. This is a disadvantage of using the traditionalmethod. Thus, a new approach is needed to determine the flownumber value.

Since the mid 1970s, several permanent deformation methodsand approaches have been proposed. The rutting models includingPower-law model [2], VESYS model, Ohio State model, SuperpaveModel, and AASHTO Model 2002 were developed [1,8]. Many datasmoothening techniques were also employed to describe the per-manent deformation curve [22,23]. Some of these included thepolynomial fitting model, moving average periods (MAPs), andthe regression technique. In the following section, these methodsare discussed.

3.1. Three-stage model

Zhou et al. [1] proposed a three-stage model to determine thethree stage (primary, secondary, and tertiary) deformation behav-ior in the flow number test. Zhou et al. [1] indicated that thePower-law model is capable and was selected to describe thedeformation curve at the primary stage. In addition to this, a sim-ple linear model was selected to represent the curve at the second-ary stage [1]. These two models are the key to form the three-stagedeformation model. More details describing the two models arediscussed in the following subsections.

3.1.1. Initiation of the secondary stageAs mentioned previously, the curve in the primary stage was fit-

ted using the Power-law model as shown below:

ep ¼ aNb ð1Þ

where ep is the accumulated permanent strain in the primary stage;N is the cycle number; and a, b are the regression coefficients. Thecumulative permanent strain was calculated using Eq. (1) and theregression coefficients were determined at the same time. The cal-culated and the measured ep were compared using the followingequation:

De ¼jep-measured � ep-predictedj

ep-measured� 100% ð2Þ

where De is the deviation; ep-measured is the measured permanentstrain; and ep-predicted is the calculated permanent strain. The initia-tion of secondary stage was determined when De is less than 3% andN determined at De < 3% was less than maximum cycle number.

3.1.2. Initiation of the tertiary stageIn this section, the data set was adjusted and the initiation of

secondary stage becomes the new origin of the coordinate axis.The accumulated strain of the secondary stage was increased inlinear function and it may be described using a linear model:

e0p ¼ cN0 þ d ð3Þ

where e0p is the accumulated strain; N is the cycle number; and c andd are regression coefficients. The regression coefficients were calcu-lated and compared with measured e0p using the equation below:

Rd ¼de0p� 100% ð4Þ

where Rd is the absolute ratio of d to current maximum e0p. The flownumber (initiation of tertiary state) occurs when Rd is less than 1%(or the D value is larger than 0) and N0 at Rd < 1% is less than themaximum cycle number.

Zhou et al. [1] revealed that this model reflected the basicmechanical properties of asphalt mixture and the FN determinedusing this model was consistent with the measured field rut depth.

Fig. 2. Typical plot of strain rate versus load cycle number and the miscalculation.

Fig. 3. Determination of flow number from creep stiffness times cycle versus cycleusing 6th polynomial regression.

3400 S.W. Goh, Z. You / Construction and Building Materials 23 (2009) 3398–3405

3.2. FNest method

Archilla et al. [22] proposed a method called FNest to determinethe flow number [22]. The authors claim that the strain rate foreach cycle number can be calculated using the equation below:

@ ePð Þi@N

¼ ðePNiþ1 � ePNi�1Þ2DN

ð5Þ

where ep is permanent strain and N is the cycle number. A five-pointmoving average period (MAP) was used to smoothen the strain ratecalculated using Eq. (5). The minimum point of this strain rate wasthen defined as FNMAP5. Archilla et al. [22] stated that the range ofload cycles used in fitting the FNest method may be defined bythe equation:

½Nlb;Nun� ¼ max 100; FNMAP5 � C � FNMAP5ð Þ;min Nmax; FNMAP5ð½þC � FNMAP5Þ� ð6Þ

where Nlb is the lower number of cycles to fit the model; Nub is thehighest number of the cycles; C is the 0.5; and Nmax is the maximumcycle number. This model also assumes that Nub 6 Nmax (Nub = Nmax

if Nub > Nmax). The data set in the range of Eq. (6) may then be fittedby an equation associated with Weibull distribution:

eP ¼1b� ln 1� N

c

� �� �1=a

ð7Þ

where b, a and c are probability distribution parameters. Archillaet al. [22] indicated that these parameters could be determinedusing an excel build-in function called solver. After determiningthese parameters, the flow number may be found using the equa-tion below:

FN ¼ c 1� exp1a� 1

� �� �ð8Þ

Archilla et al. [22] recommended that a more stable methodthat is less dependent on operator input and interoperation wasnecessary for FN measurement. The authors also comment that

the FNest for determining FN contributes with a reduction in itsvariability both within single and multiple samples, and it couldprovide a stable and uniform platform to develop a standardizedmethod for flow number determination [22].

2.1. The mathematical product of creep stiffness and cycles versuscycles plot

Bausano and Williams [24] examined the flow number by plot-ting the mathematical product of creep stiffness and cycles versuscycle. The curve was then regressed using sixth order and secondorder polynomial functions. This FN was then defined as the max-imum point on the curve of this plot. A sample of this methodusing a sixth order polynomial function to determine the flownumber is shown in Fig. 3. Bausano and Williams [24] revealed thatthe flow number using this method was found to be more repeat-able and reproducible by the lower coefficient of variations

Table 1General information of the HMA mixtures.

Mixture ID Asphalt grade Nominal maximumaggregate size(NMAS), mm

Traffic equivalentsingle axle loads(ESALs) in million

HMA 1 PG 58-22 19 610HMA 2 PG 58-28 19 610HMA 3 PG 64-22 19 630HMA 4 PG 64-28 12.5 63HMA 5 PG 64-28 12.5 63HMA 6 PG 70-22 12.5 610HMA 7 PG 70-22 12.5 610HMA 8 PG 70-22 12.5 630HMA 9 PG 52-34 9.5 61HMA 10 PG 58-34 9.5 63HMA 11 PG 64-22 9.5 610HMA 12 PG 64-22 9.5 610HMA 13 PG 70-22 9.5 630HMA 14 PG 70-22 9.5 630

S.W. Goh, Z. You / Construction and Building Materials 23 (2009) 3398–3405 3401

compared to the existing model. The authors also indicated that asecond polynomial regression was found to provide accuracy andprecision of measuring the flow number similar to the sixth orderpolynomial regression.

2.2. Francken model

Biligiri et al. [23] evaluated several mathematical models andrecommended a combined mathematical model to determine theflow number. The composite model, also referred to as FranckenModel, was utilized in the calculation [23]:

epðNÞ ¼ ANB þ CðeDN � 1Þ ð9Þ

where ep(N) is the permanent deformation; N is the loading cycle;and A, B, C, and D are regression coefficients. This model was devel-oped based on triaxial dynamic load tests under different tempera-tures and stress levels. Biligiri et al. [23] determined thesecoefficients using a statistical package. Eq. (9) was derived with re-spect to N to represent the equation for strain slope as below:

dep

dN¼ A� B� NðB�1Þ� �

þ C � D� eD�N�

ð10Þ

The strain slope was then plotted using Eq. (10). Finally, theflow number was determined by using the equation below formathematical differentiation:

d2ep

dN2 ¼ A� B� ðB� 1Þ � NðB�2Þ þ C � D2 � eD�N� �

ð11Þ

Biligiri et al. [23] claimed that this model could estimate a bet-ter flow number of conventional asphalt mixtures. The authors alsorecommended this method to be used to determine flow numberbecause this approach considered all stages of permanentdeformation.

3. Objectives

Currently, no standard flow number method is widely accepted.Researchers have been trying to discover a well-defined flow num-ber method through different kinds of approaches. Their efforts ledto the development of several excellent methods. However, thesemethods need to be more refined in order to improve its user-friendliness to engineers, researchers and even students. Theobjectives of this study are to present a new approach to determinethe flow number and compare the results with the existing meth-ods of measuring flow number.

4. Experimental design

4.1. Sample preparation

A total of 20 different Superpave HMA mixtures were collected from the jobsites and were used in this study. Table 1 shows the mixture type, different trafficlevels, and Nominal Maximum Aggregate Sizes (NMAS) that were involved in thisstudy.

Samples collected from the job sites were compacted and fabricated in theTransportation Materials Research Center of Excellence at Michigan TechnologicalUniversity. All the pre-mixed HMA samples were heated up in the oven at theircompaction temperatures. A Superpave Gyratory Compactor (SGC) was used tocompact all these samples once they reach their compaction temperatures. In thisstudy, 123 samples were compacted to two different types of air void levels(4% ± 0.5%, 7% ± 0.5% and 10% ± 0.5%). These samples were then cored andtrimmed to the size of 100 mm in diameter and 150 mm in height for the flownumber test.

4.2. Flow number test

The flow number test was conducted according to NCHRP Report 465 [5] withunconfined testing. Witczak et al. [5] stated that both unconfined and confined test-ing correlated well with field pavement performance. Before performing the test,

samples were put into the environmental chamber until they reached their effectivetemperatures. Then, the flow number test was conducted using an IPC UTM-100machine [25].

4.2.1. Stress levelIt is crucial to determine the magnitude of loading level used in each flow num-

ber test, because this will significantly affect the result. The NCHRP 465 suggestedloading levels of 69 kPa for the loading stress and 3 kPa for the contact stress whenperforming a flow number unconfined test [5,13]. These loading levels were definedfor the intermediate and high test temperatures in the flow number test. However,these loading levels might not be feasible for some of the mixtures (e.g. high trafficlevel mixtures) because the samples would not undergo tertiary flow. From a dis-cussion with Williams and based on the previous research [12,19,26], stress levelof 600 kPa (simulates from the gyratory compactor) and 30 kPa for contact stresswere determined for this test.

4.2.2. Revised effective temperatureThe effective temperature is defined as a single temperature at which the

amount of permanent deformation would occur equivalent to that measured byconsidering each season separately throughout the year [5]. The equation of effec-tive pavement temperature for rutting, which is defined by the temperature at20 mm below the surface of the pavement, is shown as below [12]:

Teff rutting ¼ 30:8� 0:12Zcr þ 0:92MAATdesign ð12Þ

where Teff rutting is the effective rutting temperature (�C); Zcr is the critical depthdown from pavement surface (mm) and MAATdesign is the mean annual air temper-ature (�C). The equation for MAATdesign is:

MAATdesign ¼ MAATAverage þ KarMAAT ð13Þ

where MAATAverage is the average annual air temperature (�C); Ka is the appropriatereliability level of 90%; and rMAAT is the standard deviation of the distribution ofMAAT for the corresponding site location. The critical depth, Zcr, is 20 mm in thiscase. The MAATaverage comes from data that was collected from Michigan State Cli-matology Office locations all over the state of Michigan. Previous studies revealedthat a Teff rutting of 39.2 �C is typically used [12,26]. In this paper, the calculation ofrMAAT was revised due to the climate in Michigan. The traditional rMAAT calculationnormally incorporates a historical MAATAverage. However, Michigan’s climate hasbeen known to have huge temperature differences between the winter and summerseasons (approximately 22 �C difference). Hence, using traditional rMAAT calculationmight not be appropriate. In this study, the rMAAT was calculated based on historicalMAATAverage values from each month in a year. The effective temperature, or the ‘‘re-vised” effective temperature, was calculated at each Michigan Department of Trans-portation (MDOT) region [27] shown in Fig. 4. An average of Teff rutting, 45 �C wascomputed from all regions and used for the calculations of this study. Two othertemperatures (39.2 �C and 40 �C) were also considered to evaluate the effect of tem-perature on flow number measurements.

5. Proposed methodology for the flow number

The proposed stepwise increase approach provides a practicaland consistent method to determine the initiation of tertiary flow.Stepwise increase means a gradual increase, or increase step bystep in mathematical terms [28]. This approach utilizes the tradi-tional method (locate minimum point on the curve of strain rateversus cycle number) and emphasizes the smoothing technique

Fig. 4. Average and standard deviation of the mean annual air temperature (MAAT) in the regions of Michigan.

Micro-Strain

3402 S.W. Goh, Z. You / Construction and Building Materials 23 (2009) 3398–3405

used to determine the flow number. Three simple steps and anassumption were applied in this method. A brief algorithm to iden-tify the flow number using stepwise approach is shown in the fol-lowing section:

Step 1: Smoothening the measured permanent deformation byre-allocating the measured results with an assumptionof permanent strain will either remain the same orincrease over the load cycle number.

Fig. 5 shows the results from the test. The non-uniform, discon-tinuous data points that led to the subjective analysis and miscal-culation of the flow number are highlighted in Fig. 6a as well. Asmentioned previously, the proposed method emphasizes thesmoothening technique and re-allocation method. The stepwise

8600

8800

9000

3500 3550 3600 3650 3700 3750 3800Cycle Number

Micro-Strain

Fig. 5. Measured permanent deformations versus cycle number.

8550

8600

8650

8700

8750

8800

04530943 Cycle Number

Micro-Strain

12

3

4 5 6

8 9 10

7

11

Fig. 6a. Reallocation of the deceptive plots.

method used in this study is shown in Fig. 6b. This method in-volves shifting the discontinuous data points forward along thex-axis (cycle number) by not changing the strain level to give astepwise increasing trend. For example in Fig. 6a, point 3 wasshifted forward to replace point 6, and points 4–6 were move back-ward to replace point 3; point 8 shifted forward to replace point10, and point 9 and 10 move backward to replace point 8. All ofthe non-uniform discontinuous data points can easily be shiftedusing the excel function called ‘‘Sort Ascending.” Fig. 6b showsthe shifted data points using the stepwise method proposed.

The curve trend of strain versus loading cycle for the entire testwas examined as well in order to ensure the stepwise (sorting)

Fig. 7. Sample of strain versus loading cycle curve before and after shifting.

8550

8600

8650

8700

8750

8800

04530943 Cycle Number

3 4

5 6

9 10 8

Fig. 6b. Modified permanent deformation versus load cycle.

S.W. Goh, Z. You / Construction and Building Materials 23 (2009) 3398–3405 3403

process did not change the curve trend significantly. Fig. 7 shows asample of strain versus loading cycle curve before and after. It wasobserved that no significant difference was found when comparingthe curve trend of strain versus loading cycle before and after step-wise process.

Step 2: Calculate the strain rate using the modified permanentdeformation result.

This step determines the strain rate using the modified data set(data set modified in step 1). The strain rate is calculated by divid-ing the permanent strain by loading cycle number at each cycle:

Strain Rate ¼ eN

ð14Þ

Fig. 9a. Comparisons of stepwise and three-stage methods.

Step 3: Determine the flow number by locating the minimumpoint of strain rate versus load cycle curve.

For this step, the flow number can be found by locating the min-imum point from the curve of strain rate versus cycle number.There is no flow number if the minimum point of strain rate versusload cycle curve is equal to the maximum cycle number. Fig. 8shows a sample of determining the flow number using the three-step-stepwise method: (1) smoothening dataset using stepwiseprocess; (2) calculate the strain rate at each cycle; and (3) locatethe minimum point of strain rate versus load cycle curve. Thisthree-step-stepwise method is simpler and more practical com-pared to other methods for determining the flow number.

6. Validation of proposed flow number method

In order to verify the applicability of the proposed approach, thestepwise method was compared with the three-stage model [1],the mathematical product of Creep Stiffness and Cycles versus Cy-cles method [24] and FNest method [22]. A total of 123 flow num-ber data were compared and shown in Figs. 9a–c. It can beobserved that the stepwise method has flow number measurementsimilar to the three-stage and the mathematical product of CreepStiffness and Cycles versus Cycles methods. The correlation be-tween stepwise method and these two methods was excellent,by showing the R-square P 0.98. The flow number measured fromthe stepwise method was significantly higher than the FNest meth-od. As mentioned previously, Archilla et al. [22] recommended thata more stable method that is less dependent on operator input andinteroperation was needed for FNest method.

In this study, the proposed stepwise method was comparedwith the traditional method. Fig. 9d shows the comparison results.

Fig. 8. Sample result of flow number tested at 39.2 �C.

Fig. 9b. Comparison of stepwise and creep stiffness times cycles versus cyclesmethods.

It was observed that the correlation between stepwise and tradi-tional method was fair (R-square = 0.59). It is worth noting thatthe traditional method may provide a misleading flow numberdue to some deceptive points as previously mentioned.

Even though the flow number can be well-defined by all themethods discussed, the proposed stepwise method was deter-mined to be most practical and easiest to compute.

7. Relationship between deformation rate and stepwise flownumber

Previous studies indicated that the rate of deformation (slope ofthe secondary flow) in the dynamic creep test correlated well with

Fig. 10. Relationship of flow number and rate of deformation at secondary stage.

Fig. 9c. Comparison of stepwise and FNest methods.

Fig. 9d. Comparison of stepwise and traditional methods.

3404 S.W. Goh, Z. You / Construction and Building Materials 23 (2009) 3398–3405

permanent deformation [14]. In addition, the rate of deformationwas an important factor for determining the final flow number[29]. In this study, flow number was computed using the stepwisemethod at 39.2 �C, 40 �C and 45 �C. Also, air void levels rangingfrom 4% to 10% were used. Fig. 10 shows the comparison betweenthe stepwise flow number and rate of deformation for all mixturestested. It is notable that the rate of deformation was computedusing the stepwise modified dataset. Observations of Fig. 10 indi-cate that an excellent relationship was found when a regressionanalysis using the equation below was employed:

Flow number ¼ a� FNbslope ð15Þ

where ‘‘a” and ‘‘b” are regression coefficients and FNSlope is the rateof deformation. Since Eq. (15) was built using different tempera-tures and air void levels, an R-square of 0.96 showed that this equa-tion is able to compute flow number of an asphalt mixture using the

rate of deformation tested at any temperature and any air void le-vel. In this case, ‘‘a” and ‘‘b” were calibrated and determined to be31753 and �1.081, respectively. Four potential benefits were iden-tified from using Eq. (15):

(1) Flow number can be computed for tests that do not undergotertiary flow.

(2) The computation of effective rutting temperature can beneglected.

(3) The duration of the dynamic creep test can be shortened.(4) The dynamic creep test could become a non-destructive test

if a lower cycle number was used.

It is recommended that more tests should be conducted to fur-ther validate the calculation.

8. Summary

This paper presents a simple approach to determine the flownumber of asphalt mixtures during a dynamic creep test. Theproposed approach provides a practical and consistent methodto determine the initiation of tertiary flow. The stepwise methodwas used as a smoothing technique in this approach to give astepwise increasing trend. The flow number was defined as theminimum point of strain rate versus load cycle number usingthe new modified data point. In order to validate the applicabil-ity of the proposed approach, this method was also comparedwith existing methods: three-stage model [1], FNest method[22] and the mathematical product of creep stiffness times cy-cles versus cycles approach [24]. The R-square P 0.98 was de-rived from these comparisons and indicated that thesemethods have shown an excellent correlation with the proposedstepwise method.

A comparison of the proposed stepwise method and the tradi-tional method were performed as well. The results show that thecorrelation between stepwise and traditional methods was fair(R-square = 0.59). However, it was noteworthy that the traditionalmethod may provide a misleading flow number due to somedeceptive points.

In this study, the rate of deformation was also evaluated andcompared with the flow number. An excellent relationship (R-square = 0.96) was found between rate of deformation and flownumber. The result also indicated that the rate of deformation fromthe modified dataset using stepwise approach can be used to com-pute the flow number.

S.W. Goh, Z. You / Construction and Building Materials 23 (2009) 3398–3405 3405

Acknowledgements

The authors also wish to acknowledge the helpful discussionswith Dr. Chris Williams and Dr. Thomas Van Dam. The researchwork was partially sponsored by the Federal Highway Administra-tion through Michigan Department of Transportation. The authorsappreciate the guidance and involvement of Mr. John Barak of theMichigan Department of Transportation as the Project Manager.

References

[1] Zhou F, Scullion T, Sun L. Verification and modeling of three-stage permanentdeformation behavior of asphalt mixes. Am Soc Civ Eng 2004;130:486–94.

[2] Monismith CL, Ogawa N, Freeme CR. Permanent deformation characteristics ofsubgrade soils due to repeated loading. Transport Res Rec 1975;537:1–17.

[3] Brown ER, Snaith MS. The permanent deformation characteristic of a densebitumen macadam subjected to repeated loading. J Assoc Asphalt Pav Technol1974;43:224–52.

[4] Brown SF, Cooper KE. The mechanical properties of bituminous materials forroad bases and basecourses. J Assoc Asphalt Pav Technol 1984;53:415–39.

[5] Witczak MW et al. Simple performance test for superpave mix design. NationalCooperative Highway Research Program; 2002.

[6] Mallick RB, Ahlrich R, Brown ER. Potential of dynamic creep to predict rutting.engineering properties of asphalt mixtures and the relationship to theirperformance, ASTM STP 1265. American Society for Testing and Materials;1995.

[7] Kaloush KE et al. Tertiary flow characteristics of asphalt mixtures. ColoradoSprings (CO, United States): Association of Asphalt Paving Technologist; 2002.

[8] Zhou F, Scullion T. Preliminary field validation of simple performance tests forpermanent deformation: case study. Transport Res Rec 2003;1832:209–16.

[9] Brown SF, Gibb JM. Validation experiments for permanent deformation testingof bituminous mixtures. J Assoc Asphalt Pav Technol 1996;65:255–99.

[10] Faheem AF, Bahia HU, Ajideh H. Estimating results of a proposed simpleperformance test for hot-mix asphalt from superpave gyratory compactorresults. Transport Res Rec 2005;1929:104–13.

[11] Witczak MW. Specification criteria for simple performance tests for rutting.National Cooperative Highway Research Program; 2007.

[12] Robinette C et al. The effects of the testing history and preparation method onthe superpave simple performance test. Savannah (GA, UnitedStates): Association of Asphalt Paving Technologist; 2006.

[13] Witczak MW, Sullivan B. Superpave support and performance modelsmanagement. National Cooperative Highway Research Program 465; 2002.

[14] Bhasin A, Button JW, Chowdhury A. Evaluation of simple performance tests onhot-mix asphalt mixtures from south central United States. Transport Res Rec2004;1891:174–81.

[15] Carpenter SH, Vavrik WR. Repeated triaxial testing during mix design forperformance characterization. Transport Res Rec 2001;1767:76–84.

[16] Little DN, Button JW, Youssef H. Development of criteria to evaluate uniaxialcreep data and asphalt concrete permanent deformation potential1993:49–57.

[17] Leahy RB, Witczak MW. Influence of test conditions and asphalt concrete mixparameters on permanent deformation coefficients alpha and mu. Seattle (WA,USA): Association of Asphalt Paving Technologists; 1991.

[18] Kanitpong K, Bahia H. Relating adhesion and cohesion of asphalts to the effectof moisture on laboratory performance of asphalt mixtures. Transport Res Rec2005;1901:33–43.

[19] Williams RC. Testing wisconsin asphalt mixture for the AASHTO 2002mechanical design procedure. Wisconsin; 2007.

[20] Kvasnak A, Robinette CJ, Williams RC. Statistical development of a flownumber predictive equation for the mechanistic-empirical pavement designguide. Transportation research board 86th annual meeting. TransportationResearch Board; 2007. p. 18.

[21] Goh SW, You Z. Simple Method to determine the tertiary flow in repeated loadtest: a step-wise method, In: You Z, Abbas A, Wang L. editors. Pavements andmaterials: modeling, testing and performance. Symposium of pavementmechanics and materials, ASCE engineering mechanics institute conference,ASCE, ASCE Geotechnical Special Publication, Minneapolis, Minnesota, May18-21; 2008. ISBN: 978-0-7844-1008-0.

[22] Archilla AR, Diaz LG, Carpenter SH., Proposed Method to Determine the FlowNumber from Laboratory Axial Repeated Loading Tests in BituminousMixtures. Transportation Research Board 86th Annual Meeting. 2007:Transportation Research Board, Report Number: 07-1901 [CD-ROM].Available from: http://pubsindex.trb.org/document/view/default.asp?lbid=801938.

[23] Biligiri KP et al. Rational modeling of tertiary flow for asphalt mixtures.Transport Res Board 2007:63–72.

[24] Bausano J, Williams C. A new approach to calculating flow number; 2007.[25] Bonaquist, RF, Christensen DW, Stump W. Simple performance test for

superpave mix design: first-article development and evaluation; 2003.[26] Robinette CJ. Testing wisconsin asphalt mixtures for the 2002 AASHTO

mechanisticdesign procedure. In: Civil and Environmental Depart-ment. Houghton: Michigan Technological University; 2005.

[27] Michigan Department of Transportation (MDOT). MDOT regions [cited 2008;<http://www.michigan.gov/mdot/0,1607,7-151-9623-36042–,00.html>.

[28] Goh SW, You Z. A simple method to determine the tertiary flow in the repeatedload test. In: 2008 Mid-continent transportation research forum. Madison,Wisconsin; 2008.

[29] Faheem A, Bahia HU. Using gyratory compactor to measure mechanicalstability of asphalt mixtures. Madison: University of Wisconsin-Madison;2004.