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Evaluation of a novel calibrated-mechanistic model to design againstfracture under Swedish conditionsDavid Gullberg a , Björn Birgisson a & Denis Jelagin aa Highway and Railway Engineering, KTH-Royal Institute ofTechnology, Brinellvägen 34, KTH, SE-100 44, Stockholm, Sweden

Available online: 27 Feb 2012

To cite this article: David Gullberg, Björn Birgisson & Denis Jelagin (2012): Evaluation of a novelcalibrated-mechanistic model to design against fracture under Swedish conditions, Road Materialsand Pavement Design, DOI:10.1080/14680629.2011.651838

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Road Materials and Pavement DesigniFirst, 2012, 1–18

Evaluation of a novel calibrated-mechanistic model to design againstfracture under Swedish conditions

David Gullberg*, Björn Birgisson and Denis Jelagin

Highway and Railway Engineering, KTH-Royal Institute of Technology, Brinellvägen 34, KTH, SE-100 44Stockholm, Sweden

Sweden has initiated the development of a new calibrated-mechanistic pavement design proce-dure to replace the current mechanical-empirical pavement procedure entitled ‘PMS Objekt’.The first phase was focused on the implementation and calibration of the viscoelastic frac-ture mechanics framework entitled ‘HMA Fracture Mechanics’, developed at the Universityof Florida. This paper outlines the implementation and calibration of a new pavement designmodule for Sweden that is based on the HMA fracture mechanics framework. Both the devel-oped design module, as well as the reference model used for calibration (PMS Objekt), ispresented in this paper. The results in thickness design after calibration of the design moduleindicate that the framework is clearly applicable for common Swedish conditions and designstandards.

Keywords: top-down cracking; Florida cracking model; IDT; PMS Objekt; mechanisticpavement design

1. IntroductionSweden has recently initiated a research programme that will develop a comprehensive calibrated-mechanistic (CM) pavement analysis and design procedure for flexible pavements. The firstphase of the development of a new CM pavement design approach was to implement a newmodule that also can account for load-related top-down cracking, which has proven to be a majormode of premature pavement failure (Jacobs, 1995; Myers, 2000; Myers, Roque, & Birgisson,2001; Matsuno & Nishizawa, 1992; Roque, Birgisson, Drakos, & Dietrich, 2004; Uhlmeyer,Willoughby, Pierce, & Mahony, 2000; Wang, Myers, Mohammad, & Fu, 2003).

The first move towards a more analytical approach to pavement design in Sweden was madeby a research team at VTI (Swedish National Road and Transport Institute), where they identifiedseveral issues with the old empirical system used prior to 1993 in Sweden. The research teamdecided to use the Kingham fatigue criterion to set up new standard-designs based on trafficclasses as a short-term solution until a full-scale analytic mechanistic/empirical design systemcould be implemented (Arm, 1992).

In parallel with this work, during 1987–1994, VTI developed the predecessor to PMS Objekt – acomputer application for analytical pavement design applying elastic theory and a fatigue criteriondeveloped based on field observations in Sweden (Djärf, Wiman, & Carlsson, 1996). The currentdesign-tool in use – PMS Objekt – ended up as a mix of these two, using many of the algorithmsdeveloped by Djärf et al. (1996) together with the modified Kingham criterion as suggested in

*Corresponding author. Email: davidgul@kth.se

ISSN 1468-0629 print/ISSN 2164-7402 online© 2012 Taylor & Francishttp://dx.doi.org/10.1080/14680629.2011.651838http://www.tandfonline.com

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the San-Remo report by Arm (1992). There is also a subgrade rutting performance criterion inPMS Objekt but it is the asphalt-fatigue criterion that dominates the final design as the minimumthicknesses for the unbound layers are set to minimize the occurrence of subgrade rutting.

The application itself has, over the years, been updated with new materials and climate dataas they have been identified and registered (Vägverket, 2008). The theory and failure criteriahowever, have remained the same over these years.

Mechanistic-empirical design procedures such as PMS Objekt have their benefits; they areusually well calibrated for existing materials and local conditions – the theory is simple andintuitive. A lot of experience of real pavement behaviour is incorporated in these kinds of modelsas the construction materials have remained the same for a long time.

There are, however, limitations with PMS Objekt. The impact of novel materials (e.g. rubberand polymer modified asphalt mixtures, etc) is difficult to estimate as the design is not linked to therheological properties of the materials. Even the determination of fatigue properties requires eitherextensive field experience with guessing or laboratory evaluation followed by field calibration.A design framework that adopts fundamental properties of an asphalt mix in its evaluation ofpavement performance holds the promise of reducing this time-consuming process as long asthe key properties are directly coupled to the actual mechanics of cracking in pavements. Thereis also no reliability concept implemented in PMS Objekt, which limits the applicability of theprogram for evaluating, for example, changes in pavement thickness as a function of increasedor decreased load and construction variability, or service level of the pavement.

The scope of the work presented in this paper is to evaluate a new CM pavement design modulefor its ability to predict pavement performance under Swedish load- and climate conditions. Theanalysis and design framework presented is an extension of the work developed by Birgisson,Wang, and Roque (2006a), in which they developed a pavement design framework based on theprinciples of viscoelastic fracture mechanics. This approach allows for the prediction of crackinitiation and crack growth in asphalt mixture subjected to any specified loading history. One keyobservation regarding this approach, is that each mix is evaluated based on its dissipated creepstrain energy limit, which acts as the threshold where healable micro-cracks propagate into non-healable macro-cracks. This is a threshold that has proven to be fundamental and independent ofmode of loading (Zhang, Roque, Birgisson, & Sangpetngam, 2001).

As an evaluation of the model’s applicability, pavement designs under representative Swedishconditions with two different types of mixtures are done. The results are compared with referencedesign thicknesses by PMS Objekt – the current analytical model is use in Sweden. In order tomake this comparison viable, the selected conditions and mixes are chosen to be in range of theempirical data that has been used to calibrate PMS Objekt.

For this comparison, version 4.2 of PMS Objekt has been used. The software is distributed asfreeware by the Swedish Transport Administration (Trafikverket) and can be downloaded fromtheir webpages (www.trafikverket.se).

This paper will also briefly describe the implementation of the HMA fracture mechanics modelinto pavement design, followed by an introduction of PMS Objekt.

2. HMA fracture mechanicsThe CM pavement design module extends from the Florida Cracking Model (FCM) developedby Birgisson et al. (2006a) and these models are based on HMA fracture mechanics with its keyfeatures:

• Damage in asphalt mixture is equal to the dissipated creep strain energy (DCSE).

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Road Materials and Pavement Design 3

Figure 1. CM design module flowchart.

• There exists a damage threshold (called DCSE threshold or DCSE limit) in asphalt mixturesthat is independent of loading mode or loading history.

• Damage under the cracking threshold is fully healable.• Once the damage (the amount of DCSE) exceeds the damage threshold (DCSE limit), a

macro-crack will initiate, or propagate if a crack is already present.• A macro-crack is not healable.

This means that the initiation and propagation of cracks in asphalt mixtures can be determinedfor any loading condition by calculating the amount of dissipated creep strain energy (DCSE) andcomparing this value with the DCSE-threshold of a mixture. The general outline of the frameworkis shown in Figure 1.

2.1. Energy ratio conceptAs the mixture properties governing fatigue performance (stiffness, creep compliance, age-hardening, and fracture resistance) are highly interrelated it is difficult to evaluate crackingperformance, even on a relative basis, simply by comparing these properties. Based on workat the University of Florida, Roque et al. (2004) introduced a parameter called the Energy Ratio

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(ER) into the HMA Fracture Mechanics Model. This parameter was found to accurately distinguishbetween pavements that exhibited cracking and those that did not.

The energy ratio is a dimensionless parameter defined as the dissipated creep strain energythreshold of the mixture divided by the minimum dissipated creep strain energy limit required forthe pavement to perform well in the field.

ER = DCSEL

DCSEmin(1)

where:DCSEL = dissipated creep strain energy limit according to Figure 2(a).DCSEmin = a calibrated parameter describing the minimum DCSE-limit required for thismixture to perform well in the field.

The relation between DCSEmin and the creep parameters D1 and m-value in a single functionis expressed in Figure 2(b):

DCSEmin = m2.98 × D1

f (St,σmax)(2)

and

f (St , σmax) = 6.36 − St

33.44 × (145.0377 × σmax)3.1 + 2.46 × 10−8 (3)

where:St = tensile strength (in MPa)σmax = maximum tensile stress at the bottom of the AC-layer (in MPa).

The minimum energy ratio (ER) required is adjusted for different traffic levels and differentreliabilities. After this adjustment this is called the optimum energy ratio (ERopt). For all but twoof the 22 field sections tested in the development of this concept the above criteria successfullyseparated un-cracked sections from those that exhibited cracking (Roque et al. 2004).

Figure 2. Dissipated creep strain energy concept.

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Road Materials and Pavement Design 5

2.2. Material properties modelsThe material properties used to evaluate resistance to cracking can be determined without perform-ing laboratory testing. To predict cracking performance, the properties required include: dynamicmodulus |E∗|, creep compliance power law parameters (D1 and m-value), tensile strength St , andthe dissipated creep strain energy limit (DCSEL). All these properties are estimated for a numberof material models based on the gradation and binder-content of the mix. Models used in the CMdesign module include:

• dynamic modulus master curve prediction using volumetric properties (Witczak & Fonseca,1996; Birgisson, Roque, Kim, & Pham, 2004);

• the global aging model (Mirza & Witczak, 1995) to predict viscosity at any time and depthin the pavement;

• estimation of the creep compliance power law parameters and the DCSE limit based on themaster curve and the aging model;

• determination of the tensile strength from the dynamic modulus of the mixture (Deme &Young, 1987)

2.2.1. Dynamic modulusIn order to calculate a pavement’s response to loading the dynamic module, |E∗|, is required.Equation (4) gives the predictive equation used here which originally was developed by Witczakand Fonseca (1996) and later had its fitting parameters (δ, α, β and γ ) improved by Birgissonet al. (2004):

log |E∗| = δ + α

1 + exp(β + γ × log(tr)(4)

where:|E∗| = Dynamic modulus in psi (1psi = 0.00689 MPa)tr = Reduced time at the reference temperatureδ, α, β, γ = fitting parameters.

The detailed expressions for δ, α, β and γ are given in terms of gradation and volumetricproperties of the mixture:

δ = 2.718879 + 0.079524 × p200 − 0.007294 × (p200)2 + 0.002085 × ρ4

− 0.01293 × Va + 0.08541Vbe

Vbe + Va

α = 3.559267 − 0.005451 × ρ4 + 0.020711 × ρ3/8 − 0.000351 × (ρ3/8)2

+ 0.00532 × ρ3/4

β = −0.513574 − 0.355353 × log(ηr)

γ = 0.37217

Where:Va = percent air void content by volumeVbe = effective asphalt content, percent by volumeρ3/4(ρ3/8, ρ4) = percent weight retained on 19 (9.5, 4.75-mm) sievep200 = percent weight passing 0.75-mm sieveηr = binder viscosity at the reference temperature in Megapoise

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This new set of fitting parameters is the one used in the CM pavement design module evaluatedin this paper.

2.2.2. Aging modelTo estimate optimum design thickness, the material is aged to its viscosity at the end of its designlife, as this state corresponds to the most critical (brittle) state of the material. To model aging,the Global Aging Model (Mirza & Witczak, 1995) is used and the temperature of interest is setequal to the mean average air temperature. Viscosity at mix/laydown conditions is:

log log (η) = A + VTS × log(TR) (5)

where:η = binder viscosity in centipoises (10−2 poise)TR = temperature in RankineA, VTS = regression constants

Aged surface viscosity is:

log log(ηaged) = log log(ηt=0) + Af t1 + Bf t

(6)

where:t = time in monthsAf ,Bf = field aging parameters, f (Temp, MAAT )

From these equations, viscosity at any depth and at any time of aging can be estimated as:

ηt,z = ηt(4 + χ) − χ × ηt=0 × (1 − 4 × z)4 × (1 + χ × z)

χ = 23.82 × e−0.0308×MAAT(7)

where:MAAT = mean average air temperature in deg. Fahrenheit (1◦F = 9/5 + 32◦C)

z = depth in inches (1 inch = 25.4 mm)

ητ = aged surface viscosity in Mega poises.

2.2.3. Tensile strengthThe HMA fracture mechanics framework applies the correlation between a mixture’s tensilestrength and its stiffness at a loading time of 30 minutes (discovered by Deme & Young, 1987):

St =5∑

n=0

an(log Sf )n (8)

a0 = 284.01, a1 = −330.02, a2 = 151.02, a3 = −34.03,

a4 = 3.7786, a5 = −0.1652

where:Sf Sf = λr × |E∗| at t = 1800 sλr Stiffness reduction factor. Birgisson et al. (2004) suggest a value of 0.4, which is also

used here.

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Road Materials and Pavement Design 7

2.2.4. Creep compliance parameters and DCSE limitBy using the dynamic master curve with tensile reduction, the creep compliance power lawparameters can be determined:

D(t) = D0 + D1tm (9)

The D0 and D1 can be obtained from the asymptotic values of λr × |E ∗ | as follows:

log(D0) = −δ − α − log λr

log(D0 + D1) = −δ − α

1 + e β− log λr

(10)

where parameters δ, α, and β are obtained from the mixture volumetric properties and the binder’sviscosity. By taking the derivate of equation (9) with a suitable modification (m0) and then addingan additional term that accounts for aging, Birgisson et al. (2006a) presented a predictive equationfor the m-value:

m = m0 + κ

log log η(11)

m0 = αγ × exp(β + 3γ )

[1 + exp(β + 3γ )]2 (12)

where:κ = Constant with a suggested value of 0.408 (Birgisson et al., 2004)η = Viscosity in centipoises

Using these material properties the dissipated creep strain energy can be estimated as:

DCSEL = cf × StmD1

103(1−m)(13)

where:cf = a function of binder viscosity, suggested value = 6.9 × 107 (Birgisson et al., 2006a).

This is the threshold the design module uses together with the energy ratio-concept to separategood designs from designs prone to cracking.

3. Current model in use – PMS ObjektPMS Objekt is what is referred to as a mechanistic-empirical design method and is used in Swedento design against two main modes of failure: fatigue cracking and subgrade rutting. In addition,the heave due to frost can be estimated. The model uses horizontal strain at the bottom of theAC-layer to estimate the number of allowed load-repetitions before fatigue-cracking occurs andvertical strain at the top of the subgrade to estimate the allowed number of load repetitions allowedbefore severe rutting in the subgrade develops. The failure criterion used for fatigue cracks inasphalt-concretes is given by the Swedish transport administration in its design guide Vägverket(2008):

Ntill,bb ≥ Nekv

Ntill,bb = 365∑mi=1

niNbb,i

Nbb,i = fs × 2.37 × 10−12 × 1.16(1.8Ti+32)

ε4bb,i

(14)

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where:Nekv = equivalent number of standard axlesNtill,bb = total number of allowed standard axles with regard to fatigueNbb,i = number of allowed standard axles for the AC layer during climate period iεbb,i = horizontal tensile strain in the bottom of the AC layer for climate period ini = length of climate period in daysT = pavement temperature in ◦C for climate period ifs = correction factor for cracked pavements; fs = 1.0 for new constructionsm = number of climate periods

In most cases fatigue will end up being the effective design criteria for Swedish pavementsas the recommended construction techniques prescribe high-quality base and sub-base materialswhich, for moderate traffic levels, makes sub-base rutting a secondary failure criterion (Vägverket,2008).

It should be noted that in the theoretical framework of this approach, where the horizontal strainis calculated in the bottom of the AC-layer, cracks propagate upwards through the pavement (Djärfet al., 1996). This contradicts the more recent studies, such as the COST 333 study (EuropeanCommission, 1999) and ‘Top down cracking: Myth or reality?’ (Jolt, 2001), which both indicatethat top-down cracking is the more common mode of failure in pavements in Europe. This failuremode is not captured mechanistically by the model. However, as PMS Objekt is calibrated againstfield pavements, without considering the cause of crack-development, the assumption is madethat the top-down mechanism is also captured empirically within the model.

PMS Objekt uses the Palmgren-Miner rule approach and divides the year into four periods(thaw, summer, autumn and winter) to account for seasonal variations in temperature and thusthe change of modulus for the unbound layers. No damage is accumulated during the winter as

Figure 3. PMS Objekt flow chart.

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Road Materials and Pavement Design 9

Figure 4. Correlation between predicted (PMS Objekt) and observed pavement life at Crack Index = 250(Göransson, 2004).

it is assumed that the ground is frozen. A user can specify the mean temperature and length ofeach season, and a modulus for each season is calculated. This returns a weighted (based onrelative damage) number of allowed standard axle-passes (Dual tyre – 100 kN, 800 kPa) beforethe pavement fails. A flow chart for the process is shown in Figure 3.

The documentation for the model mentions that reliability is something yet to be implemented(Djärf et al., 1996). The version of PMS Objekt used in this study does not include statistics as apart of the design process. Thus, reliability is not a parameter that can be varied in PMS Objekt.

In PMS Objekt, the pavement is made up by pre-defined layers/materials that are commonlyused for road construction in Sweden. The most important properties for the material are theresilient modulus (for each season, respectively), and Poisson’s ratio (the default value is 0.35for all materials). PMS Objekt also automatically corrects the stiffness of the bound layers asthey grow in thickness to simulate the depth-dependent aging effect. This means that a thickerasphalt-bound layer is represented by a slightly lower modulus than a thinner layer.

In a validation of PMS Objekt by Göransson (2004) against field performance, the generalconclusion is that a pavement with a design life of 20 years will fail after approximately 16–19years, depending on the definition of failure in the field. Figure 4 shows the correlation betweenestimated and actual life length at Crack Index 250 on a scale from 0–1600, where a higherCrack Index represents a more cracked surface. It should be noted that traffic volume and axleloads were estimated in this validation, and not actually measured values. Further on, materialproperties were gathered from the PMS Objekt database, so any construction variability issueswere disregarded, leading to a possible over-estimation of the predicted life length. The correlationbetween predicted (by PMS Objekt) and actual pavement life is shown is Figure 4.

4. Evaluation of the applicability of the CM design moduleA comparison between the CM design module and the traditional Mechanistic/Empirical methodwas made for a combination of asphalt-concretes, temperatures and traffic. The asphalt concreteABT 11 is a dense graded mix with a maximum aggregate size of 11 mm while the AG 22is an asphalt-bound base layer with a maximum aggregate size of 22 mm. ABT over an AG

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is a recommended and very common structure for traffic levels up to about 10 million ESALs(Vägverket, 2008) while the base-only (AG-only) structure is used for traffic levels around 1million ESALs due to its inferior wear- and deformation properties compared with dedicatedwearing courses. In PMS Objekt’s material database, these two are the two standard materialsused when the wearing course and bound base course are added from the material database to thestructure the user wishes to evaluate. The combination of materials and climate combinations ismade up of 24 different scenarios:

Materials:

• ABT 11 + AG 22 (160/220)• AG 22 (160/220)

Table 1. Climate data.

Location Region Climate zone MAAT

Göteborg V. Götaland 1 7◦CFalun Dalarna 3 5◦CKiruna Norrbotten 5 2◦C

Figure 5. Swedish climate zones (figure from PMS Objekt).

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Road Materials and Pavement Design 11

Temperatures:

• 2 , 5 and 7 degrees Celsius

Traffic:

• 1, 2, 5 and 10 million ESALs

The temperatures used were selected from the annual mean temperatures for the climate zonesused by PMS Objekt to predict material properties. Temperatures and their corresponding geo-graphical location and climate zone are shown in Table 1 and a map of all the climate zones areshown in Figure 5. Material gradation and binder specifications are shown in Table 2.

The standard binder used in PMS Objekt predictions is a B180, having a penetration value of160–220, and this was interpreted as a PG 52-28, as the HMA fracture mechanics framework usesSuperPave parameters rather than penetration-grading of bitumen.

The same base construction was used for both the models and the standard values in PMS Objektfor unbound materials where transferred to the CM design module for layered elastic evaluation.For all unbound materials the ‘summer’ value was used in the developed design module as it justuses the mean average air temperature (MAAT ) to account for climate while PMS Objekt estimate

Table 2. Gradation and binder specifications.

Mix 19 mm 9.5 mm 4.75 mm 0.075 mm Air-voids Binder content Binder

ABT11 100 85 55 10 2.5% 6.0% B160/220AG22 90 55 40 8 5% 4.5% B160/220

Figure 6. Layer structure of the analysed pavements.

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Table 3. Traffic and reliability.

ESALs (million) Reliability % Classification

ESALs ≤ 1 70 Local/collector roads1 < ESALs < 3 75 Low duty streets3 ≤ ESALs < 5 80 Medium duty streets5 ≤ ESALs < 10 85 Medium to heavy trafficESALs ≥ 10 90 Highways

Table 4. Traffic and optimum ER, (Birgisson et al., 2006).

ERopt = f (x : ESALs in 10 millions)

Reliability (%) x < 0.14 0.14 ≤ x < 0.8 x ≥ 0.8

50 0.112 x + 0.65 0.311 x + 0.62 0.114 x + 0.7870 0.162 x + 0.65 0.388 x + 0.62 0.146 x + 0.8175 0.192 x + 0.65 0.423 x + 0.62 0.156 x + 0.8380 0.214 x + 0.65 0.4545 x + 0.62 0.170 x + 0.8485 0.241 x + 0.65 0.491 x + 0.62 0.187 x + 0.8690 0.276 x + 0.65 0.546 x + 0.61 0.212 x + 0.88

a resilient moduli for each season of the year. Poisson’s ratio was set equal to 0.35 for all unboundmaterials, as by PMS Objekt default.

The layer structures of the two structures modelled are shown in Figure 6 and these structurescorrespond to the default layers suggested by PMS Objekt. The scope of the design thicknessiteration is to find the optimum thickness of the AC-layer just below the wearing course. Thetype of AC-base is limited to an AG 22 as it represents the standard bound base-material in PMSObjekt’s material database.

To estimate stress in the material, a Swedish standard axle was used in a linear elastic analysis.The axle consists of a dual tyre setup with a 100 kN axle-load, a 300 mm centre to centre wheelspacing and a tire pressure of 800 kPa.

Reliability was estimated based on traffic levels as shown in Table 3. The reliability valuesare based on the AASHTO/NCHRP guidelines (National Cooperative Highway Research Board,2004) while the energy ratio equations in Table 4 are the set of equations used by the FloridaCracking Model for roads with one million ESALs and up (Birgisson, Wang, & Roque, 2006b).

Running the developed software for a single case takes about 2–3 seconds from the point allin-data is given by the user. If a full pavement-life curve with a yearly analysis and sensibilitydata is plotted, the software needs another 3–4 seconds before all results can be presented.

5. Results and calibrationTables 5 and 6 present the most important material properties obtained by modelling with theparameters described in the HMA fracture mechanics section of this paper. DCSEL is the Dis-sipated Creep Strain Energy threshold at the temperature of interest, St is the modelled tensilestrength (at the surface) and E∗ is the predicted dynamic modulus. Noticeable is the increasein dynamic modulus, and thus the tensile strength of the AC. After 20 years it is roughly threetimes higher than at the point of construction (T = 0). These are all surface values – in the designprocedure, the different AC-layers are assigned their stiffness from the middle of the layer usingthe viscosity-depth relation according to equation (7).

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Road Materials and Pavement Design 13

Table 5. Mix properties at T = 0.

DCSEL Surface |E∗| StMix [kJ/m3] [MPa] [MPa]

ABT 11 at 7◦C 36.40 4900 0.90ABT 11 at 5◦C 30.60 5500 0.95ABT 11 at 2◦C 22.90 6500 1.05

AG 22 at 7◦C 32.30 5600 0.95AG 22 at 5◦C 27.15 6300 1.00AG 22 at 2◦C 20.30 7400 1.10

Table 6. Mix properties after 20 years of aging.

DCSEL Surface |E∗| StMix [kJ/m3] [MPa] [MPa]

ABT 11 at 7◦C 0.73 16000 2.70ABT 11 at 5◦C 0.35 17300 3.00ABT 11 at 2◦C 0.10 18000 3.30

AG 22 at 7◦C 0.65 18000 2.80AG 22 at 5◦C 0.30 19400 3.10AG 22 at 2◦C 0.10 21000 3.40

Table 7 shows the Optimum thicknesses for a different number of ESALs over the designperiod (1, 2, 5 and 10 million respectively) calculated by PMS Objekt, the un-calibrated CMdesign module and finally the calibrated CM design module. All thicknesses were rounded up tothe nearest 5 mm.

In Figures 7 and 8, examples of the results before and after calibration are plotted for two of theclimate and material scenarios investigated. Before calibration, the results were, in general, closeto those of PMS Objekt for traffic levels between 1.4 million ESALs and 5 million ESALs overthe design period in climate zones 1 and 3. For traffic levels lower than those 1.4 million ESALs,the fracture mechanic model overdesigned the AC-thickness which led to calibration of the ER-equations in order to address this. Above 5 million ESALs, the developed model underestimatedthe total thickness up to 10%, especially in climate zone 5. In absolute terms – no differences largerthan 20 mm (for the highest traffic level) were observed, and for the most common structure atthese traffic levels, the ABT wearing course over an AG base course, the results before calibrationare almost identical to the reference in the two mildest zones even before calibration. Figure 9shows this structure with an ABT wearing course for the three climate zones investigated at atraffic volume of 5 million ESALs.

For the AG-only structure, the CM-design module generally under-predicts the thicknessneeded compared to the reference. This can be related to the fact that the gradation and bindercontent of the AG gives it a higher modulus and tensile strength, without sacrificing too much ofits creep properties and DCSE-limit (Tables 5 and 6). In this study, no adjustment to the AG’svoid content due to after–compaction, when the material is used as a wearing course, had beendone.

Calibration-wise, just a small increase in the constant term for these traffic levels was enoughto obtain a much better fit with the results from PMS Objekt over a majority of traffic levelsand temperatures. For the AG 22, the fit at one million ESALs became somewhat worse aftercalibration of the ER equations at the coldest temperature used in the prediction, while all other

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Table 7. Estimated AC-thicknesses. Before and after calibration.

1M 2M 5M 10MMix [ESALs] [ESALs] [ESALs] [ESALs]

PMS ObjektABT 11 at 7◦C 80 105 140 160ABT 11 at 5◦C 100 120 150 170ABT 11 at 2◦C 120 130 160 195

AG 22 at 7◦C 85 115 140 165AG 22 at 5◦C 95 120 150 175AG 22 at 2◦C 120 130 160 195

CM un-calibratedABT 11 at 7◦C 95 105 135 155ABT 11 at 5◦C 105 120 145 165ABT 11 at 2◦C 120 130 155 175

AG 22 at 7◦C 90 100 130 150AG 22 at 5◦C 100 110 140 160AG 22 at 2◦C 115 125 150 175

CM calibratedABT 11 at 7◦C 90 110 140 165ABT 11 at 5◦C 100 125 150 175ABT 11 at 2◦C 110 130 165 190

AG 22 at 7◦C 80 105 140 165AG 22 at 5◦C 90 120 150 175AG 22 at 2◦C 105 130 160 185

Figure 7. AC-thickness for AG 22 in climate zone 3.

scenarios were improved in terms of constancy to PMS Objekt designs. The calibrated relationsare shown in Table 8.

Figures 10 and 11 show examples of how the calibration improves the predictions. As expectedfrom the results, at low traffic levels the design by PMS Objekt drops to about 50% reliabilitycompared with un-calibrated designs by the new design tool. At the other end of the traffic volume

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Figure 8. AC-Thickness for ABT 11 + AG 22 in climate zone 1.

Figure 9. AC-thickness for an ABT 11 + AG 22 in all three climate zones with a traffic volume of 5million ESALs.

Table 8. Optimum ER after calibration.

ERopt = f (x : ESALs in 10 millions)

Reliability (%) x < 0.14 0.14 ≤ x < 0.8 x ≥ 0.8

50 0.112 x + 0.62 0.311 x + 0.65 0.114 x + 0.7870 0.162 x + 0.62 0.388 x + 0.65 0.146 x + 0.8175 0.192 x + 0.62 0.423 x + 0.65 0.156 x + 0.8380 0.214 x + 0.62 0.4545 x + 0.65 0.170 x + 0.8485 0.241 x + 0.62 0.491 x + 0.70 0.187 x + 0.9090 0.276 x + 0.62 0.546 x + 0.70 0.212 x + 1.05

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Figure 10. AC-thickness for different reliability for an AG 22 in climate zone 3 before calibration.

Figure 11. AC-thickness for different reliability for an AG 22 in climate zone 3 after calibration.

spectra, PMS Objekt designs approach 95–99% reliability compared with un-calibrated values.After calibration, the reliability of PMS Objekt designs, in all scenarios but two (out of 24),ends up between 70 and 90% reliability when compared with the CM design module. This alsoindicates that the assumed reliability distribution in Table 3 is somehow empirically accountedfor in PMS Objekt designs.

6. Summary and conclusionsThis paper presents the first phase of the development of a new calibrated mechanistic pavementdesign framework for Sweden. The initial development focused on the implementation of theHMA fracture mechanics framework into pavement design and the subsequent testing of the

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method against the current (PMS Objekt) design tool used in Sweden. Two standard and repre-sentative designs were compared with regard to optimizing the designed pavement for resistanceto cracking in three difference climate zones. The designs were first evaluated with a model usingan energy-based threshold for crack development (HMA fracture mechanic model) and secondlywith a model using a damage-ratio approach based on an allowed horizontal tension at the bottomof the AC layer (PMS Objekt). The later model has been used for road and highway design inSweden for more than 15 years.

Assumptions on material properties, climate and reliability levels were made to allow for adirect comparison between the two models discussed. After calibration to account for reliabilityat low and high traffic levels, the overall discrepancy between the two models is no more than 5%for the whole range of ESALs (1–10 million), climates (zones 1–5) and material combinations.

As the developed design tool accurately predicts design thicknesses under such diverse condi-tions as Floridian compared with Swedish, within the 10% margin even before calibration, thereis a clear indication that the material models and the failure criterion are both valid well outsidetheir range of initial calibration. Furthermore, as the implemented CM-design module formulatesthe failure criterion from tensile strength and the viscoelastic properties of the material, it canbe used to predict the performance of new mixtures and improved binders without building anextensive, empirical material database. The developed design framework also incorporates relia-bility as a parameter, which gives the designer another tool to optimize the thickness with regardto economic aspects.

Further work will include a review and update of the aging model and the response model,where the scope is to move away from a linear elastic model to a model that captures more of therheological behaviour of asphalt concretes and their stress redistribution as cracks appear in thepavement.

ReferencesArm, M. (1992). SAN REMO - Ny dimensionering av vägöverbyggnader i BYA på kort sikt. Vägavdelningens

vägkonstruktionssektion, VTI.Birgisson, B., Roque, R., Kim, J., & Pham, L.W. (2004). The use of complex modulus to characterize the

performance of asphalt mixtures and pavements in Florida. Florida: Report to the Florida Departmentof Transportation.

Birgisson, B., Wang, J., & Roque, R. (2006a). Addendum to ‘Implementation of the Florida cracking modelinto the mechanistic-empirical pavement design’. Gainesville: University of Florida.

Birgisson, B., Wang, J., & Roque, R. (2006b). Implementation of the Florida cracking model into themechanistic-empirical pavement design. Gainesville: University of Florida.

Deme, I.J., & Young, F.D. (1987). Ste. Anne test road revisited twenty years later. Proceedings of theCanadian Technical Asphalt Association, 32, 254–283.

Djärf, L., Wiman, L.G., & Carlsson, H. (1996). Dimensionering vid nybyggnad. Linköping: VTI.European Commission (1999). EUR 18906 - COST 333 - Development of New Bituminous Pavement Design

Method. Luxembourg: Office for Official Publications of the European Communities.Göransson, N.-G. (2004). VTI notat 2-2004: ‘Validering av PMS Objekt’. Linköping: VTI.Jacobs, M.M.J. (1995). Crack Growth in Asphaltic Mixes. PhD Thesis, Delft University of Technology,

Netherlands.Jolt, J. (2000). Top-down Cracking: Myth or Reality?. The World Bank Regional Seminar on Innovative

Road Rehabilitation and Recycling Technologies. Amman, 24–26 October.Matsuno, S., & Nishizawa, T. (1992). Mechanism of Longitudinal Surface Cracking in Asphalt Pavement.

Seventh International Conference on Asphalt Pavements, University of Nottingham, Vol. 2.Mirza, M.W., & Witczak, M.W. (1995). Development of a global aging system for short and long term aging

of asphalt cements. Journal of the Association of Asphalt Paving Technologists, 64, 393–430.Myers, L.N. (2000). Development and propagation of surface initiated longitudinal wheel path cracks in

flexible highway pavements. PhD Thesis, University of Florida. Florida.

Dow

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18 D. Gullberg et al.

Myers, L.N., Roque, R., & Birgisson, B. (2001). Propagation mechanisms for surface-initiated longitu-dinal wheel path cracks. Transportation Research Record No 1778, Transportation Research Board,Washington, DC.

National Cooperative Highway Research Board (2004). Guide for mechanistic-empirical design of new andrehabilitated pavement structures. National Cooperative Highway Research Board.

Roque, R., Birgisson, B., Drakos, C., & Dietrich, B. (2004). Development and field evaluation of energy-based criteria for top-down cracking performance of hot mix asphalt. Journal of the Association ofAsphalt Paving Technologists, 73, 229–260.

Uhlmeyer, J.S., Willoughby, K. Pierce, L.M., & Mahoney, J.P. (2000). Top-down cracking in WashingtonState asphalt concrete wearing courses. Issues in pavement design and rehabilitation. TransportationResearch Record No. 1730. Washington, DC: Transportation Research Board.

Vägverket (2008). VVTK VÄG. Borlänge: Vägverket.Wang, L.B., Myers, L.A., Mohammad, L.N., & Fu, Y.R. (2003). Micromechanics study on top-down

cracking. Transportation Research Record No. 1853: Journal of the Transportation Research Board,121–133.

Witczak, M.W., & Fonseca, O.A. (1996). Revised predictive model for dynamic (complex) modulus ofasphalt mixtures. Transportation Research Record, No. 1540, 15–23.

Zhang, Z., Roque, R., Birgisson, B., & Sangpetngam, B. (2001). Identification of suitable crack growth lawfor asphalt mixtures using the superpave indirect tensile test (IDT). Journal of the Association of AsphaltPaving Technologists, 70, 206–241. Florida: University of Florida.

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