Significant Findings from Full-Scale Accelerated Pavement Testing (2004)

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47 CHAPTER FIVE ENHANCEMENT OF MODELING IN PAVEMENT ENGINEERING INTRODUCTION Pavement performance is a measure of the extent to which a pavement fulfills its principal objective. Performance models are tools to predict performance; they may ulti- mately be used in pavement management systems, in the structural design of pavements, and in the development of performance-related specifications. Jooste et al. (1997) re- ported that APT provides a window on pavement perform- ance, which can possibly be used to predict how the pave- ment will perform under real traffic. This chapter presents models developed and/or validated through APT for use in the aforementioned applications. APT programs have pro- duced a wide range of models, both theoretically based and empirical, and focus on physical phenomena covering APT processes or related applications of test data. The useful- ness and application of the models that have been validated will be explored with due regard to their limitations. Some models that nominally fall outside the scope of the study are also discussed because they provide a basis for further application of APT. This chapter explores the phenomenological modeling of pavement damage and the generalization of models by making them dimensionless and thus increasing their ap- plicability. Models developed as part of APT research are discussed, including asphalt pavement failure criteria, for example, for subgrade and base layer permanent deforma- tion, asphalt layer permanent deformation, and asphalt fa- tigue and cracking. Aspects of modeling concrete pave- ment performance are also addressed. Before discussing the wide variety of applications that were found in the lit- erature, the results from the questionnaire survey will be presented. QUESTIONNAIRE SURVEY The responses to Questions 5.1 to 5.5 on modeling are re- flected in Figures C39 to C41 in Appendix C. These were synthesized and the results are contained in the following list. • Models that are most frequently being used with APT are based on elastic layer analysis, as could be ex- pected, but FE analysis is used almost as frequently. • Stress–strain modeling and deformation modeling are used most frequently; however, as could be expected, deflection modeling and back-calculation of moduli are used almost as often. Fatigue modeling has also received considerable attention. Load equivalency does not rank as high, probably because the latest computer hardware and software enables designers to cater to very specific selected loads, which allows the designer to select a specific traffic mix for the pur- pose of designing any load configuration. • Instrumentation used to gather modeling data most frequently uses strain gauges, although some facili- ties opted not to use them because of the high rate of loss of such gauges. Displacement gauges, such as the Multi-Depth Deflectometer (MDD), proved to be equally popular. Pressure cells are also used, albeit not as frequently. Subgrade moisture is also fre- quently being monitored by sensors. Views of the respondents to the survey on modeling are presented in Table D5 in Appendix D. MODELING PAVEMENT DAMAGE Pavement damage occurs as a result of traffic and envi- ronmental loading. Molenaar et al. (1999) showed that the phenomenological progression of damage lends itself to modeling using S-shaped curves. Damage, such as asphalt cracking, normally develops slowly during some period of initiation; the rate of damage then accelerates with further loading. Finally, after a certain amount of damage has de- veloped, the rate of progression decreases. This S-shape failure trend may be described using the Weibull distribu- tion, which can be written as ( )       −−= β exp1 N ntFw (3) where Fw(t) = probability that failure has occurred be- fore time t, n = number of load repetitions at time t, N = number of load repetitions at which a de- fined failure occurs, and β = curvature parameter. Figure 12 shows examples of Weibull distributions for various values of β (as shown in the legend), using a non- dimensional number of load repetitions scale n/N, to repre-

48 0% 20% 40% 60% 80% 100% 0 0.5 1 1.5 2 2.5 3 n/N P ro ba bi lit y of fa ilu re 0.5 1 2 3 5 FIGURE 12 Weibull probability of failure distribution for different β-values. TABLE 1 SOME MATHEMATICAL MODELS USED TO DESCRIBE DAMAGE WITH LOADING Models Equation Nbay ⋅+= Linear 2NcNbay ⋅+⋅+= Quadratic L+⋅+⋅+⋅+= 32 NdNcNbay Polynomial )exp( Nbay ⋅⋅= Exponential Nbay ln⋅+= Logarithmic bNay ⋅= Power ( )NbNay ⋅⋅= Geometric ( )Nay /1= Root ))exp(1/( Ncbay ⋅−+= Logistic )exp( dNcbay ⋅−⋅−= Weibull Nbay /+= Hyperbolic )1/()( 2NdNcNbay ⋅+⋅+⋅+= Rational ))2/()(exp( 22 cbNay ⋅−−⋅= Gaussian sent the relative damage that occurs with loading over time. When the ratio n/N is equal to 1, the probability of failure is 50%. This may represent a 50% loss in stiffness or a 50% cracked area. With additional loading the rate of deterioration diminishes progressively. Note that similar curves may be established for other failure scenarios. Molenaar et al. (1999) noted that the complete S curve seldom develops fully in practice, because road authorities will not allow pavements to deteriorate to such a great ex- tent. This is in contrast to APT tests that may be continued until total failure occurs. While the Weibull distribution is used to model the probability of pavement failure over time, a variety of mathematical models are used to describe the progression of damage (y) with loading (N) as shown in Table 1. Regression constants are shown as a, b, c, and d.

49 Multiple (linear or nonlinear) regression analysis may be used to determine regression constants. Regression analysis is a statistical method that uses the relationships between two or more quantitative variables to generate a model that may predict one variable from the other(s). Hand et al. (1999) stated that the term multiple linear re- gression is employed when a model is a function of more than one predictor variable. The objective behind multiple linear regression is to obtain adequate models, at a selected confidence level, using the available data, while at the same time satisfying the basic assumptions of regression analysis, which include that • Severe multicollinearity does not exist among predic- tor variables, • Influential outliers do not exist in the data, and • Equal variance exists among residuals (normality). The objective is accomplished by selecting the model that provides the greatest adjusted coefficient of determina- tion (R2) and lowest mean-square error for given data. Turtschy and Sweere (1999) evaluated different models of pavement damage as part of the PARIS (Performance Analysis of Road Infrastructure) project in Europe. Dete- rioration data were collected from 900 in-service test sections under real traffic and 44 APT-trafficked sections. It was found that power models work well with rutting data, whereas loga- rithmic models are suited to cracking models. The authors compared failure criteria measured using APT with that measured on the in-service roads under real traffic. They did not model the initial stage of cracking and rutting in APT studies. They reported that one of the main factors affecting this initiation; that is, aging of the AC, does not occur in the short time scale of APT tests. Furthermore, because in-service pavements are repaired before maintenance, damage data col- lected from these pavements are in an intermediate stage. They concluded that because APT results indicated that the linear functional forms are appropriate for the intermediate stage, the linear form is suitable for modeling the propaga- tion of cracking and rutting under real traffic. One of the major shortcomings of modeling pavement performance using the mathematical models described above is that the models may have limited applicability and may only be valid for the conditions and sites for which they were established. For this reason, Molenaar et al. (1999) suggested that generalized models be obtained by making them dimensionless. This is done by relating the damage as a relative ratio to the cause of damage, also rep- resented as a relative ratio, in the following form: β   = T t D d (4) where d = amount of damage at the time of inspection t, D = amount of damage at which the pavement is assumed to have reached end of life at time T, and β = constant depending on the type of damage and structure. Molenaar et al. (1999) pointed out that the use of such power models is problematic in cases of damage types for which the exponent β is larger than 1. They reported that such power models do not allow pavement condition pre- dictions to be made in cases where maintenance is already overdue; that is, in cases where the condition is beyond the terminal, condition D. Numerous computer models have been developed to es- timate the displacements, stresses, and strains within simu- lated pavement systems. Models vary from those using elastic multilayer theory (De Jong et al. 1973; Wardle 1977; Kopperman et al. 1986) to others that account for nonlinearity. The latter include visco-elastic VESYS (Kenis 1978), VEROAD (Hopman 1996), and elasto- plastic models (mechano-lattice). Yandell and Behzadi (1999) have also used the mechano-lattice model to illus- trate the influence of loading direction on elasto-plastic pavement response. Residual stresses and strains that ac- cumulate in pavements trafficked in one direction only dif- fer from those when the direction of travel is allowed to reverse. Yandell has also compared the mechano-lattice model to pavement response determined using CIRCLY (Wardle 1977) and VESYS based on ALF-accelerated test- ing of different pavements. Input parameters define pave- ment structures, load configurations, and material charac- teristics. In some cases, the models have been further developed to estimate pavement performance in terms of rutting and fatigue by incorporating appropriate transfer functions (Huang 1993; Chatti et al. 1999a). These models include iterative algorithms to account for seasonal and load variations. The large number of iterations required to characterize the performance of asphalt pavements has led to the use of simplified approaches based on Odemark’s layer transformation theory. APT has assisted in the devel- opment of these models in that displacement, stress, and strain estimations may be validated using instrumented APT test sites. Furthermore, transfer functions used in the models may be refined based on the results of APT tests. MODELING OF ACCELERATED PAVEMENT TESTING SUBGRADE RUTTING PERFORMANCE Modeling of permanent deformation of subgrade materials is usually expressed in terms of (elastic) stresses or strains on top or within the subgrade layer and in its simplest ap- plication generally takes the form of the following log–log (power) relationships.

50 Rut depth may be related to trafficking in the same way that it may be related to subgrade strain. Odermatt et al. (1999) indicated that HVS tests were done at different wheel loads, and they were able to develop a relationship between rut depth and wheel load with trafficking as shown in Equation (9). βαε Npz ⋅= (5) βασ Npz ⋅= (6) where ( ) 27.04816.00117.0 NPRD ⋅−⋅= (9) εpz = permissible vertical strain on top of subgrade, σpz = permissible vertical stress on top of subgrade, N = number of standard axle loads, and α,β = regression constants. where RD = average surface rut depth, mm; P = wheel load, kN; and N = number of passes. These equations may be implemented in mechanistic pavement design and evaluation systems based on linear elastic material properties. The equations indicate that the stresses and strains within subgrades increase quite rapidly during the early loading cycles and then tend to increase at a much slower rate because of shear distortion and densifi- cation of the materials. This equation is similar to Equation (5), indicating that the α constant in that equation is a function of wheel load. The AASHO Road Test rut depth data were used by Finn et al. (1986) to develop a permanent deformation model for subgrade rutting. They found that the rate of rutting was strongly related not only to traffic and stress on top of the base, but also to surface deflection. Two rutting models were developed for pavements with thin asphalt surfacing layers [less than 150 mm (6 in.) thick] and those with full-depth asphalt. These models are shown in Equations (10) and (11) for thin and thick asphalt layers, respectively. Odermatt et al. (1999) developed models for predicting surface rut depths resulting from subgrade deformations under HVS trafficking. Strains within the subgrade were measured using the ε-mu coil system. Dynatest soil pres- sure cells were used to measure the stresses on the surface under the HVS loads. Equation (7) shows the subgrade rut- ting model developed, expressed in terms of elastic vertical subgrade dynamic strain. cσ Nd43RR log118.1 )18(log167.0log3.4617.5log − −+−= (10) 55.3ε121 vERD ⋅−= (7) c NdRR σlog666.0 )18log(658.0log717.0173.1log + −+−= (11) where RD = rut depth, mm; εv = subgrade vertical elastic strain; E = elastic modulus; with R2 = 0.89. where RR = rate of rutting in micro-inches per axle repetition, d = surface deflection in mils under a load of 40 kN (9,000 lb), σc = vertical compressive stress at the asphalt- base interface (psi), and N18 = number of 18-kip single-axle repetitions/ 100,000. Odermatt et al. (1999) noted that rutting models based on elastic strains are inaccurate for predicting rutting in wet, soft soils, a condition commonly found during thaw weakening periods. During these periods, there may be no, or only weak, relationships between elastic strains and rut depth. In these cases it is more practical to estimate rutting based on plastic strains. The following equation shows such a relationship developed by Odermatt et al. that also takes the form of the log–log equations indicated previously: Chen and Lin (1999) adopted a similar approach to model the permanent deformation of two TxMLS test sites in Texas. They related the rutting to surface deflection measurements determined from FWD tests. The main drawback of this approach is that the models are specific to test sites on which data are collected. Furthermore, one is unable to pinpoint the source of failure and differentiate between the relative rutting in the respective pavement layers. 49.0 0545.0 vpRD ε⋅= (8) where RD = rut depth, mm; and εvp = subgrade accumulated permanent strain.

51 12 10 R ut D ep th , m m 8 6 y = 0.004x 0.59264 FIGURE 13 Subgrade rutting model of TxMLS tests on Pad F5 in Victoria. The model shown in Figure 13 was derived relating the rut depth on the surface to applied TxMLS loads for one of the test sections using data provided in the paper by Chen and Lin (1999). The model described by Equation (5) fits the data well. Theyse (1997) mentioned that two types of data gener- ated during an HVS test are used to develop the permanent deformation models on which the design transfer functions for subgrade deformation are based. These are the in-depth deflection and permanent deformation data obtained from the MDD measurements taken at regular intervals during an HVS test. Test data from a number of HVS tests, selected from the moderate and wet regions in South Africa, were used for the development of the permanent deformation models. A multidimensional conceptual model for perma- nent deformation was also developed and calibrated with HVS test data for pavement foundation and structural layers of different material qualities. These models provide per- manent deformation design transfer functions at different expected performance reliabilities for unbound pavement layers in South Africa. Elastic moduli were back-calculated from the peak de- flection values at the layer interfaces for the HVS test sec- tions under investigation as opposed to the back- calculation of layer moduli from the deflection bowl. The plots of permanent deformation against vertical strain show no clear correlation between these two parameters. The plots of permanent deformation against vertical stress indi- cate a better correlation between the applied stress and the resulting permanent deformation. This contradicts current design practice, where the permanent deformation of the pavement foundation is usually linked to the vertical strain calculated at the top of the foundation layers. It was there- fore decided to develop permanent deformation transfer functions for the pavement foundation with vertical stress as the critical parameter. The rutting model is given in Equation (12).    −= 1cBsc eNePD σ (12) where PD = permanent deformation, mm; N = number of repetitions (E80 standard axles); σc = vertical compressive stress on top of the subgrade, kPa; and c,s,B = regression constants. Theyse (1997) stated that the regression constants c and s in Equation (12) do not change for different material types. Because the HVS tests were done on pavements consisting of different materials, he was able to determine the regression constant B for the different materials. This approach extended the applicability of the performance model. The SMDM has been used in South Africa for a number of years (Theyse et al. 1996). This is a mechanistic– empirical design method that includes fatigue transfer functions for asphalt surfacing, asphalt base, and lightly cemented layers, as well as permanent deformation transfer functions for unbound structural layers and the roadbed. All of these were developed through the SA–HVS pro- gram. The method is based on a critical layer approach whereby the shortest layer life of the individual pavement layers determines the pavement life. This approach may be suited to the fatigue failure of bound layers, but does not allow for each of the pavement layers to contribute to the R2 = 0.9944 2 0 0 100000 600000 700000 200000 300000 400000 500000 TxMLS Axles

52 total surface rut. Current research is therefore aimed at de- veloping permanent deformation models for individual pavement layers, to enable the designer to predict each layer’s contribution to the total permanent deformation of the pavement system. Ullidtz et al. (1999b) proposed the following three equations (strain, stress, and energy density models, re- spectively) to model permanent deformation of subgrade materials: B zpz NA εε α ⋅⋅= (13) B z pz p NA    ⋅⋅= σε α (14) B z z pz 2p NA     ⋅⋅⋅= εσε α (15) where εpz = vertical plastic strain in microstrain at depth z, vertical εz = resilient strain in micro- strain at σ ess (atmospheric pressure), A,α, N = number of load repetitions. char- cterize the behavior of real pavement materials. esign and analysis system. The equation is as fol- ws: depth z, z = vertical compressive stress at depth z, p = a reference str β = constants, and The models were implemented to predict the perform- ance of pavements trafficked using the Danish Road Testing Machine. Strains within the subgrade layer were monitored using Linear Variable Displacement Transformer-based soil strain cells. Strain response monitored using the strain cells was related to mathematical models based on various multi- layer methods, including a simplified approach to elastic layer theory using the Boussinesq equation with Odemark’s layer transformation. Ullidtz et al. (1999b) concluded that the models as developed allowed a reasonable estimation of subgrade permanent deformation, although they empha- sized that the models simplify the material response and that more sophisticated models are required to better a Newcomb et al. (1999) reported on a subgrade rutting model developed exclusively as part of the Mn/ROAD pro- gram that has subsequently been implemented in a pave- ment d 3.949 15 ε 1105.5    ⋅⋅=N  v (16) here N = of ESALs to obtain a 12.5 mm rut, εv = vertical strain on top of the subgrade. halt Institute (AI) sub- rade rutting criterion shown here. v (17) here εv = rain on top of the subgrade, but modify it to account for rutting accumulation Rut depth (RD) contributed by the unbound layers was assumed to accum sug- est that the value for d in Equation (18) may be determined by substitut follows: − criterion as used earlier may be verly conservative for pavement sections with asphalt lay- the development of a new subgrade strain model that substantially red esses of overl 0.1450.012ε −⋅= N cvs (20) wher ive strain on top of the subgrade, and relatively thin asphalt layers (25 to 85 mm) over base and subgrade structures (135 to 350 mm thick) with the w number and Epps et al. (1999) used the Asp g 484.49 ε1005.1 −− ⋅⋅=N w N = number of ESALs to obtain a 12.5 mm rut, and vertical st in the pavement structure. ulate as follows: eNdRD ⋅= (18) where d and e are experimentally determined coefficients. Least-squares analyses based on WesTrack APT data g ing for N shown in Equation (17) as e vfd )ε101.05( 4.4849− ⋅⋅⋅= (19) Based on HVS testing of sections with relatively thick asphalt layers (>150 mm), Harvey et al. (1999) reported that the AI subgrade strain o ers thicker than 150 mm. Pidwerbesky et al. (1997a), using CAPTIF APT testing of five different asphalt pavements, investigated subgrade rutting criterion for asphalt pavements. Investigations led to uced the required thickn ays. e εcvs = maximum vertical compress N = number of load repetitions. This criterion was established for pavements having lo

53 subgrade CBR ranging from 4% to 28%. They pointed out that no single subgrade criterion is appropriate for all con- ditions. Furthermore, the strain criterion as only a function of the number of axle load repetitions cannot be used alone. The environmental conditions, material properties (especially with respect to the granular base and subbase layers), and construction quality must be considered in the design of new pavements and overlays. The New Zealand researchers argued that because vertical compressive strains in unbound granular layers under thin asphalt sur- face layers can be equal in magnitude to vertical compres- sive strains in the subgrade under such pavements and can thus be a significant contributor to fatigue of the surfacing layer and permanent deformation, the unbound granular strains should also be considered in the modeling of thin asphalt pavements. Under a thicker HMA surface layer, the vertical compressive strains in the unbound granular pavement layers are substantially smaller than the vertical compressive strain in the subgrade and may therefore not be significant. where S = rut d h (mm ST rut d h at t n = applied number o s, N num of lo mm, and b cons t = 0.4 The r epth 18 m he depth at which maintenance is require less an 1). It was pointed out that the constant b is specific to d from the subgrade model own in Equation (5). This indicates that the β constant in q of the subgrade or other response variables such as ubgrade performance. This includes material roperty parameters that may be determined from triaxial ept ) at time t, = ept he end of pavement life = 18 mm, f load repetition = ber ad repetitions to a rut depth of 18 = tan 1 (from LINTRACK APT trials). ut d of m is considered to be t d (this ensures that b is th the sand subgrade used in the LINTRACK tests that con- trolled the subgrade deformation. A comparison of the APT subgrade deformation data with the subgrade strain criteria developed by Shell indicated that design criteria estab- lished for subgrades based on the Shell method should consider a reliability of 85%. The formulation of the subgrade rutting model shown in Equation (21) may be derive In their investigation, Pidwerbesky et al. (1997a) found that the magnitudes of actual vertical compressive strain measured in the unbound granular layers and subgrade are substantially greater than the levels predicted by the mod- els on which some designs are based. Their conclusion was based on the Shell, Austroads, and old New Zealand Road Board flexible pavement design procedures for the same number of loading repetitions to failure. sh E uation (5) is also a function of the subgrade material. For the APT tests done by Odermatt et al. (1999), the β constant in Equation (9) is 0.27, specific to the silty-sand subgrade used in the HVS tests. The β constant in the model described in Figure 13 is 0.59 for a clayey subgrade. The subgrade permanent deformation models described thus far have either been related to stresses and strains on The relationship between vertical compressive strains in the materials and the cumulative loading becomes stable after the pavement is compacted under initial trafficking (in the absence of adverse environmental effects). The New Zealand Road Board subgrade criterion placed emphasis on loading history. Using APT the New Zealand research- ers found that the effect of cumulative axle loading has substantially less influence on the response and perform- ance of unbound granular pavements than is implied in the pavement models that are the basis of the flexible pave- ment thickness design procedures. The pavement models have been calibrated to in-service pavements using empiri- cal data from field studies. Hence, environmental factors and construction quality must have a significant influence on the pavement performance, but current flexible pave- ment design procedures emphasize the effect of load repe- titions and only implicitly consider the other two major factors. top those determined from FWDs. None of the models account for the material properties of the subgrade materials. Molenaar et al. (1999) noted that this is a shortcoming of performance models determined using APT and that mate- rial characterization is useful to improve the applicability of these models. In the case of subgrade materials, there is an understandable reluctance to include material properties in performance models given the location of the materials in the pavement structure. It would be necessary to remove these materials for laboratory testing, which would disturb the in situ state of the materials. Nevertheless, material characterization may be included in the modeling of sub- grade deformation. This factor can have an influence on APT, because modeling is sometimes done simplistically. Tseng and Lytton (1989) illustrate this and show that de- formation models should be a function of not only stress and strain, but also material properties, as Equation (22) indicates. This lends support to the close interrelationship between APT and material testing. The following reference does not relate directly to APT applications but illustrates the point. In their model, Tseng and Lytton (1989) propose as fol- lows for s Molenaar et al. (1999) identified the following trend in subgrade rutting that may be used in remaining life esti- mates. Note that this model is dimensionless. b N n ST S   = (21) p

54 tests on subgrade materials. The model considers the mois- ture content of the subgrade material. Note that the model also accounts for the stress-dependent nature of subgrade materials. In the next section, the modeling of APT asphalt rutting performance is discussed. MODELING OF ACCELERATED PAVEMENT TESTING ASPHALT RUTTING PERFORMANCE h N pN v r p ⋅ε       ε ε=ε β –exp)( 0 (22) Generalized APT models of asphalt rutting performance are often similar to those for subgrade performance, ex- pressing permanent deformation in terms of strains within the asphalt layer instead of strains on top of the subgrade. The visco-elastic nature of asphaltic materials requires that the influence of temperature and frequency (rate of load- ing) be considered. where εp(N) = plastic strain accumulated during N load repetitions for the layer; εr = resilient strain imposed in lab test to obtain material properties ε0, ρ, and β; εv = average vertical resilient strain in the layer as obtained from the primary response model; and h = thickness of the layer. Williams et al. (1999) used the following relationship [similar to Equation (5)] to establish a correlation of rutting observed from APT trials at WesTrack to results of re- peated shear at constant height tests: εp = a · Nb (25) The ratio ε0/εr is estimated according to the type of ma- terial, granular or subgrade soil. where For granular soils θσ=    ε ε 003077.0–06626.0–80978.0log 0 c r W +0.000003Er θσ++=β 001806.003105.09190.0–log cW –0.0000015Er (23) θσ++=ρ 0003784.045062.178667.1–log cW rc E0000105.0–W002074.0– 2 θσ εp = percent permanent strain, N = number of load applications, and a,b = modeling constants. They report that there are two very important criteria that need to be emphasized. The first criterion is the selec- tion of an appropriate test temperature that reflects the in- service temperature at which the pavement will be ex- pected to perform. The second issue is the assumption of laboratory compaction simulating field compaction. Stud- ies are currently being conducted at the FHWA that indi- cate significant discrepancies between field compaction and several laboratory compaction devices. This compac- tion issue should be resolved before implementing a per- formance test in a mixture design process. For subgrade materials dc r W σ=    ε ε 11921.0–09121.0–69867.1–log 0 + 0.91219logEr ddcW σ+σ+=β 017165.00000278.09730.0–log 2 θσ+ cW 20000338.0 (24) ddc 2W σσ++=ρ 40260.0–000681.0009.11log θσ+ cW 20000545.0 Meng et al. (1999) reported on ALF tests of five differ- ent stabilized base pavements. They modeled surface rut- ting of the base in the form of Equation (5) and reported α and β regression constants for the different pavements tested. They found that rutting was confined to the asphalt surfacing layer, but also attributed part of the rutting to the deterioration of the asphalt–base interface. This deteriora- tion was related to the ingress of water through cracks in the asphalt layer. A difference in temperature and rainfall patterns during testing of the different pavement sections discussed by Meng et al. (1999) complicates the interpretation of the performance data. An example is the case of two test sec- tions constructed having the same asphalt and base thick- ness but using different base materials that were tested us- ing the same wheel load. The performance of the sections where Wc = water content (percent), σd = deviator stress (psi), σθ = bulk stress = sum of principal stresses (psi), and Er = resilient modulus of the layer (psi).

55 differed significantly; however, the performance cannot be attributed to differences in base material because of the dif- ferent temperatures and rainfalls monitored during the tests on these sections. Epps et al. (1999) assumed that rutting in asphalt was controlled by shear deformation. In simple loading, perma- nent shear in the asphalt is assumed to accumulate accord- ing to the following expression: ( ) cei Nbaγ γτexp ⋅⋅= (26) where γi = permanent (inelastic) shear strain at a 50 mm depth, ic analysis, train, N = number of axle load repetitions, and a,b The equation indicates the relationship between plastic phalt accounted for by evaluat- g i jKRD γ⋅= (27) The VESYS m cting permanent deforma- τ = shear stress determined at this depth us- ing elast γe = corresponding elastic shear s ,c = regression coefficients. and elastic deformation. Rutting estimates are computed based on elastic shear stress and strain (τ, τe) at a depth of 50 mm beneath the edge of the tire. Epps et al. (1999) stated that densification of the asphalt is excluded in the rutting estimates because it has a comparatively small in- fluence on surface rutting. Time hardening of the as in the stiffening of the binder and rutting in the asphalt layer as a result of shear deformation is determined from the following equation: odel for predi tion also relates plastic and elastic response as shown in the following model, although the modeling constants shown further account for the visco-elastic nature of as- phaltic materials: αε N⋅ µ⋅ε= (28 here p = percent permanent strain, ε = percent resilient strain, ions, and µ, determined from re- peated load laboratory testing. Lijzeng (1 PT tests done us- ing the Laboratory Test Track in The Netherlands to evalu- ate ru n binders. He n h relations were previously de- tween the stiffness f the asphaltic mix and its bituminous binder under long rp  α ) w ε r N = number of load applicat α = modeling constants a 999) of Shell reported on A the tti g characteristics of asphalt using modified oted that suc termined using static creep experiments, which turned out not to be suitable for modified binders. In the Shell Pavement Design Manual (1978), the effect of the bituminous binder on permanent deformation is in- corporated by means of a relationship be o loading time (viscous) conditions. vbitvmix SqbS ,, logloglog += (29) where Smix,v dition Sbit,v = viscous component of the stiffness of its bi- tuminous binder, and b,q = parameters specific to a certain asphalt mix. The parameter S is obtained from the following equa- tio = stiffness of mix under rutting con s, bit,v n: 03η weq vbit tW S ⋅=, (30) tw = as a measure of traffic spee Weq = num heel passes obtained from traffic spectrum, and 0 = bitumen viscosity at average paving tem- perature during service life of the road. a . Having deter iffness of the mix, the rut depth in the asphalt layer, ∆h, is then calculated using where wheel loading time d, ber of standard w η This equ tion accounts for climate and traffic loading mined the st σ vmix, where S hkh 0⋅⋅=∆ (31) h = th lt layer, σ0 = standard wheel, and k = a ess is an important material property in asphalt avement engineering and is required to model pavement struc e theory. As part of the comprehensive LINTRACK APT program, Sabha et al. (199 d a le to predict ickness of aspha contact stress of the coefficient. Stiffn p tur s when using multilayer 5) id comparison of methods availab

56 the s Material characterization parameters are also included in asphalt permanent deformation modeling of APT data. Epps et al. (1999) reported a regression equation based on WesTrack data that accounts for the binder content and air voids in the asphalt mix as shown here. tiffness m the bitumen stiffness. They rec- mmended that the formula of Francken (1977) [Equation of a mix fro o (32)], which allows a prediction of the maximum value for the mix stiffness based on the volumetric properties of the mix, be used. ( ) ( )aV b ab ab eV VV VVE 1.041056.3),( −+⋅=∞ (32) where ,( ab VVE∞ ) = maximum mix modulus at maxi- mum bitumen stiffness (MPa), volum Vb = percent bitumen in mix by volume. The dynamic modulus of bituminous materials is a com las- tic stif the i inter- nal damping f t m - scribing the stress– relationship of visco-elastic materials. T ab lu s ommonly referred to as the dynamic modulus. E 10 mm, asp V = percent air void content, and i ts. coarseA finesplusAfinesA VPA VAPA VAPAAESALs airasp airasp airasp ⋅+ ⋅+⋅+ ⋅⋅+ ⋅+⋅+ ⋅+⋅+= 8 76 5 2 4 2 3 2 1010ln (34) Va = percent air voids in mix by and e, where SALs10 = number of ESALs to a rut depth of P = percent binder content by weight of the mix, air A = regression constan plex modulus fness and in which the real part represents the e maginary part characterizes the o he aterials. It is therefore used for de strain he so te value of the complex modulus i c The terms “fines,” “finesplus,” and “coarse” assume values of 1 when sections containing specific mixes are analyzed and 0 otherwise. Thus, for a fine gradation, for example, the equation reduces to Fonseca and Witczak (1996) developed the following empirical model for estimating the dynamic modulus of asphalt mixes as a function of material properties: 00000101.0008225.0261.0 −+−= pE )log7425.0log716.0( 4/38/3 2 8 2 200200 0164.00001786.0– η−−+ ++ f pp p (33) V ff = effective bitumen content by volume, 4 = percent retained on the 3/4 in. sieve by to- tal aggregate weight, p3 e by to- tal aggregate weight, p . 4 sieve by total and p200 = percent retained on the No. 200 sieve by total aggregate weight. 2639.0 9 aspair asp PV P ⋅+ ⋅− log /34 4 0000404.0002808.087.1 415.003157.000196.0 ++ +−−+ abeff beff a pp VV V Vp 1 e where E = asphalt mix dynamic modulus in 105 psi, η = bitumen viscosity in 106 poise, f = load frequency in Hz, 10 169.0 19.48ln ESALs ⋅− 43.= (35) ibed a methodology developed to predict cumulative rutting over time using incremental rut depth modeling and including material characterization. The b f that it takes into acc unt the combined effects of environmental condi- tions and time hardening, with particular emphasis on tem- perat e it e intent was to c e effects, using a direct relation- ship t the Superpave binder specification, on the mixture behavior at WesTrack in regression models. The resulting model could then be applied to environments outside of Hand et al. (1999) descr Va = percent air voids in the mix by volume, be p3/ /8 = percent retained on the 3/8 in. siev 4 = percent retained on the No aggregate weight, ene it of the methodology developed is o ure s ns ivity in the early life of the pavement. Th apture thes o

57 TA VARIAB TO PREDICT ASPHALT RUTTING (Hand Description BLE 2 LES USED Traffic Initial oids fic mum gyrations Dust proportion SA ft2/lb FT Microns #4GRAD50 n/a p200 Percent Sbit kPa hange in rut depth in pr ent —ESALs, Delta SALs, or cumulative ESALs in-place air v et al. 1999) Nomenclature Units ESAL, DESAL, or CESAL ESALs Avi Percent Avt Percent AC Percent (twm) Gmmi, Gmmd, Gmmm Percent VMA Percent VFA Percent DP n/a Blended aggregate surface area Asphalt film thickness rcent passing the 4.75 mm and 0.3 mm sieves In-place air voids as a function of time or traf Asphalt content relative to the design optimum Percent of Gmm at initial, design, and ma Percent voids in mineral aggregate Percent voids filled with asphalt xi Ratio of pe Percent passing the 0.075 mm sieve Binder stiffness C evious increm DR P D mm Cumulative rut depth to previous increment pth in previous increment to CRDP D mm Ratio of change in rut de cumulative rut depth to previous increment CP n/a SAL = equivalent single-axle load; DESAL = delta equ cum e-axle load; Avi = r voids in-place; Avt = air void time; AC = asphalt concrete; twm = ent of Gmm at design gyration ht of mix; Gmm = maximum mm = perc mm at ma sity; Gmm f Gmm at initial gyrations; Gmmd = perc with ent of G r = nineral aggregate; VFA = voids filled hange in rut depth in previous increment; DC ea; n/a thickness k, from which data rs and verifying the methodology. The rut mode d is compreh r variables shown in Table 2. f the critical elements of this procedure was in , = the a = h calt E ivalent single-axle load; CESAL = ulative equivalent singl ai total weig theoretical den i = percent o s; Gm ximum gyrations; VMA = voids-in- m asphalt; DP = dust proportion; SA = surface a ot applicable; FT = film ; DRDP = c P = ratio of DRDP to CRDP. WesTrac were used in identifying input paramete l develope ensive and includes the potential predicto One o de- termini ture, S ple lin develo ermanent deformation predictions were made based on apable of predicting o 8 9 10 (36) where Ai = regression constants AV percent air voids in sphalt mix, AC thickness of the asp oncrete AKV = kinematic viscosity of the asphalt binder, les at ed, base layer, SD = peak surface deflection, CSRB = compressive strain at the top of the e aggre- ranular subbase. SD may either be calculated u easured using a FWD. The validity of the rut model was evaluated using APT on two ented pavement sections on I-96 in Lansing, Michi- an. Chatti et al. (1999a) reported that the MICHPAVE com- puter pro c the rutting performance of the t ec n Hug a 1 onsidered spe- cific f s fl the four wheel paths of TxMLS test sections. Ruts in the different whe e pavement lane. T he least rutting was usually selected as the benchmark rut. ng the stiffness as a function of pavement tempera- ESAL = number of equivalent single ax uperpave binder properties, and aging. Using multi- which the rut depth is being calculat ear regression techniques, the model was then ped as a function of stiffness and 10 other variables. P this model for WesTrack Superpave mixtures and predicted rut depths successfully compared with observed perform- ance. The remaining step will be to calibrate and verify the model using data generated in multiple climatic zones. One f the keys to the model is that it is co n nlinear behavior. Even though the model predicts nonlinear behavior, it may not be sensitive enough to the effect of asphalt contents above the optimum level where rutting behavior may be very nonlinear. Chatti et al. (1999a) reported on a rut model developed and incorporated into the MICHPAVE computer program that is a function of a number of variables associated with the respective layers of the pavement structure and pave- ment response. The rut model is shown here and considers deformation of the pavement structure as a whole. AKVAAC AAVAARut A ⋅+⋅+⋅+= 54321 log + A6 · ESAL + log (A7 = CS) + SD + A · (T – A ) + A · log MRB + A11 · log B + A12 · log MRRB + A13 · log CSRB + A14 · TBTSB T = average annual air temperature, MRB = resilient modulus of the base layer, MRRB = resilient modulus of the roadbed soil, B = thickness of the base layer, CS = compressive strain at the top of the roadbed soil, and TBTSB = total equivalent thickness of th gate base and g The peak surface deflection sing a mechanistic model or m instrum g gram su cessfully predicted est s tio s over a range of conditions. o et l. ( 999b,c) and Hugo (2000) c actor in uencing the relative rutting of el paths w re compared in terms of a benchmark he wheel path with t

58 A model was be- tween the other ruts known as “Affected Rut(s)” and the “Bench t, uence factors: • Temperature (F ), • u re s • ia o • Wheel load (F ), and • Tir e ur tp The quantitativ alysis of the rutting performance was based on the assumption that the rut depth is determined by the ti e ur- rently and formulated to define the relationship mark Ru ” in terms of five infl t sponse (F ), Struct ral Mater l c mpliance after processing (Fm), l e (F ). e pr ss e an cumula ve ffects of five factors that occur conc RBFFFFF tp tp l l m m s so For simplicity, the α and β factors were initially set to ent MLS tests, the o pro- ortional to the pressure. Modeling the rutting in this manner al influence on rutting performance to be fluence factors. A T TESTING MODELING OF SPHALT FATIGUE AND CRACKING PERFORMANCE tive tests such as FWD allow the performance f the pavement structure to be expressed in terms of sur- w the stiffness of the upper layers of a pavement to be m red. If cracking is apparent, this may be mapped and re- Fatigue of asphalt layers is often related to horizontal g stress- or strain-controlled, repeated load- g tests, with or without rest periods. These models lend jected the avement test section to a unidirectional moving load, with ingle and dual tires, at a speed of 16.9 km/h. The axle load eam rom e asphalt test sections for laboratory fatigue testing. All ) 846.10 − (38) t t )()s(Rut.Affected.T tal βββββ ⋅⋅⋅⋅α= (37) where BR is defined as the “benchmark” rut, and α and β are regression factors. in themselves to incorporation into mechanistic pavement structural design and analysis systems. As part of the SHRP study, Tayebali et al. (1994) evalu- ated the fatigue performance of a thin asphalt pavement section (90 mm of AC over 320 mm of base) at FHWA’s ALF. The full-scale accelerated fatigue test sub p s was 106.8 kN, and the tire pressure was 965 kPa. B specimens (63 mm × 51 mm × 381 mm) were sawed f th tests were performed under the controlled-strain mode of loading at a frequency of 10 Hz (sinusoidal loading with no rest periods) and at a temperature of 20°C. Fatigue tests were summarized in the form of relationships between fa- tigue life and initial strain and initial dissipated energy per cycle. The following equations were developed using linear regression analysis: (81.425 ⋅= wNf ( ) 574.308 ε108.959 −− ⋅⋅=fN (39) where N = fatigue life; ε0 = initial dissipated energy per cycle, psi. w0 = initial peak to peak tensile strain, microstrain; and equal 1. With the results from the increased tire pressure tests it was found that the structural response was overem- phasized, and β was changed to 0.5. This value satisfied the equation. From the data of the three independ m del appears to be sound. It gave reasonable results on the origin of the rutting and, with the increased tire pres- sure test, it showed the effect on rutting to be directly p lowed the proportion of Chatti et al. (1999b) used these relationships and the SAPSI-M program to estimate the fatigue lives of the ALF test sections. The SAPSI-M program uses multilayer the- ory to calculate the stress and strain response of a pave- ment system under loading. Chatti et al. reported good comparisons of estimated and measured fatigue lives de- pending on estimates for subgrade stiffness. Based on a similar approach, Newcomb et al. (1999) re- ported the following transfer function also developed as part of Mn/ROAD tests for flexible pavements [see also Equation (16)]: 206.3 6 11083.2    ⋅⋅=fN (40) determined for each of the in CCELERTED PAVEMEN A Fatigue of APT test sections may be quantified by monitor- ing the deterioration of pavement stiffness with trafficking. Nondestruc o face deflection. As the structure weakens, the deflection the surface increases. Seismic tests such as SASW allo on oni- to  ε t where N = number of cycles to the onset of fatigue εt of the asphalt layer, microstrain. lated to fatigue performance. tensile strains that may occur at the bottom of layers under loading, leading to the classic bottom-to-top cracking. Fa- tigue models developed in this way are usually based on fatigue characterization of the asphaltic materials in the laboratory usin cracking, and = transverse strain at the bottom

59 This equation represents the onset of cracking in a rela- vely thin asphalt surface over a dense-graded base on a silty– low-volume road section failed after ions of a 35 months of tr ayer, mode of ading, rest periods, healing, etc. Furthermore, these mod- 997) and De la Roche and Rivière (1997) ported on LCPC fatigue tests of different pavement sec- tions with vary Fatigue was related to surface de onitored d traffickin f different trapezoi- al and beam fatigue tests (stress and strain-controlled, d without rest periods) were done on specimens moved from untrafficked areas of the test sections to characte e d. The g n of a shift fact own in the following equation that re- lates the laboratory-determined and field APT fatigue re- ti clay subgrade. This the application of approximately 22,000 repetit 6-kN, 5-axle truck. This represented 2 years and 7 affic. The approaches described have drawbacks in that the models developed, based on laboratory testing, can only estimate the number of cycles until the initiation of crack- ing. The propagation of the crack through the asphalt must then be taken into account. This is usually done by multi- plying the number of cycles to crack initiation by a factor that depends on the thickness of the asphalt l lo els assume that cracking occurs beneath the asphalt layer and cannot account for top-to-bottom cracking. Odéon et al. (1 re ing asphalt thicknesses. flection, and cracking was m g of the sections. A number o uring d with an re riz the fatigue behavior of the materials teste fati ue life of the materials is expressed as a functio or (k) sh sults: ( ) bcal k N 1 6 610     θε⋅ ε⋅= (41) where N = theoretical fatigue life of the pavement structure, εcal = calculated strain beneath the asphalt at the onset of trafficking (determined using lin- ear elastic multilayer theory), ε6(θ) = strain causing the failure of the laboratory sample after 1 million load applications at a temperature of θ°C, b = slope of laboratory fatigue curve, and tests better represent fatigue monitored in the APT sts. Ranking of laboratory fatigue and APT fatigue of structures, however always the same. Molenaar et al hat the trend line that escribes the modulus with respect number of load repetitions can be described very ell in a nondimensional form using k = shift factor relating laboratory and field APT fatigue performance. Shift factors ranging between 0.8 and 4.1 were calcu- lated. In determining strains within the asphalt using elastic theory, Odéon et al. (1997) reported that the use of rectan- gular imprints instead of circular imprints to represent tire pressure distributions in the elastic theory analysis reduced the difference between measured and calculated strains, particularly for the structures having thinner asphalt layers. The introduction of rest periods in laboratory fatigue tests reduced shift factors. They found that the controlled stress fatigue te , were not . (1999) reported t decrease of the asphalt d to the w NE0 n⋅5.0 (42) where n = ap N = nu s at which E = 0.5 0 E0 d En = m fter n load repe- titions. y tempera- re. Common laboratory mix stiffness–temperature rela- e usual temperature orrection procedures become less adequate. At the end, there is almo pendency remainin Sherwo on an analysis of APT ata from FHWA ALF tests, did not find a significant rela- between percentage area cracking and crack ngth. They related fatigue cracking to the binder stiffness property s crease in G*sinδ (after T r as- phalt pavements (100 mm) based on a 50% cracked area. They were u sinδ for thicker a a Molenaar et al. (1999) modeled cracking of LIN- En −= 1 plied number of load repetitions, mber of load repetition E , = modulus of the undamaged asphalt layer, an odulus of the asphalt layer a Molenaar et al. (1999) questioned whether a pavement has really failed if the asphalt modulus has decreased to 50% of its original value. Equation (42) does not account for hardening or densification of the layer with initial traf- ficking as reported by some researchers (Hugo et al. 1999b). Localized strain measurements in the AC layer quickly lose their general meaning for the entire structure as soon as distress develops (not necessarily visible at the pavement surface), because local strains are strongly influ- enced by this distress. At the start of the performance test, the asphalt stiffness was strongly influenced b tu tionships can then be used to correct measurements to a reference temperature. When distress develops, however, the (declining) back-calculated AC layer stiffness becomes less temperature-dependent, and th c st no temperature de od et al. (1999), based g. d tionship le G* inδ. They indicated that an in R FOT) relates to lower fatigue life for thinne nable to relate fatigue life and G* sph lt pavements. TRACK test sections in The Netherlands using the Weibull distribution discussed previously and shown in Equation

60 Equation (3). They found that the β constant in the equa- tion was related to the thickness of the asphalt layer being tested. ELASTO-PLASTIC BEHAVIOR OF UNBOUND MATERIALS A unique application of HVS data is the work done by Wolff (1992). He used the South African HVS data to develop a mechanistic model for use in a design model for granular pavement materials. His aim was to simu- late the actual behavior of granular materials under APT. In this analysis, he assumed the material to be in a stress state well below the yield stress condition, which is the situation in a functional pavement. His method is akin to methods employed by Kenis modeled by a funciton that lates an invariant of backcalculated stress induced by deformation of the layer. The lat- r is a value selected in accordance with design guidelines. nt layers must not exceed e appropriate design standard. Naturally, deformation in ) based on the AASHO oad Test. This preliminary field fatigue curve for FSHCC avements was found to be similar to the fatigue resistance atory. (1978) and Yandell and Behzadi (1999) in which the permanent strain that takes place during each load cycle is taken into account. The nonlinear elasto-plastic behavior of the unbound granular material is modeled in two phases. In the first phase, he uses the nonlinear elastic finite-element program MICHPAVE (Chatti et al 1999) for backcalculating material parameters from measured deflections. In the second phase, the elasto- plasticity of the material is re the HVS wheel loads to the plastic strain measured relative to repetitiions of wheel loads. Using this method in an iterative manner, he was able to accumulate the permanent strain in predefined pavement lay- ers and relate this to the total te The basis of his model is S–N curves (with N being the number of load reversals that will cause structural failure at peak stress S) that were used as transfer functions for rut- ting. The S–N curves were developed by Wöhler, and they are used in the mechanical engineering field (Wolff 1992). For the development of the transfer function, failure had to be defined as a specific terminal permanent strain value. Wolff developed a series of S–N curves that could be used to determine cumulative permanent strain. This required the determination of the stress induced in a layer by a wheel load in accordance with the material parameters that he determined from HVS testing. This yielded a point on the S–N curve where the vertical axis represents invariant stresses and the horizontal axis shows the load repetitions. Wolff opted to use theta, the octahedral normal stress for his model. By using HVS data for a variety of materials, he was able to develop a series of S–N curves that could be used to determine cumulative permanent strain. He then used Miner’s hypothesis to determine the cumulative strain as a result of different wheel loads trafficking the pave- ment. A value smaller than unity is then taken to be accept- able, whereas failure is considered to occur as soon as it exceeds unity. In the design process, the sum of the perma- nent strains in each of the paveme th the bound layers has to be added to the value developed in the unbound materials. The method was very successfully applied to low-volume road pavements, where the unbound material dominates the structure. CONCRETE MODELING Because of the limited extent of APT testing done on con- crete pavements (see Figure C16), it is understandable that related modeling of APT performance is also limited. Roesler et al. (1999) reported that not all techniques and instrumentation used in HVS testing of asphalt pavements can be used successfully in concrete pavement testing. They do warn against increasing the load incrementally during concrete tests, pointing out that this can lead to er- rors, because Miner’s Law or cumulative damage theory does not work well for sequenced loading conditions in concrete. Therefore, changing the load in the middle of an APT test can make quantifying the fatigue results difficult. With concrete testing, emphasis is placed on the perform- ance of the joints, dowel bars, load-related cracking, and the bearing capacity of the subgrade beneath the concrete slabs. Roesler et al. (1999) defined failure as when there is a visual crack on the surface of the concrete slab. Test locations have failed with longitudinal, transverse, or corner cracks. Figure 14 (Roesler 1998) shows the results of the HVS fatigue tests on FSHCC pavements relative to the Portland Cement Association fatigue curve, beam fatigue curve based on 50% probability of fatigue failure, PCC slab fa- tigue curve taken from laboratory tests, and field fatigue curve by Vesic and Saxena (1970 R p of PCC slabs in the labor To evaluate the fatigue resistance of the FSHCC pave- ment versus conventional fatigue curves for PCC, bending

61 -0.05 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 Number of Repetitions to Fatigue Failure FIGURE 14 Comparison of FSHCC and PCC fatigue performance. stresses in the slab were back-calculated from measured flections. These back-calculated stresses were then by the 90-day flexural strength of the concrete to ine what the applied stress ratio was in the slab dur- HVS testing. The stress ratios greater than one were d to the results obtained for fatigue life curves de- from beam tests. The calculation of stresses in the re also complicated by the curling of the slabs and ntial shrinkage (Roesler 1998). Similar findings ported by Balay and Goux (1994). acher and Snyder (1999) evaluated the load trans- g efficiency of joints in concrete pavements as a sub- SUMMARY From the review it was apparent that an imme of APT is that pavement performance may be m rectly. This is possible because many of the factors i encing performance can be controlled, including • Wheel loads (magnitude, wandering, rest period • Tire pressures, • Pavement structures (compaction, layer th drainage, etc.), • Pavement materials (gradations, binder etc.), 0.15 0.35 0.55S urve FSHCC AASHO Rd. Test 0.75 tre 0.95 1.15 1.35 1.55 1.75 ss R at io Beam PCA Curve Slab C edge de divided determ ing ascribe veloped slabs we differe were re Emb ferrin LF for trafficking in the laboratory. They used the fol- wing equation: With this expression, perfect load transfer (where both s than 70% to be unsatisfactory and may onsider retrofitting load transfer devices in such cases. diate benefit odeled di- nflu- s, etc.), ickness, contents, ent temperatures (only when tests are per- formed within environmental chambers), and • Subgrade moisture conditions (only when pavement structure test pits or w tests are done within time windows between seasonal riations). A wide range of models have been developed as part of APT ar , • Pavement damage, • S g e • Asphalt rutting performance, on sidiary study to the Mn/ROAD program, using the Minne- • Pavem A lo LTE (percent) = (dUL/dL) × 100 (43) where LTE = percent load transfer efficiency, dUL = deflection of unloaded side of crack/joint, and dL = deflection of loaded side of crack/joint. sides of the crack/joint deflect equally under an applied load) exists when the ratio is 100%. Conversely, no load transfer exists when the ratio is 0% and both sides of the joint or crack move independently. Many agencies consider LTE values of les c s are constructed within hen va rese ch including ub rad rutting performance, • Asphalt fatigue and cracking performance, • Elasto-plastic behavior of unbound materials, and • Concrete performance. APT performance modeling usually does not include ride quality because the restricted lengths of test areas make the collection of representative and reliable data

62 longitudinal unevenness difficult. This is not serious, be- ause riding quality is not necessarily related to the struc- deforma- on through observation of in-service highways. ns to APT modeling of pavement per- fo tors t ress. These are primarily limited to en- vi must taken into account. Furthermore, it is not always po servic e traf- fic failur mode based to other sites. This has motivated the de- elopment of models based on probabilistic approaches, ariability. It has also necessitated e normalization of data to reference parameters. tests are often ex- press , stresses, and strains w nce mod- el us- in pavement structures. These odels may be defined using linear elastic theory, FE e Modeling of APT data also requires a definition of fail- ure. This failure is related to performance parameters such as pavement response (displacement, stress, and strain) and material characteristics. The shift to modeling pavement performance in terms of structural performance, instead of functional performance, indicates the trend to express per- formance in more fundamental terms. This allows a better definition of failure. The cause of failure may be related to specific structural components; for example, fatigue of an asphalt layer or permanent deformation of the subgrade. Modeling the performance of specific structures alone restricts the applicability of performance models if material characterization of the structural components is neglected. This is particularly important with the development of pavement design systems and performance-related specifi- cations. For this reason, attention has been given to the re- lationships between observed performance under traffick- ing and the performance as predicted from pavement analyses using material characteristics determined in labo- ratory testing. This topic is discussed further in chapter seven. c tural condition of the pavement as Croney and Croney (1998) pointed out in their discussion of the AASHO road test. They argue that it would be more cost-effective to evaluate riding quality in terms of cracking and ti There are limitatio rmance. APT cannot directly account for time-related fac- hat influence dist ronmental influences, although traffic-related influences also be ssible to relate APT performance to the performance of in- e pavements under conventional traffic. Real-tim ked pavements are subject to maintenance before pavement e. Perhaps the most significant shortcoming of APT ling, however, is the lack of applicability of models on one site v including the use of artificial neural networks (Abdallah et al. 1999), to account for v th Models developed based on APT ed in terms of displacements ithin pavements layers. Application of performa s requires that these response parameters be estimated g mathematical models of m m thods, equivalent thickness, or other multilayer approaches. Pavement response is verified using strain gauges or coils or pressure cells placed in APT test sections. Researchers should recognize that instrumentation of test sections may disturb the materials in which these devices are placed.