Background

III. CALIBRATION, SELECTION, AND UNCERTAINTY QUANTIFICATION

III.2 Background

The two primary permanent deformation predictive models investigated in this dissertation are the MEPDG predictive model and the NCHRP Report 455 WesTrack Level 1-B predictive model. Each model assumes that permanent deformation in a pavement system is the accumulation (sum) of the permanent deformation through all layers of the pavement system. Different models are necessary for describing the permanent deformation in bound and unbound layers. Deformation in the unbound layers is assumed to be a function of vertical compressive strain by both the MEPDG and WesTrack models, though different forms of the mechanistic equations were utilized by the two predictive models. Further, the models for the unbound layers were calibrated with different empirical data. The MEPDG investigated numerous mechanistic models and selected a model derived by El-Basyouny and Witczak. (6) The MEPDG utilized LTPP data to calibrate this model. The WesTrack model utilized the Asphalt Institute equation and empirical data from the WesTrack project.(4)

The significant distinction between these two predictive models comes in the predictive model for the bound layers which differs due to the underlying assumptions of the mechanistic behavior that causes permanent deformation in the asphalt concrete layer.

The MEPDG model assumes that permanent deformation is the result of axial strain and the WesTrack model assumes that shear deformation is the cause of deformation.

The MEPDG predictive model for predicting permanent deformation for asphalt pavements is derived from empirical data obtained from LTPP data and linear elastic analysis of the asphalt layer(s). The model form in the asphalt layer is based on a constitutive relationship initially derived from laboratory repeated load permanent deformation tests:

𝜀_𝑝

𝜀_𝑟 =𝑎𝑇^𝑏𝑁^𝑐 (III.1)

Where the plastic strain (ε_p) is expressed as a function of N load repetitions, a pavement temperature T, the resilient strain ε_r, and regression coefficients a, b, and c. This model form comes with the assumption that the permanent deformation is a function of vertical plastic deformations and not a function of plastic shear deformations. The MEPDG discusses three major stages of pavement rutting and concludes that the primary and secondary stages describe most practical applications. Previous research indicates that these two stages are predominantly impacted by vertical strains and it is only the tertiary stage at which shear deformation must be considered for predicted performance. (6) The mechanistic model for asphalt deformation is modified with the inclusion of calibration regression coefficients (β) (Equation III.2) which are calibrated with LTPP data.

𝜀𝑝

𝜀_𝑟 = 𝛽_𝑟𝑖𝑎𝑇^{𝛽𝑟2𝑏}𝑁^{𝛽𝑟3𝑐} (III.2)

The MEPDG comments that the form of this predictive model is quite simple as the permanent strain is determined by evaluating the resilient strain. The resilient strain is defined by a simple equation, assuming elastic behavior, including only the material’s elastic modulus, Poisson’s ratio and the state of stress due to the applied traffic loading.

The calibration process for the model of permanent deformation in the asphalt layer is performed by minimizing the error between actual and predicted performance, utilizing Equation III.1 where a layered elastic analysis program is used to determine the resilient strain. The regression coefficients are derived from non-linear regression based on the NCHRP 9-19 Superpave Experiment and the calibration factors are derived from LTPP sections located in 28 different states. (6)

The NCHRP Report 455 develops a number of permanent deformation models by investigating direct regression analyses as well as regression based on mechanistic- empirical analyses utilizing the data from the WesTrack project. Permanent deformation in the asphalt concrete layer for these models is based on the assumption that shear deformation governs deformation. One WesTrack formulation, based on M-E analysis, is a least squares regression between predicted total permanent deformation and the WesTrack rutting data. The regression equation is developed by estimating the rut depth of all layers through the procedure shown in FIGURE III.1. The process requires evaluating the impact of RSST-CH data on temperature and moduli of elasticity. Stresses and strains in the pavement structure are calculated by elastic analysis at key locations including: 2 inches below the surface at wheel edges and at the top of the sub-grade layer.

The accumulation of these strains is used to estimate rut depths and the regression process iterates until the M-E model regression coefficients converge. Regression utilizing equivalent single axle loads (ESALs) and mix parameters is then performed between the calibrated M-E model and the empirical data from the WesTrack experiment.

FIGURE III.1 NCHRP 455 Regression Analysis Procedure

The WesTrack Level 1-B equation for permanent deformation (rdHMA), derived by the regression procedure previously described, is defined as the product of a regression coefficient (κ) and the permanent (inelastic) shear strain (γⁱ).

𝑟𝑑𝐻𝑀𝐴 =𝜅𝛾^𝑖 (III.3)

Where:

𝛾^𝑖 =𝑎 ∗exp (𝑏𝜏𝛾^𝑒𝑛^𝑐) (III.4)

Permanent (inelastic) shear strain (γⁱ) is defined as a function of elastic shear stress (γ^e) and shear strain (τ), the number of axle load repetitions (n), and regression coefficients a, b, and c. The regression coefficient is determined empirically outside the scope of the NCHRP project and is defined as a function of HMA thickness. Similar to the MEPDG model, layered elastic behavior is assumed and is necessary in calculation of the elastic shear stress and corresponding shear strain values in the WesTrack Level 1-B model. The elastic analysis utilizes the moduli of elasticity as determined empirically through the RSST-CH laboratory results.

Once the NCHRP M-E model is calibrated, a final regression model is derived relating the M-E model to mix parameters. One recommended regression model

presented by the NCHRP report is shown in Equation III.5 and includes mix parameters:

percent of asphalt content (Pasp), percent of air void content (Vair), percent of aggregate finer than a No. 200 sieve (P200), and ESALs. The terms fine plus and coarse take the

value of unity when the mix is equivalent to the corresponding WesTrack mix design and zero otherwise. This equation is the formulation chosen for analysis and comparison in this dissertation.

ln(𝑟𝑑) =−6.1651 + 0.309941 ln(𝐸𝑆𝐴𝐿) + 0.00294305𝑉_𝑎𝑖𝑟² + 0.0688276𝑃_𝑎𝑠𝑝² − 0.0657803𝑃𝑎𝑠𝑝𝑃200+ 0.600498(𝑓𝑖𝑛𝑒 𝑝𝑙𝑢𝑠)−1.59167(𝑐𝑜𝑎𝑟𝑠𝑒) +

0.21327 ln(𝐸𝑆𝐴𝐿) (𝑐𝑜𝑎𝑟𝑠𝑒) (III.5)