Temporal Homogenization Modeling of Viscoelastic Asphalt Concretes and Pavement Structures under Large Numbers of Load Cycles

This paper aims to introduce a highly efficient computational model compared to the current cycle-by-cycle simulation strategy to compute the viscoelastic responses of asphalt concretes and pavement structures under large numbers of load cycles. An explicit constitutive relation for viscoelastic solids in multiple time scales was developed based on the temporal homogenization. The original initial-boundary value problem was divided into a global part in the slow time scale and a local part in the fast time scale. Two simulation studies were presented to validate the computational accuracy and efficiency of the proposed model: (1) a cylindrical asphalt concrete subject to a uniaxial cyclic compression load, and (2) a pavement structure subject to a locally cyclic loading. The laboratory test results and field measurements were compared with the modeled responses to validate the models before comparing with the reference solutions. Results indicate that the temporal homogenization-based viscoelastic model saves considerable computational cost and maintains a satisfactory accuracy. The absolute values of relative error of the modeled responses between the time homogenization and reference solutions are lower than 1% and 4% for the cylindrical asphalt concrete and pavement structure under locally cyclic loadings, respectively. Based on the proposed computational approach, only 4 min are needed to model the response of a cylindrical asphalt concrete subject to ${10}^4$ repeated load cycles under a uniaxial compression load. The computational time is reduced from 7 h of the reference solution to 38 min of the temporal homogenization solution to model ${10}^3$ load cycles of a viscoelastic pavement structure.

This study introduces a highly efficient computational model to compute the viscoelastic responses of asphalt concretes and pavement structures under large numbers of load cycles. Multiple time scales were applied to an explicit constitutive relation of asphalt concretes to obtain the formula of global and local initial-boundary value problems. Its computational accuracy and efficiency were verified by comparing the temporal homogenization-based solutions with the testing results and reference solutions for a cylindrical sample and a pavement structure. It is the basis for the long-term pavement performance prediction after including the fatigue damage analysis in the present temporal homogenization framework. By successfully implementing a mechanistic framework for the long-term pavement performance prediction, the pavement design can more rely on the material inherent properties instead of using redundant empirical transfer functions. It is promising that the local calibrations of the current empirical performance transfer functions can be minimized as the proposed pavement long-term performance predictions depend on the material inherent properties and constitutive models.