In relation to the development of a Rolling Wheel Deflectometer (RWD), which is a non-destructive testing device for measuring pavement deflections, a finite element model for obtaining the soil/pavement response has been developed [1]. The RWD is operating at traffic speeds and the soil model is therefore subjected to a moving transient dynamic load. Perfectly Matched Layer (PML) [2] is used as absorbing boundary conditions in order to prevent reflections of the waves propagating through the soils due to the dynamic loading. As the load is moving with high speed, the formulation is in the moving frame of reference [3].

To accurately predict pavement response, proper material characterization is needed. Flexible pavements are commonly modeled as multilayer linear elastic systems. However, asphalt behaves as a viscoelastic material because its response to induced loading depends on temperature and load frequency and can be modeled in different ways. A finite element model can quickly reach high computational cost, thus a simple, time-efficient viscoelastic model is preferable.

The viscoelastic behavior of asphalt can be described by a relaxation format of the constitutive relation with four parameters; two elastic moduli defining the minimum and maximum stiffnesses of asphalt in relation to frequency, a time scale parameter controlling the relaxation time and a differential fractional order characterizing the interpolation between low and high frequency regimes [4]. Assuming the most common interpolation shape by setting the fractional order equal to one, the system is reduced to only 3 parameters and the formulation can be implemented in the finite element model without increasing the computational cost significantly.

In this paper a formulation of the relaxation format of viscoelastic behavior is developed in translated coordinates with efficiently absorbing boundary conditions (PML). The viscoelastic properties of the formulation are illustrated through numerical examples.          

References

[1] S. Madsen, S. Krenk and O. Hededal, Perfectly Matched Layer (PML) for transient wave propagation in a moving frame of reference. Proceedings of the Fourth International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, COMPDYN 2013, pp. 4379-4388. Kos, 2013.

[2]  R. Matzen, An efficient finite element time-domain formulation for the elastic second-order wave equation: A non-split complex frequency shifted convolutional PML. International Journal for  Numerical Methods in Engineering, 88, 951-973, 2011.

[3] S. Krenk, L. Kellezi, S.R.K. Nielsen and P.H. Kirkegaard, Finite elements and transmitting boundary conditions for moving loads, in Proceedings of the Fourth European Conference on Structural Dynamics, EURODYN’99, Vol. 1, 447-452. Balkema, Rotterdam, 1999.

 [4] S. Krenk, Damping mechanisms and models in structural dynamics. Proceedings of the Fourth International Conference on Structural Dynamics, EURODYN 2002, Vol 2, Munich, Germany, 2002.