An exploration of a thermal extension of Burgers model for the simulation of the deformation of asphalt under dynamic stress
Creators: name: Fox, Alise
Publisher: name: University of the Sunshine Coast, Queensland
Year: 2020
Subjects: industrial mathematics
rheological modelling
pavement modelling
burgers model
viscoelasticity

description: An understanding of the viscoelastic behaviour of asphalt pavements can deliver better pavement design. Contemporary engineering practice is to characterise asphalt viscoelasticity using the dynamic modulus, defined as the magnitude of the complex modulus. This modulus, representing the ratio of stress to strain, is a function of time of stress loading and temperature, and is typically represented using master curves. While the dynamic modulus provides a simple estimation of a strain response to an applied stress, it fails to predict response-lag or degree of permanent deformation. Another approach is to use combinations of standard rheological elements, such as springs and dashpots, to develop rheological models as differential equations that describe observed dynamic responses and behaviours. For example, Burgers standard rheological model is composed of four rheological elements that together, can be used to simulate a broad range of viscoelastic deformation behaviours. While studies have been published in which a variety of rheological models are used to calculate the viscoelastic moduli of asphalt pavements, few studies use those models to simulate the dynamic strain response of asphalt as a function of time, temperature, and loading frequency. This project explored the feasibility of using a rheological modelling approach to simulate the strain response in asphalt to a dynamically applied stress. Experimental strain response data were collected by applying cyclic stress loading to asphalt core samples over a range of temperatures and loading frequencies. The second-order differential equation, that represents Burgers Model, was solved for each experimental data set. The optimum coefficients of the model, for each data set, were determined iteratively using a gradient descent method to minimise the difference between the model solution and the experimental strain response. The optimal step-size for each iteration was determined using the Barzilai-Borwein method. The standard Burgers Model was unable to simulate the stress-strain nature accurately across all experimental datasets, and an extended form of the model, a Generalised Burgers Model GBM), was shown to be more successful. The coefficients of the GBM were assumed to follow an Arrhenius-style function for temperature dependency, and which was further modified to include the influence of driving frequency. Although the resulting model should theoretically be able to simulate the strain response to a dynamic stress loading on asphalt at any specified temperature, acceptably good simulations were only observed in experimental cases where the loading frequency was 3 Hz or slower. Simulation of the strain response to higher-frequency stress loading, using internally-calculated coefficients, proved to be challenging and, in spite of considerable investigation, the modelled behaviour remained erratic for those cases. Investigation of the cases for which the GBM fails indicates that the model appears to be highly sensitive to the coefficient values, and the limited quantity and reliability of experimental data is likely to have limited the accuracy of the calibration of the equations for model coefficients. Overall, the GBM is shown to provide an accurate representation of dynamic strain response when its coefficients are custom-fitted, but lacks stability when coefficients are calculated for the specified conditions using the proposed equations.