On the use of linear viscoelastic constitutive relations to model asphalt

Abstract

In this article, the appropriateness of modelling asphalt using linear viscoelastic constitutive relations is explored. Towards this, a rate-type nonlinear viscoelastic model recently proposed by Santoshreddy et al. (2011) is used and it is shown that the stress relaxation and creep response of asphalt are influenced by the type of experiment, initial rate of displacement (or loading) and the stress and strain measure used. Furthermore, it is shown that the creep and stress relaxation functions are not dependent functions as required by the linear viscoelastic theory, even in the range of values of engineering strain and stress in which the linearity property holds approximately. These observations lead one to conclude that linear viscoelastic models maybe inappropriate to model asphalt.

Keywords:

• viscoelastic models
• asphalt
• stress relaxation
• creep
• uniaxial extension
• shear

Notes

^1. Development of tangential as well as normal displacement when subjected to shear stresses will not be exhibited by incompressible materials whose Cauchy stress, σ, is of the form , where p is the Lagrange multiplier used to enforce the constraint of incompressibility, d is the symmetric part of the Eulerian velocity gradient and is the material response function which depends on the material being tested. Newtonian fluids belong to this class of materials whose tangential and normal displacements are uncoupled.

^2. Engineering stress is defined as the force acting per unit un-deformed area and engineering strain is the change in length per unit un-deformed length.

^3. True strain is defined as the change in length per unit deformed length.

^4. Logarithmic strain is the natural logarithm of the ratio of deformed length to un-deformed length.

^5. See Spencer (2004) for a detailed discussion of the issues here.

^6. According to Mehrotra and Svrcek (1986), the density of Athabasca bitumen at 15°C changes from 1005 to 1020 kg/m³ when the pressure is increased from 0.10 to 10.34 MPa. Thus, for a 100 times increase in pressure, the volume change is nearly 1.5%, suggesting that asphalt could be assumed to be nearly incompressible. While the hydrostatic stress causes only a small volume change, it is possible that some other stress field could cause a more significant volume change. Thus, even though the assumption that asphalt subjected to any stress field will undergo only isochoric motions needs more experimental validation, this assumption is made.

^7. Though here results for are only presented, the case for which is also studied and identical results obtained.

^8. Though the results for tensile Cauchy stresses are only presented, the study reveals that it holds for compressive Cauchy stresses too.

^9. Though the results for tensile engineering stresses are only presented, the study reveals that it holds for compressive engineering stresses too.