Materials and Structures

, Volume 48, Issue 7, pp 2339–2351 | Cite as

Linear and nonlinear viscoelastic behaviour of bituminous mixtures

  • Quang Tuan Nguyen
  • Hervé Di Benedetto
  • Cédric SauzéatEmail author
Original Article


As it is the case for all materials, the behaviour of bituminous materials becomes nonlinear when the strain (stress) amplitude level increases. In this study, only “small” nonlinearities (where the applied strain amplitudes are lower than 100 µm/m) of a bituminous mixture are investigated. An improved complex modulus test campaign has been carried out on cylindrical samples. Sinusoidal cyclic loadings in tension and compression were applied at different temperatures (from −26 to 50 °C) and different frequencies (from 0.01 to 10 Hz). During sinusoidal loadings, for each temperature and frequency, three levels of strain amplitude (lower than 125 µm/m) were applied to characterize nonlinearity. Measurements of complex modulus E * and complex Poisson’s ratio ν * characterizing the viscoelastic properties of the material in 3 dimension case (3D) are introduced. From experimental results, nonlinearity of bituminous mixture is observed even at small strain amplitudes on both norm and phase angle of complex modulus. It is verified that the effect of nonlinearity is dependent on the considered equivalent temperature–frequency couple, which imply the respects the time temperature superposition principle. Moreover, the observed nonlinearity acts in the same direction in the E * Black’s diagram, and Cole–Cole diagram when increasing strain level. The viscoelastic linearity limits for tested material, which vary with equivalent temperature–frequency couple, are also presented. For the considered strain amplitude levels, no nonlinearity was observed on complex Poisson’s Ratio. A model with a continuum spectrum called 2S2P1D (two Springs, two Parabolic elements, one Dashpot), developed at the ENTPE (Ecole Nationale des Travaux Publics de l’Etat), is used to simulate the linear viscoelastic behaviour of tested bituminous mixtures. An improved version of this model is proposed to introduce nonlinear properties.


Bituminous mixture Nonlinearity Linear viscoelasticity Complex modulus Modelling 


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Copyright information

© RILEM 2014

Authors and Affiliations

  • Quang Tuan Nguyen
    • 1
    • 2
  • Hervé Di Benedetto
    • 1
  • Cédric Sauzéat
    • 1
    Email author
  1. 1.LGCB & LTDS (UMR CNRS 5513)University of Lyon/Ecole Nationale des Travaux Publics de l’Etat (ENTPE)Vaulx-en-Velin CedexFrance
  2. 2.Department of Civil EngineeringUniversity of Transport and CommunicationsHanoiVietnam

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