Damage Mechanics Constitutive Modelling of Bituminous Mixtures Under Complex Loading

Bituminous pavement mixtures are complex composite materials whose mechanical response under repeated traffic loading is governed by time-dependent viscoelasticity, progressive micro-crack initiation and propagation, and irreversible permanent deformation—phenomena that interact nonlinearly across temperature ranges spanning −20 °C to 70 °C in tropical and semi-arid climates. This paper presents a comprehensive continuum damage mechanics (CDM) constitutive framework for bituminous mixtures that couples a generalised Maxwell viscoelastic model, represented by a Prony series with N = 5 relaxation arms, with a scalar damage evolution law derived from the thermodynamic dissipation inequality. The damage variable D ∈ [0,1] evolves as a function of cumulative dissipated pseudo-strain energy density, mix-specific material parameters, and temperature through an Arrhenius shift factor. Permanent deformation (rutting) is modelled via a viscoplastic flow rule with isotropic hardening calibrated to dynamic creep test data. The constitutive model is implemented in a finite element framework using the UMAT user-material subroutine interface and validated against dynamic modulus, fatigue beam bending, and Hamburg wheel-tracking laboratory data for three bituminous mix types: dense-graded asphalt (Mix A), stone mastic asphalt (Mix B), and high recycled asphalt pavement content mix (Mix C). Model predictions of fatigue life agree with measured values to within ±18% across the parameter space, and rut depth predictions fall within ±15% of Hamburg test measurements. A global sensitivity analysis using Sobol indices identifies the damage initiation energy threshold and the temperature shift function as the dominant model parameters governing fatigue life predictions. The model is further a