A non-linear thermo-viscoelastic rheological model based on fractional derivatives for high temperature creep in concrete

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• Fractional viscoelastic creep model is proposed for concrete at high temperatures. • Model parameters are calibrated using existing experimental data. • Accurate representation of experimental data is achieved with only few parameters. • Time-varying stresses and temperatures can be efficiently modelled. • Model can be applied to concrete under fire or high temperature working conditions. In this paper, a novel non-linear thermo-viscoelastic rheological model based on fractional derivatives for high temperature creep in concrete is proposed. The rheological model consists of a linear springpot unit placed in series with a second springpot used for non-linear creep which activates under high stress and temperature. The model parameters which include the dynamic viscosities of the springpots and the fractional exponent are calibrated using existing experimental data of basic creep strain in concrete under constant stress and temperatures for various aggregate types. The power law form of the naturally resulting creep compliance allows an accurate representation of experimental data with the use of only a few model parameters. Furthermore, the variable-order fractional differential stress-strain equation provides a compact method for analytical and numerical modelling of basic creep under conditions of time-varying stress and temperature. In addition, applications of the proposed model to determine axial deformations in columns and transverse deflections in beams under constant and varying temperatures are demonstrated.