Abstract
In order to quantitatively describe the time-varying mechanical properties of asphalt mixture during creep process, a nonlinear viscoelastoplastic creep model was proposed, by using variable-order fractional calculus. The differential order of the variable-order fractional element of the model is no longer constant, but a variable that changes with time, which reflects the changes of the mechanical properties of the material during the creep process. Whereas the tertiary creep phase is modeled by the viscoplastic element with time-varying viscosity, which is attributed to damage evolution. The uniaxial creep compression tests of AC-13C asphalt mixture under different stress levels (0.7 MPa, 0.9 MPa, 1.1 MPa, 1.3 MPa, 1.5 MPa, 1.7 MPa) were carried out with MTS-809 testing machine at 25 °C, and the test results were analyzed by the model using Levenberg–Marquardt optimization algorithm. It is shown that creep damage occurs when the applied stress exceeds a certain critical value, and the damage incubation time depends on the applied stress level. The higher stress decreases the damage incubation time. The model is in good agreement with the experimental results, and is applicable to describe the entire creep process, which consists of primary, steady and tertiary stages. Moreover, the variation of the model parameter can describe the change of viscoelastic properties of the material during the creep process. The differential order of the variable-order fractional element is constant during the primary creep stage, indicating that the creep behavior of the asphalt mixture is linear viscoelastic in small strain range. For the same stress level, the fractional order of the steady creep stage is greater than that of the primary creep stage, and it increases with the increasing stress level, which shows that the viscous behavior in the steady creep is more remarkable than that in the primary creep, and the higher the stress level, the more prominent the viscous performance exhibits.
Highlights
Asphalt mixture is a typical viscoelastic-plastic multiphase composite material, which has complex rheological properties
According to the above two types of creep behavior and their characteristics, a fractional viscoelastoplastic creep model consisting of variable order fractional viscoelastic element and time-varying viscosity dashpot element will be constructed to analyze and describe the creep behavior of asphalt mixture
This stage can be modeled by the first variable ordervariable fractional viscoelastic element, as marked by (1) in the dashed box, of the model shown in Figure 4: At low stress levels (σ ≤ ), the asphalt mixture only exhibits the primary creep and steady creep
Summary
Asphalt mixture is a typical viscoelastic-plastic multiphase composite material, which has complex rheological properties. Some researchers have proposed viscoelastic and viscoplastic constitutive models for asphalt mixture on the basis of constant-order fractional derivative, there is no report about the analysis of the mechanical behavior of asphalt mixture based on variable-order fractional differential theory. The model can describe the whole creep process including primary, steady and tertiary stages, it uses variable-order fractional elements to model the primary and differential will be constructed to study the creep behavior of asphalt mixture at various stress levels.
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