# A Creep Model of Asphal Mixture Based on Variable Order Fractional Derivative
## 1 Introduction  
Asphal mixture is a typical viscoelastic-plastic multiphase composite material, which has complex rheological properties. Asphal pavement has been widely used in the highway construction because of the advantages of no connection joints, low noise and short construction period, and more than 95% of the current highway pavement in China is asphalt pavement. Due to the increasing traffic volume and the significant increase in axle load, the failure of asphalt pavement becomes increasingly serious. The major pavement diseases are rutting, potholes, and cracking. Creep is one of the mostimportant mechanical properties of the asphalt mixture, and it is directly relevant to the rutting behavior. Therefore, it is of great significance to predict the creep behavior of the asphalt mixture by establishing its reasonable constitutive model. Up to now, many constitutive models have been proposed and applied to study the dynamic viscoelastic and static viscoelastic behaviors of asphalt mixture, which can be divided into two categories in general: integral constitutive model and differential constitutive model. Considering the fact that the multiple integral constitutive models with too many parameters are rarely adopted by practical engineering, the study of the integral constitutive model mainly focuses on the single integral constitutive model. As for linear viscoelasticity, the Boltzmann superposition principle is adopted; as for nonlinear viscoelasticity, the modified Boltzmann superposition principle and the reduced time models are adopted [1; 2]. The Schapery single integral constitutive model has been widely used to analyze of nonlinear viscoelastic mechanical behavior of asphalt mixtures [2; 3; 4; 5]. In the study of the differential constitutive models, the classical models, such as the Kelvin model, the Maxwell model and the Burgers model, consist of the series and/or parallel combination of springs and dashpots, and are generally used to describe the linear viscoelasticity with the advantages of simply, intuition and clear concept. [PERSON] et al. [6] used the generalized Kelvin model, the generalized Maxwell model and the Burgers model to describe the creep behavior of asphalt mixture at various temperatures, and showed that the generalized Kelvin model and the generalized Maxwell model are superior to the Burgers model in describing the variation of viscoelastic properties of asphalt mixtures with loading time. In order to describe the nonlinear viscoelastic mechanical behavior, the influences of viscoplasticity and damage were taken into consideration, and the corresponding modified models were proposed on the basis of linear viscoelastic constitutive models. [PERSON] et al. [7] proposed a viscoelastic damage constitutive model for asphalt mixture under cyclic loading, which was constructed by coupling the Burgers model with the modified Chaboche damage model. [PERSON] et al. [4] combined the [PERSON]'s nonlinear viscoelastic model and the modified [PERSON]'s viscoplastic model to characterize viscoelastic and viscoplastic behaviors of compressed asphalt mixture. [PERSON] et al. [5] suggested a coupled nonlinear viscoelastic, viscoplastic and hardening-relaxation constitutive model for asphalt mixtures, and verified it by the dynamic moduli and repeated creep-recovery tests. Moreover, the differential operators in the above mentioned classical differential constitutive models are local integer differentials. However, the fractional differential operators are nonlocal and applicable to describe the memory characteristics of viscoelastic materials [8]. It has become a research focus in the study of viscoelasticity, because of the advantages of few parameters and high accuracy [8; 9; 10]. [PERSON] et al. [11] used a simple fractional viscoelastic model to evaluate the performance of asphalt binders at low service temperatures through the damping ratio and dissipated energy ratio. [PERSON] et al.