Research On Dynamic Viscoelastic Fractional Constitutive Model Of Asphalt Binders And Mixtures

Asphalt mixture,as a kind of typical viscoelastic composite material,can be affected by irregular traffic loading and changing of ambient conditions in its service life.Therefore,the mechanical properties of asphalt mixture show the obviously dynamic characteristics under the irregular loading and changing temperature.At the same time,the designed parameters of asphalt pavement have changed from static parameters to dynamic parameters in China.Therefore,the dynamic mechanical properties of asphalt pavement materials have been abstracting more and more attention in the road engineering community.The establishment of a reasonable and accurate viscoelastic dynamic model of asphalt pavement materials can not only objectively characterize the viscoelastic characteristics of asphalt pavement materials,but also can effectively predict the mechanical response of asphalt pavement structure,and providing a reference for asphalt mixture design and pavement disease prediction.At present,the existing dynamic viscoelastic mathematical models can not fully describe the viscoelastic properties of asphalt mixture(cannot describe the loss modulus);the classical viscoelastic constitutive models have too many parameters and the physical meaning of parameters are not clear when characterizing the viscoelastic properties of asphalt mixture.In view of this,based on the viscoelastic fractional derivative theory and the numerical optimization method,this dissertation established the dynamic viscoelastic fractional derivative constitutive models of asphalt mixture,and deduced the fractional derivative constitutive models of asphalt binders based on the models of asphalt mixture.Finally,the viscoelastic fractional derivative model was applied to assess the phase structure of warm mix asphalt and derive the temperature spectrum of asphalt materials.The main contents and conclusions of this dissertation are as follows:(1)The dynamic modulus tests of various asphalt mixtures were performed with different temperatures and loading frequencies.Based on the characteristics of viscoelastic model,the principle of principal curve fitting was proposed,and the objective functions were established based on the least absolute relative error criterion(LARE)and the minimum absolute relative product error criterion(LPRE).Compared with the traditional least square method(LS),the fitting results of different objective functions on the master curve of viscoelastic mathematical models and mechanical models were analyzed.The rationality of LARE and LPRE objective functions were verified in the proceding of master curve construction by using different asphalt mixtures.(2)Based on viscoelastic solid mechanics models: four parameter fractional derivative Zener model(FDZ),five parameter fractional derivative model(FPFD)and improved five parameter fractional derivative model(IFPFD),the master curves of viscoelastic function of the above three fractional derivative models of asphalt mixtures were constructed by using the time-temperature superposition principle and LARE objective function.Then the master curves of viscoelastic function of the proposed models were compared with the existing MHN model.It is found that FDZ model,FPFD model and IFPFD model adopt a set of parameters(i.e.4-5 model parameters)to describe all master curves of viscoelastic function for asphalt mixture,which meet the requirement of viscoelastic Kramers-Kronig relationship,and the model parameters have clear physical significance.Compared with FDZ model,model parameter ? was added in both FPFD model and IFPFD model,which could better describe the asymmetry of viscoelastic function and the peak width of loss modulus of asphalt mixture.Compared with MHN model,the stress-strain-time(frequency)constitutive equations of FPFD model and IFPFD model could be obtained through the numerical fitting in the proceding of the main curve construction,which could also be used as the constitutive equation of asphalt pavement for structural mechanics analysis.(3)According to the dynamic modulus test results of large-size hexahedron specimens(?,? and ?)of asphalt mixture in three directions,the definition of modulus ratio was established.It was found that the modulus ratio of asphalt mixture was less than 1 under the same frequency(5Hz or 10Hz)at the temperature of 21?,and the modulus ratio showed a decrease with an increase of particle size of mixtures,which indicated that the dynamic mechanical properties of shear compaction specimens were anisotropic.Secondly,master curves of dynamic modulus and phase angle were established in three directions for hexahedron specimen,measured values in three directions showed that the mixtures existed anisotropic properties in the wide frequency range,and the constitutive equation of the viscoelastic IFPFD model were established in three directions for the hexahedron specimen.(4)Viscoelastic fractional derivative liquid models describing the asphalt binders were established.Firstly,the linear viscoelastic range of six kinds of asphalt binders were determined by strain scanning test;secondly,the black diagram was drawn according to the frequency sweep test results,and the mechanical properties(solid or liquid)of asphalt binders were determined according to the graph characteristics.Finally,the four-parameter,five-parameter and improved five-parameter viscoelastic fractional derivative liquid models were obtained based on the solid model by changing FDZ model,FPFD model and IFPFD model.Five kinds of asphalt binders were used to verify the rationality of the above three fractional derivative liquid models.(5)Based on the dynamic rheological test results of warm mix asphalt,the van GURP Palmen diagram and Han curve were obtained,the failure temperature of timetemperature equivalent principle and phase structure changing characteristics could be judged by this two curves for warm mix asphalt respectively;while the main curves of viscoelastic function were constructed by fractional derivative model integrated the advantages of the above two graphs,and the rheological characteristics of its viscoelastic function in long time zone was more comprehensive for the failure temperature judgment of time-temperature equivalence principle and phase structure analysis.The microcrystalline structure of warm mix additives was found by X-ray test in warm asphalt binders,which provided a micro explanation for the change of rheological properties and phase structure of warm mix asphalt in long time zone.(6)Considering the effect of temperature on the mechanical properties of asphalt and asphalt mixture,the fractional derivative freqency spectrum model of asphalt was extended to the temperature spectrum based on the frequency temperature image mathematical relationship,and the fractional derivative temperature spectrum models describing liquid and solid materials were also established.Through the verification of temperature scanning test results of base asphalt,polymer modified asphalt and asphalt mortar,it was found that the fractional derivative temperature spectrum model of asphalt could well describe the change trend of viscoelastic parameters with temperature by a set of model parameters,which indicated that the temperature spectrum model could characterize the viscoelastic characteristics of asphalt in the temperature range.In addition,based on FDZ model,a five-parameter fractional temperature spectrum model was also established for asphalt mixtures,and the rationality of the model was verified by the dynamic modulus test results at the same frequency(5Hz or 10Hz)and with different test temperatures.