The Nonlinear Rheological Behaviors Of Modified Asphalt Based On Lissajous Curves

Asphalt has obvious rheological characteristics under load,and the asphalt will easily be in a nonlinear rheological state when it is subjected to large amplitude loads during actual use of the pavement.At present,the researches on the nonlinear rheological properties of asphalt is limited.In order to study the rheological properties of modified asphalt under nonlinear response,the modified asphalts such as SBS modified asphalt and rubber powder modified asphalt were studied in this paper.Based on the research method of Lissajous curve,this paper studied the nonlinear rheological properties of asphalt by analyzing the geometric characteristics of Lissajous curve and the variation law of viscoelastic parameters,and the relationship between different rheological properties was studied by analyzing the physical changes of Lissajous curve in cyclic physical process.Firstly,a 70#neat asphalt was selected.Three kinds of polystyrene-butadiene（SBS）modified asphalts with the contents of 3%,5%and 7%and two kinds of rubber powder modified asphalt with the contents of 15%and 20%were prepared respectively.Their linear and nonlinear rheological properties were studied by oscillating frequency scanning test,oscillation time scanning test and flow scanning test.Secondly,based on the analytical method of Lissajous curve geometry,the strain response is decomposed into elastic and viscous parts by decomposition method,and the variation law of the elastic or viscous Lissajous curve of asphalt under different load conditions is analyzed.Based on the elastic Lissajous curve and the viscous Lissajous curve,the Pipkin spectrum in the stress-frequency domain can be established.The nonlinear rheological properties of modified asphalt is studied by analyzing the shape change of the Lissajous curve and the corresponding elastic strain component curve and the viscous strain component curve.Then,based on the analysis method of Lissajous curve parameters,the decomposed elastic and viscous strain equations are brought into the Chebyshev polynomial,and the nonlinear parameters c₃ and f₃ of elastic strain and viscous strain are proposed to analyze the nonlinearity rheological properties of modified asphalt.The nonlinear graphical parameters of elastic and viscous response are proposed:minimum stress elastic compliance J_M’,maximum stress elastic compliance J_L’,minimum stress mobilityφ_M’and maximum stress mobilityφ_L’to analyze the modified asphalt under load.The elastic and viscous changes under the action,and the nonlinear rheological properties of the modified asphalt under stress and shear thinning under load are studied according to the stress hardening index S and the shear thinning index T.Furthermore,based on the analysis method in the frequency domain of Lissajous curve,the Fourier transform method can be used to convert the strain response curve in the time domain to the higher order spectrum in the frequency domain,the variation law of the relative intensity ratio of the third order harmonics I₃/I₁ is used to describe the nonlinear rheological characteristics of different modified asphalts as a function of stress level and load frequency.At the same time,based on I₃/I₁,the nonlinear quantitative parameter Q is proposed and its zero-stress stability value Q₀ is used to analyze the significance of the nonlinear rheological properties of different modified asphalts.Finally,based on the Lissajous curve,the correlation of different rheological properties is analyzed,and the physical changes of asphalt in a cycle are studied.Based on the variation of physical processes of tension-yield-destruction-reorganization,the apparent cage model of asphalt is established.The apparent cage modulus of the asphalt and the rheological properties of the dynamic and static yielding were analyzed.Then,the relationship between the apparent cage modulus of the asphalt and its elastic storage modulus and the relationship between the dynamic shear flow of the asphalt in the Lissajous curve and the static flow of the asphalt were established to establish the correlation between different rheological properties.