| As an external barrier to prevent the intrusion of natural precipitation into the roadbed,the wa-terproofing structure for the subgrade in high-speed railway is one of the key measures to ensure the long-term service ability of the subgrade.As a new type of waterproofing structure,the full-section asphalt concrete substructure has been highly valued in the field of high-speed railways in recent years.It has a significant effect on the control of diseases such as frost swelling and thawing and sinking of the subgrade in the frozen and cold regions.At present,the design of the material composition for the asphalt concrete substructure has been studied in depth,while there was no systematic and perfect calculation theory and design process for its structural design.Based on this,in regard of CRTSIII ballastless track structure with independent intellectual property rights in China,this paper selected a reasonable fractional derivative constitutive model to characterize the dynamic viscoelastic properties of the asphalt concrete substructure in the full temperature domain and systematically investigated the working state of the asphalt concrete substructure under the train load and ambient temperature.The failure modes and structural design methods of the asphalt concrete substructure were clarified,which provided the basis for material optimization and structural design of the asphalt concrete substructure.The main work carried out in this paper and the corresponding research findings were as follows:(1)Based on the definition of fractional order calculus,the mechanical properties of fundamen-tal elements of fractional order derivatives were introduced,and the differences between traditional integer order constitutive model and fractional order constitutive model were compared.Based on the Grünwald-Letnikov definition of fractional derivatives,a numerical stress algorithm was derived for a spring-pot element and it was found that the stress of spring-pot element at one incremental step was not only related to the strain in previous incremental step,but also to all historical strains and incre-mental time duration.A user-defined material subroutine was prepared in the finite element software for fractional derivative constitutive model and verified against the analytical solution and test results,and results showed that the derived numerical calculation method was accurate and reliable.(2)Based on the finite element simulation results and field measurements,the dynamic stress frequency response curve for the roadbed surface in ballastless track was obtained by the fast Fourier transform method.The dynamic response of the roadbed surface layer under the train action was found to be in the frequency range of 0-20 Hz,and the dynamic modulus test in the highway could be used to test the dynamic viscoelastic properties of the asphalt concrete for the railway substructure.The dynamic modulus test was used to study the dynamic characteristics of the field coring samples in the full temperature domain based on the Beijing-Zhangjiakou high-speed railway test section project.The problem of identifying viscoelastic parameters of complex modulus in the frequency domain was solved by the optimization method.The results of the viscoelastic function fitting and the analysis of the statistical parameters showed that the fractional derivative model was overall better than the gen-eralized Maxwell model and required fewer parameters,which can accurately reflect the viscoelastic information within and outside the range of the test data and was more suitable for describing the dynamic viscoelastic properties of asphalt concrete substructure in the full temperature domain.(3)A coupled vehicle-track-subgrade numerical analysis model based on a preferred fractional order constitutive model was developed to calculate and verify the dynamic characteristics of bal-lastless track structure with asphalt concrete sublayer under the train load.The temporal and spatial distribution of dynamic response indicated that the most unfavorable longitudinal loading position for dynamic response of asphalt concrete layer was at the structural joints of base plate.The dynamic response is mainly influenced by the width of the base slab in the transverse direction and about 10 m in the longitudinal direction.The lateral influence range of the dynamic response was mainly in the width of the base plate,while the longitudinal influence range was about 10 m.In the longitudinal strain frequency response curve of the asphalt concrete layer,the second peak frequency played a ma-jor role in controlling the longitudinal strain response,which was approximately proportional to the train speed and the scale factor was related to the length between vehicle centers.The dynamic modu-lus corresponding to this peak frequency could be used as the equivalent modulus for the elastic model approximation.Compared with traditional waterproofing structure,when the asphalt concrete layer was introduced to the track structure,the energy dissipation effect caused by its viscoelastic properties helped to reduce the overall vibration level and vertical deformation of the track and subgrade.(4)Based on the heat transfer principle,the temperature effect analysis model of ballastless track structure was established to analyze the spatial and temporal distribution of temperature field,and the corresponding estimation formula was also proposed.The surface temperature of the asphalt concrete layer at the shoulder and the center line could be expressed linearly as a function of solar radiation and air temperature.The monthly average temperature of the asphalt concrete layer below the base plate could be expressed linearly as the monthly average air temperature.The negative temperature gradient within the upper track structure was the main cause of passive stretching on the surface of asphalt concrete layer.This phenomenon could be effectively mitigated by laying composite geotextiles at the structural joints,which should be 1 to 2 m long on each side of the structural joints.(5)Based on numerical analysis of dynamic response and temperature effects of asphalt concrete layer,the possible failure modes of asphalt concrete layer during service were summarized into three categories: low-temperature crack,fatigue crack under train load,and passive tensile failure at the structural joints of base plate.Based on semi-analytical finite element theory,a simplified calculation model under train load was established.Considering the traffic parameters,temperature conditions,and material parameters,a structural design flow was formed.A graphical user interface program for structural design was also developed,which could provide design guidance for actual projects. |
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