The Dynamic Response Of A Pile-Supported Periodic Viaduct To A Moving Mass

It is well known that the high speed railway has a strict requirement on the settlement of the roadbed.Since the viaduct can solve the settlement of the soft soil effectively,the viaduct has been widely used in the high speed railway.At present,since the design speed of the modern high speed train is reaching 400 km/h,it is thus crucial to account for the inertial effect of the moving train when conducting the design for the modern railway.The investigation about the dynamic response of the viaduct due to a moving mass is fundamental to the further research about the dynamic response of the viaduct due to a moving train.This paper focuses on the problem of dynamic response of the pile-supported periodic viaduct to a moving mass,and the inertial effect of the moving mass is analyzed.The results obtained in this paper can be used as the theoretical basis for the design of the periodic viaduct and the regulation of the speed of the train.The main researches conducted in this study are as follows:(1)The dynamic response of a periodically-supported continuous beam(PSPB)to a moving mass.Firstly,the interaction force between the moving mass and the PSPB(mass-beam)is expanded into the Fourier series,and one of them is called a Fourier component of the mass-beam force.By using the Fourier transform and sequence Fourier transform methods,the dynamic response of the PSPB to unit Fourier component moving load(UFML)is represented by an integral of the response function over the generic span.The response function of the PSPB is derived via the transfer matrix method.By using the coupling condition between the mass and the beam as well as the aforementioned dynamic response of the PSPB to the UFML,the Fourier coefficients of the mass-beam interaction force can be determined.Superposition of the responses of the PSPB to all components of the mass-beam interaction force yields the overall response of the PSPB to the moving mass.Based on the proposed model,the dynamic response of the PSPB to a moving mass is analyzed.(2)The dynamic response of the rigidly-supported periodic viaduct(RSPV)to a moving mass.Similarly,the mass-viaduct interaction force is expanded into the Fourier series first,each term of which represents one component of the interaction force.By using the Fourier transform and sequence Fourier transform methods,the dynamic response of the RSPV to UFML is represented by an integral of the frequency-wavenumber domain response function over the generic span of the periodic viaduct.The frequency-wavenumber domain response function of the RSPV is derived via the transfer matrix method.The time domain response of the RSPV to UFML can be recovered by applying the inverse Fourier transform to the frequency domain response.With the mass-viaduct coupling condition and the dynamic response of the RSPV to the UFML,the mass-viaduct interaction force can be obtained.With the superposition principle,the overall dynamic response of RSPV to moving mass is obtained.The dynamic response of RSPV to the moving mass is analyzed by numerical simulations.(3)The dynamic response of the pile-supported periodic viaduct(PSPV)to a moving mass.Based on the boundary element method,the coupled model for the half space soil and pile foundations is developed,and then the compliances of the periodic pile row are obtained.Likewise,the mass-viaduct interaction force is expanded into the Fourier series.By using the Fourier transform and sequence Fourier transform methods,the dynamic response of the PSPV to UFML is represented by an integral of the frequency-wavenumber domain response function over the generic span of the periodic viaduct.The frequency-wavenumber domain response function of the PSPV is derived via the transfer matrix method.With the mass-viaduct coupling condition and the dynamic response of the PSPV to the UFML,the mass-viaduct interaction force can be obtained.With the superposition principle,the overall dynamic response of PSPV to moving mass is obtained.Using the model for the dynamic response of the PSPV subjected to a moving mass,the dynamic response of the PSPV to a moving mass is analyzed.The research of this paper show that the magnitude of the mass and the speed of the mass are two determinant factors affecting the mass-structure interaction force;when the magnitude of the mass is small,the inertial effect of the moving mass is negligible,and the moving mass can be simply treated as a moving load.However,with increasing magnitude of the mass,the inertial effect of the moving mass usually becomes more and more obvious and needs to be accounted for.Besides,with increasing speed of the moving mass,the inertial effect of the moving mass usually becomes more significant.