Inversion Of Ground Vibration Source By Urban Railway Traffic In Frequency Domain

Urban rail traffic is one of the most effective ways to solve traffic problems in large cities, mean while the noise and vibration caused by rail traffic play a role of bottleneck to fast development of urban railway. The vibration source and wave propagation are dealt with a lot worldwide. Many researches in recent years are focused on three-dimensional (3D) calculation of train-track-ground overall system. An insurmountable difficulty in the calculation is that the cutoff high frequency of the time domain solution is quite low, only a dozen Hertz, since the discrete grid size has to be greater than meters, and is far from the main frequency band of observed vibration from urban rail traffic. In addition, from the 3D's point of view, vibration observed at any point very near to the rail is excited by not only the nearest traffic, but also traffic before or after that nearest one. This fact makes the source study quite difficult.As a significant part of the Key Project, Environmental Vibrations Caused by Railway Traffic in Urban Area and Its Propagation, supported by National Natural Science Foundation of China, 3D calculation of ground vibration from urban rail traffic in frequency domain is developed, and power spectrum density (PSD) of rail-wheel unevenness is successfully inversed with guideline of the innovative idea to inverse the vibration source from the observed ground vibration data in this dissertation, in order to provide proper support to theoretical analysis on the environmental vibration for the development of urban rail traffic.Firstly, a coupled train-track-ground model for dynamic analysis is built with simplifications to describe the one dimensional infinity of the track and the half-space infinity of the layered ground in geometrics, the three dimensional wave propagation under ground in physics, and the dynamic interaction between running train and static track, and between the latter and ground. The ground is modeled by a damping-elastic layered half-space. Its Green's function in frequency-wavenumber domain is derived in detail. Based on the Green's function, the vibration solution of the track-ground coupling system exited by an unit harmonic line load is worked out, and therefore a transfer matrix at the rail top surface in a coordinates moving with the train is obtained from integration of the system responses in frequency domain. The train-track-ground dynamic interaction excited by unit harmonic unevenness is calculated, and the responses of ground vibration to stochastic wheel-rail unevenness are then obtained. The ground vibration of a given ground model from harmonic unevenness is calculated numerically. The displacement waveforms show that subsidence in moving reference system caused by running axle weight attenuates rapidly with distance to the track, as a characteristic of quasi-static deformation. The waves from different wheel pairs are interfered, if the wave number of harmonic unevenness is not 0, the fact implies a Doppler effect caused by the running train. The spectra show that ground vibration is multi-frequency even if the unevenness excitation is set with a single frequency; the fact implies a characteristic of vibration from running excitation. The higher frequency of the unevenness excitation is given, the higher frequency of ground vibration appears with a wider frequency band. The frequency range of the calculated ground vibration from stochastic wheel-rail unevenness is from 5Hz to 85Hz and mainly in between 40 Hz to 60Hz that is similar with those from the observed data from rail traffic in urban area.The above dynamic analysis of ground vibration of train-track-3D ground coupling system is combined with Genetic Algorithm. A joint inversion scheme for parameters in source function from wheel-rail unevenness and one of track structure as ballast bed stiffness is therefore designed. The stability of the inversion algorithm in the given solution space is validated by several virtual inversion. The source function is inversed from the observed data near the No. 13 Beijing urban railway, and the results of VALs are quite close to those observed. The amplitudes of the inversed excitation PSD are lower than those of FRA 6th level spectra of the United States in the range of wave length longer than 1.2 meter, that implies the evenness of urban rail in Beijing is better than those of the best main railway in the United States, while the PSD amplitudes are higher than those of FRA 6th level spectra in the range of wave length shorter than 1.2 meter, that fact must be not from the unevenness of the track, but from the irregularities of wheels including geometric and elastic irregularities, such as wheel flats, axle eccentricities, tread out-of-round. The urban rail traffic is not very fast, and then this range of short wave length is exactly corresponding to the main frequency band of vibration from the traffic. The excitation with wave length shorter than 1.2 meter must be underestimated, and the ground vibration in the main frequency band must be underestimated badly, if take only the track unevenness spectrum as the source in researches at present worldwide. It must be improved very much if take wheel-rail unevenness spectrum as the source, as suggested in this dissertation. Relatively to the fact that the track spectrum describes just the unevenness of track, the wheel-rail spectrum describes the unevenness between the wheel and rail, with not only the unevenness of track but also the irregularities of wheels. To inverse the unevenness between the wheel and rail from observed data of ground vibration is really an effective way to get these two excitations comprehensively, and there is no other ways to achieve that at present.In order to be applied for the complicated situation at site with shallow ground water in coast and river regions, Biot's equation in the Cartesian coordinates is solved by means of the integral transformation. The Haskell-Thomson Transfer Matrix technique is adopted to derive the Green's Function of vertical ground displacement in frequency-wavenumber domain. The ground displacement caused by unit harmonic point excitation is calculated by means of the Green's Function. The result shows that the calculated ground vertical displacement decreases with the increasing of the soil porosity, the higher frequency is taken the more obvious influence of the porosity on result appears. The lower permeability of the soil is taken, the smaller ground displacement amplitude is calculated, and the faster the displacement attenuates with distance. The influence of permeability on the calculated high frequency vibrations is more distinct than the low ones. The result shows clearly the viscous coupling effect between the fluid and solid phases in soil. Through comparison of the result with those calculated from one-phase medium model, the possible overestimation of ground vibration at saturated soil site by urban rail traffic from the one-phase medium model is pointed out, and the higher frequency component excited, the worse overestimation obtained.The ground vibration at saturated layered site from urban rail traffic is calculated by taking the Green's Function of saturated layered model into the dynamic coupling analysis of the train-track-3D ground overall system. The result shows that the vibration amplitude at saturated dense sand site with high shear module may lower than that at soft clay site, mean while the frequency band of the vibration may be narrower. The ground vibration energy at saturated site is mainly in frequency band of 20Hz-80Hz, and the energy of high frequency vibration attenuates with distance much more quickly than those of low frequency vibration. The PSD amplitudes of ground vibration at far site decreases even more quickly, the corresponding frequency band is a little bit narrower since the dynamic interaction between flow and solid phases. The bigger b value, Biot viscous coupling parameter is taken, the stronger viscous coupling between the two phases, the lower ground vibration level must be. The effect of b value on the vibration is similar in some degree with a frequency-dependent viscous damping effect, so that is much more obvious on high frequency vibration than low one, stronger on far field vibration than near field one. Three virtual inversions are carried out, and the source functions inversed are very close to the given ones. The result demonstrates that the inversion scheme and strategy designed in the dissertation is also completely applicable for the source inversion caused by urban rail traffic at saturated site.In conclusion, calculation of 3D dynamic interaction of train-track-ground overall system is carried out in frequency domain in the dissertation, the difficulty of low resolution for high frequency component calculation of 3D overall system model in time domain is overcome. The inversion of wheel-rail unevenness PSD is achieved successfully by the Genetic Algorithm. The result shows that it is a powerful approach to detect quantitatively the simultaneous action of track unevenness and wheel irregularities.