Demonstration Of Source Function Inversion Of Vibration Caused By Urban Rail Traffic

As a summary of the last part research work of the Key Project by NationalNatural Science Foundation "Environment vibration caused by urban rail traffic andits propagation feature"(50538030), the dissertation demonstrates a mentionedconclusion which is needed to make deep research, improves the data processing toremove the background vibration from the observed environment vibration causedby urban rail traffic and discusses the application of frequency-wavenumberspectrum, demonstrates and perfects the development the dynamic Green Functionmethod in frequency-wavenumber domain to calculate3dimensional response oftrain-track-ground system and its capability to inverse the wheel-track spectrum, onthe basis of the breakthrough achieved by the whole team of the project.Firstly, the feasibility of time-space domain method to simulate theenvironment vibration caused by urban rail traffic in frequency band10Hz to80Hz,in general, and60Hz to80Hz in near field, is demonstrated. With unit harmonicexcitation with frequencies2Hz,10Hz,30Hz and60Hz on surface of a threedimension model with single layer overlaid on half space, the vertical displacementamplitudes at the points with distance5meters-20meters from the exciting point arecalculated by wave finite element with transmission boundary conditions. For thedemonstration, the calculations are carried out repeatedly with four discrete gridsizes from1m,2m,5m to10m. From the comparison of the results with those by thedynamic Green Function method in frequency-wave number domain, the error incalculation in time-space domain is showed obviously. For a given excitingfrequency, the smaller the grid, the smaller error by the finite element calculation;for a given grid size, the lower the frequency, the smaller error the finite elementcalculation; the reliability of the three dimension finite element simulation of wavewith frequency in band60Hz-80Hz with grid size from stability study mainly byone-dimension analysis, is not ensured even the maximum size rule is now widelyadopted in two or three dimensional analysis. A preliminary quantitative rule forthree dimension analysis is that the maximum grind size should be less than1/25ofthe minimum interesting wavelength. Mean while, it is also pointed out that the calculation stability is also depends on the discrete step in time domain, themaximum step should be0.0001second if the discrete grid is taken as1m, forsimulation of common urban rail traffic caused environment vibration. That meansthe calculated amount must be very large, the time consumed must be quite long inthe case, so that it may take one week on a personal computer for simple casecalculation.Removing background vibration noise in observed records of trafficenvironment vibration is an important step to increase the Signal to Noise Ratio anddemonstrate the characteristic of traffic environment vibration. The shortcomings ofexisting methods to remove the background vibration noise in observed records oftraffic environment vibration is analyzed, an idea to take into account thecross-relativity between background vibration and the observed vibration is putforward, the auto-cross spectrum method is developed as a new method to removebackground vibration and increase the ratio of signal to noise. A case fordemonstration is built as that the vibration recorded in time period long before thetrain passing is taken as background vibration, that recorded while the train ispassing as environment vibration, and that superposed by the two as observedvibration. An environment vibration is obtained by the background vibrationremoved from the observed vibration from the auto-cross spectrum method. Themethod is then verified by comparing the result vibration with the environmentvibration in this case, as the result shows that the background noise can removedmore effectively, the power spectrum, time history, vibration level VAL andweighted level VLz of the obtained environment vibration are all closer to those ofthe environment vibration.The superiority of array observation is that the auto-correlation andcross-correlation characteristic of each point can reflect the spatial structure ofvibration field of urban rail traffic. In order to discuss the effect of source of urbanrail traffic on spatial structure of the vibration field, total power spectrum andpower spectra of some short time periods are calculated by maximum likelihoodmethod from environment vibrations recorded at6points on a rectangular arraywhile a train is passing it, and frequency-wave number (F-K in brief) spectra ofvibration fields in the short time periods are then calculated, the variation of the features of those power spectra in one by one time period is analyzed. Theorientation of the train to the array center (corresponding to the position of the trainon the rail) in each time period is determined from the corresponding F-K spectrum.The result shows the capability to infer the passing process of the train from the F-Kspectra of vibration field on array, and to compute the train speed. It demonstratesthat the moving speed of exciting source of traffic environment vibration couldacquired directly from the above F-K spectra, if the short time periods are taken asshort enough. Ground vertical displacements on model of single soil layer overlaidon half space with excitation on surface are calculated by means of the dynamicGreen Function method in frequency-wave number domain.The capability of the method to deal with the local amplification in attenuationof ground vibration that phenomenon has been observed in some measurements ofenvironment vibration caused by rail traffic, is demonstrated. The results show thatlocal amplification is controlled by an important burried velocity interface, thelocation and intensity of the amplification depends on the ratio of elastic modului ofthe media in the both sides of the interface (i. e. impedance ratio), the thickness ofthe overburden layer, exciting frequency and damping ratio of the overburden layer,from analysis of influence on the amplification of factors as modulus ratio of halfspace to overburden layer media with seven values1,5,6,7,8,9and10,overburden layer thickness with four values3,5,7and9meters, exciting frequencywith seven values16Hz,48Hz,56Hz,64Hz,72Hz,80Hz and108Hz, overburdenlayer damping ratio with three values0.025,0.05and0.1. In general, the largerimpedance at the interface, the more obvious amplifying; keeping the otherconditions the same, the closer of directly arriving time of surface wave to thearriving time of refraction wave from the interface governed by the overburdenlayer thickness, the more obvious amplifying; the closer of the peaks of the wavesgoverned also by the exciting frequency, the more obvious amplifying; the smallerdamping ratio of the overburden layer, the more obvious amplifying. A mechanismof the local amplification in environment vibration attenuation is explained from theresults with a brief analysis of wave propagation paths. The reliability of calculationof rail traffic environment vibration by the dynamic Green Function method infrequency-wave number domain is verified by the way. In order to fit the requirement to analyze the environment vibration at site withshallow groundwater, the dynamic Green Function in frequency-wave numberdomain on saturated layered ground is derived in rectangular Cartesian coordinatesystem based on the model suggested by Men FuLu for wave propagation insaturated porous medium, and by Haskell-Thomson transfer matrix method. Groundvertical displacements of four site models are calculated from a degeneration byreplacing the values of saturated soil parameters as ρ2=0.0001kg/m~3, f=1,Ew=0.0001Pa, b=0.0001Pa·s/m~2, so that the site models are very close to those insingle phase medium. The formulas and the program of the dissertation are verifiedby comparing the results with the published results of the corresponding singlephase medium models. Ground vertical displacements of model with singlesaturated layer overlaid on half space by unit harmonic excitation with eightfrequencies10Hz,20Hz,30Hz,40Hz,50Hz,60Hz,70Hz and80Hz are calculated.The feasibility of the developed dynamic Green Function method infrequency-wave number domain to simulate the vibration field by urban rail trafficat site with shallow ground water is demonstrated by comparing the results withthose published by Wang (2011) based on Biot model for the same models. Meantime, the reliability of the method developed by Wang is also demonstrated. Thephysical meaning of parameters in Men Fulu’s model is unambiguous, thus themethod of this paper is more convenient in practice application.Finally, the feasibility of inversing excitation source function with theadvantage in array data observed from several trains is tested and demonstrated bymeans of the method developed by project team to calculate vibration on threedimensional train-rail-ground coupled system in the frequency-wave numberdomain. PSD amplitudes corresponding five wavelengths are selected tocharacterize exciting source function, speed of the train and the un-damped stiffnessof ballast and embankment are selected to build inversion parameter vector with theabove five together, and the value ranges of the seven are estimated from a virtualinversion. The objective function is constructed by the vibration acceleration levelsof four points, and the observation data of the two trains during rush hour inmorning and close to the flat peak period at noon are used, and constraint hasincreased. The wheel/rail uneven (round) spectrum of Beijing No.13rail line is inversed. The reliability of the inversion excitation source function is analyzed andverified though comparison of calculation result used another point measured data.The new method to inverse wheel and rail uneven (round) spectrum of the urban railtraffic according to the surface of the vibration on array observation data close tothe rail is improved.In conclusion, six innovation achievements on environment vibration causedby urban rail traffic and its propagation are worked out, such as limitations of timedomain calculation, the improvement to remove the background vibration noise, andacquiring of moving speed of the vibration source from F-K spectra, mechanism oflocal amplification in environment vibration attenuation, dynamic Green Functionin frequency-wave number domain in saturated layered ground based on Men FuLumodel and joint inversion of wheel-rail uneven (round) spectrum parameters fromarray data observed from several trains. The dynamic Green Function method tocalculate the response of three dimensional system of train-track-ground infrequency-wave number domain and the innovational idea to inverse wheel-railuneven (round) spectrum as the exciting source from data observed on array close tourban rail traffic according to the surface of the vibration on array observation datathe rail are demonstrated and completed.