Theoretical Study Of Structural Vibration And Mach Cone Phenomenon In Ballastless Track-subsoil Of High Speed Railway

With the increasing speed of high speed railway,the environmental vibration caused by high speed trains is becoming more and more obvious.Especially,when the foundation soil is soft soil,the Mach cone phenomenon appears,which makes the foundation soil vibration obviously increase.Therefore,how to accurately simulate the vibration of track and foundation caused by train loads becomes one of the key problems in the planning and construction of high-speed rail.In this paper,on the basis of the structural characteristics of the high-speed railway ballastless track-foundation soil system,a 2.5-dimensional boundary element-finite element(BEM-FEM)coupling method is proposed,and the dynamic interaction model of ballastless track and foundation soil is established.The boundary element coefficient matrix is deduced by the thin layer method,and the BEM-FEM coupling theory is accomplished and the system equaton of the track slab-foundation soil structure is obtained and realized by programming.The vibration responses caused by quasi-static train axle load and moving wheel axle load with track irregularity are calculated.And the Mach cone phenomenon caused by the high speed in the track foundation soil system is emphatically analyzed.In this paper,the train axle loads are simplified as moving constant force load and moving load series.When the load speed is low,the displacement response of track and foundation soil has obvious symmetry,and the vibration response with a smaller influence range.When the load speed is high,the vibration response attenuates in the form of fluctuation and the influence range increases.The obvious Maher line appears in the displacement nephogram of the foundation.For moving load series,when the load speed is low,the displacement response is periodic.When the load speed is high,due to the influence of Maher cone phenomenon,displacement of the foundation has no periodicity,and the vibration is mainly concentrated after the load series passes through.When considering single harmonic harmonic load caused by track irregularities,the vibration response attenuates in the form of fluctuation under different load moving speeds.However,the attenuation curve fluctuates greatly when the load speed is high.For different load types,when the load velocity exceeds the shear wave velocity of foundation soil,the vibration propagates in the foundation soil in the form of waves,and the velocity of the propagation in the foundation soil lags behind the load moving velocity,resulting in the vibration response mainly concentrated behind the moving load.And the surface displacement response of the foundation appears Maher cone phenomenon.