Reduction Of Subway Train-induced Vibrations By 2.5D Finite/Infinite Element Approach

Subway traffic is convenient for people to travel,while the environmental vibration caused by trains cannot be ignored.The environmental vibration induced by the trains will interfere with the normal life of the residents along the routes,prevent the precision instruments from working properly,and even cause the cracking of ancient buildings.Therefore,it is of great practical significance to study the surface vibration isolation measures caused the subway trains.Due to the traditional two-dimensional(2D)method cannot precisely simulate the speed effect,whereas a fully three-dimensional(3D)model is too time-consuming in practice,a 2.5D finite/infinite element approach is presented by Yang to study the isolation of surface vibration caused by the subway.The following studies have been carried out:(1)By the triple Fourier transformation method,the analytical solutions of the steady-state dynamic response of the half space subjected to a moving load,including the responses of displacement,velocity,acceleration,and the stress-strain.(2)The 2.5D numerical solution is compared with the theoretical solution to ensure the accuracy of numerical method.The dynamic response of the semi-infinite space subjected to a moving load has been studied by the 2.5D finite/infinite element approach.(3)The application of the 2.5D method is extended to study the surface vibration caused by underground trains.The parameter analysis is carried out on the isolation effect of the ground vibration of the trenches induced by the subway.Factors such as depth,width and position of the trenches,as well as load speed,are taken into account.The effects of in-filled trenches with different materials are also considered.Based on the research work above,the following conclusions are drawn:(1)the shear stress is affected by the "Critical velocity effect" mostly,which reaches a maximum of 0.8 times the vertical stress when the load speed reaches critical speed.(2)The Mach wave effect can be observed in stress response when the load velocity exceeds the critical wave velocity.The transmission direction of waves has a fixed propagation angle with the load without self-frequency.But it does not with the load with self-frequency.(3)The frequency of ground-borne vibration induced by subways ranges from 0 to 60 Hz.Response above 20 Hz decays more quickly,that in the range of 0 to 20 Hz decays slowly.As the distance increases,the ground-borne vibration decreases gradually,but the vibration amplification occurs locally.(4)When the open trench is set up,vibration amplification occurs in front of it.The overall vibration isolation effect on its rear is significant.The vibration isolation effect of the open trench is greatest affected by depth,and the vibration isolation effect is obvious for higher frequency bands above 10 Hz,while it is poor for 0 to 10 Hz low frequency.(5)Vibration amplification is smaller in front of the in-filled trench,The vibration isolation effect is significant only within twice the depth of the in-filled trench.The vibration-isolation effect of the in-filled trench is greatly affected by its width,and the wider the in-filled trench,the better the vibration-isolation effect.(6)The vibration isolation effect of the in-filled trench is obviously affected by the materials.To a certain extent,the more rigid material,the better the vibration isolation effect,the softer the flexible material,the better the vibration isolation effect.For vibration isolation in the lower bands of 10 ～ 20 Hz,rigid materials are superior to flexible materials.