The influence of the frequency-dependent stiffness of rail pad on the frequency distribution of vibrations created by a subway train running in tunnel is investigated using a frequency-domain algorithm. The theoretical approach combines vehicle–track coupling dynamics and spectrum analysis using the finite element method. The proposed approach is validated by a comparison with measured data. The comparison further shows that the theoretical approach and the selection of calculation parameters are reasonable and they create high calculation accuracies in the considered frequency range. Compared with a constant stiffness pad, the frequency-dependent stiffness of rail pad has little effect on vibrations below the one-third octave center frequency of 25 Hz; however, it significantly changes the vibrations observed above that center frequency. It is also found that simply increasing the constant stiffness of rail pad can lead to predictions of the vibration that have only a small error in either the low-frequency or high-frequency domains.
WangYFLiKXuXM. Transport energy consumption and saving in China. Renew Sustain Energy Rev2014; 29: 641–655.
2.
YangXLiXZiyouG. A cooperative scheduling model for timetable optimization in subway systems. IEEE Trans Intell Transport Syst2013; 14(1): 438–447.
3.
Xu XM, Li K, and Li X. Research on passenger flow and energy consumption in a subway system with fuzzy passenger arrival rates. Proc IMechE, Part F: J Rail Rapid Transit 2014; 229(8): 863–874.
4.
KangLJWuJJSunH. A practical model for last train rescheduling with train delay in urban railway transit networks. Omega2015; 50: 29–42.
5.
KangLJWuJJHuijunHJ. Departure time optimization of last trains in subway networks: mean-variance model and GSA algorithm. J Comput Civil Engng2014; 04014081: 1–12.
6.
KurzweilG. Ground borne noise and vibration from underground rail systems. J Sound Vib1979; 66(3): 363–370.
7.
MadshusCBessasonBHarvikL. Prediction model for low frequency vibration from high speed railways on soft ground. J Sound Vib1996; 193(1): 195–203.
8.
Hanson CE, Towers DA and Meister LD. Transit noise and vibration impact assessment. Report FTA-VA-90-1003-06, 2006. Washington, DC: US Department of Transportation.
9.
VerbrakenHLombaertGDegrandeG. Verification of an empirical prediction method for railway induced vibrations by means of numerical simulations. J Sound Vib2011; 330: 1692–1703.
10.
VerhasHP. Prediction of propagation of train-induced ground vibration. J Sound Vib1979; 66(3): 371–376.
11.
KrylovVV. Generation of ground vibration by superfast trains. Appl Acoust1995; 44: 149–164.
12.
ShengXJonesCJCPetytM. Ground vibration generated by a harmonic load acting on a railway track. J Sound Vib1999; 225(1): 3–28.
13.
ShengXJonesCJCThompsonDJ. A theoretical model for ground vibration from trains generated by vertical track irregularities. J Sound Vib2004; 272: 937–965.
14.
XiaHCaoYMDegrandeG. Theoretical modeling and characteristic analysis of moving-train induced ground vibration. J Sound Vib2010; 329: 819–832.
15.
TakemiyaH. Simulation of track−ground vibrations due to a high-speed train: the case of X-2000 at Ledsgard. J Sound Vib2003; 261: 503–526.
16.
CelebiE. Three-dimensional modelling of train-track and sub-soil analysis for surface vibrations due to moving loads. Appl Math Comput2006; 179(l): 209–230.
17.
FrançoisSLambaertGDegrandeG. Local and global shape functions in a boundary element formulation for the calculation of traffic induced vibrations. Soil Dyn Earthq Eng2005; 25: 839–856.
18.
AndersenLJonesCJC. Coupled boundary and finite element analysis of vibration from railway tunnels—a comparison of two- and three-dimensional models. J Sound Vib2006; 293: 611–625.
19.
YangYB. Train-induced wave propagation in layered soils using finite/infinite element simulation. Soil Dyn Earthq Eng2003; 23: 263–278.
20.
GuptaSDegrandeGLombaertG. Experimental validation of a numerical model for subway induced vibration. J Sound Vib2009; 321: 786–812.
21.
HungHHChenGHYangYB. Effect of railway roughness on soil vibrations due to moving trains by 2.5D finite/infinite element approach. Engng Struct2013; 57: 254–266.
22.
ConnollyDGiannopoulosAFordeMC. Numerical modelling of ground borne vibrations from high speed rail lines on embankments. Soil Dyn Earthq Eng2013; 46: 13–19.
23.
ForrestJAHuntHEM. A three-dimensional tunnel model for calculation of train-induced ground vibration. J Sound Vib2006; 294: 678–705.
24.
KaoKAHuntHEMHusseinMFM. The effect of a twin tunnel on the propagation of ground-borne vibration from an underground railway. J Sound Vib2011; 330: 6203–6222.
25.
JonesSHuntH. Voids at the tunnel-soil interface for calculation of ground vibration from underground railway. J Sound Vib2011; 330: 245–270.
26.
DegrandeGSchevenelsMChatterjeeP. Vibrations due to a test train at variable speeds in a deep bored tunnel embedded in London clay. J Sound Vib2006; 293: 626–644.
27.
SanayeiMMauryaPMooreJA. Measurement of building foundation and ground-borne vibrations due to surface trains and subway. Engng Struct2013; 53: 102–111.
28.
MaesJSolHGuillaumeP. Measurement of the dynamic railpad properties. J Sound Vib2006; 293: 557–565.
29.
DingDYLiuWNGuptaS. Prediction of vibrations from underground trains on Beijing metro line 15. J Central South Univ Technol2010; 17(5): 1109–1118.
30.
ZhaiWMSunX. A detailed model for investigating vertical interaction between railway vehicle and track. Veh Syst Dyn1994; 23(Suppl 1): 603–615.
31.
ChenGXPanHLongaHLiaX. Dynamic constitutive model for soil considering asymmetry of skeleton curve. J Rock Mech Geotech Engng2013; 5: 400–405.
RenXWTangYQXuY. Study on dynamic response of saturated soft clay under the subway vibration loading I: instantaneous dynamic response. Environ Earth Sci2011; 64(7): 1875–1883.
34.
TanHMGaoZB. Comparison of maximum dynamic shear moduli of lab and site tests for saturated soils. Disast Adv2012; 5: 1471–1473.
