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The operation safety of ultra-small-spacing subway tunnels is seriously threaten by long-term, high-frequency, low amplitude train vibration loading. Although the vibration loading generated by the train is small each time, the durability of the tunnel structure may be reduced or even cracked under long-term impact. To study the spatial distribution law of vibration acceleration of ultra-small-spacing tunnels under train moving loading, a three-dimension numerical model was established for a subway-track tunnel with a design speed of 120 km/h, and the spatial distribution law of vibration acceleration of the subway track system and surrounding rocks of the tunnel with single train running, double trains running in the same direction and double trains running in the reverse direction were analyzed. Results show that the vertical acceleration of the wheel-rail contact point is always the largest in the longitudinal direction, and the vertical acceleration of waist of the middle rock pillar wall is about 60% of the bottom of the roadbed. The vertical acceleration of the surrounding rock of the tunnel satisfies the distribution law of the exponential function in both the horizontal and vertical directions. The vertical acceleration propagates along the midline to both sides in the lateral direction, the vertical acceleration attenuates about 80% at 6 m and 95% at 10 m. The vertical acceleration at the waist of the middle rock pillar wall is the largest in the vertical direction, and its attenuate sharply to both ends of the rock pillar. After 10 m, the attenuation rate gradually becomes gentle. The obtained conclusions can provide the theoretical base in the design and construction of similar engineering.

To determine the energy attenuation and energy reflection coefficients in layered foundation is the key factor to reveal the dynamic response characteristics of the high-speed railway foundation. Based on the foundation test model under the dynamic loading of the high-speed railway, the energy attenuation and energy reflection coefficients were introduced and the attenuation formulas of the vibration acceleration in the layered foundation were deduced. Five scale models of 1:1, 1:2, 1:5, 1:10 and 1:20 are established respectively by using Abaqus technique. The energy attenuation mechanism and interfacial energy reflection characteristics in the layered foundation were analyzed. Results show that it is appropriate to use vibration acceleration to characterize the propagation rule of the energy attenuation in the layered foundation. The size effect equations of the energy attenuation and energy reflection coefficients in the layered foundation are deduced and the size effect of the energy attenuation is revealed. Based on the nonlinear relationships among the energy attenuation coefficient, the model scale, the loading amplitude and the vibration frequency, the energy attenuation equation of the scale test model is constructed. The reliability of the theoretical and simulation results is verified by the scale test model. The conclusions obtained in this study can provide a reference for a similar engineering practice.

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