A coupling analysis method of foundation soil dynamic responses induced by metro train based on PDEM and stochastic field theory

Foundation soil is an important medium for vibration wave propagation in the running of metro train. The spatial variability of soil properties has an important influence on vibration response. The parameters of foundation soil are often determined. Based on the probability density evolution method (PDEM) and stochastic field theory, a coupling model of the metro train-track-shield tunnel-foundation soil is established. The stochastic field is expressed by the series of stochastic variables and deterministic space functions by the Karhunen-Loeve Expansion (KLE) method. The stochastic parameters of the cross-section of tunnel-foundation soil are specified to simulate the stochastic field of foundation soil. Based on PDEM, the environmental vibration caused by metro trains in shield tunnels is studied. The results of ground surface vibration displacement under different metro train speeds are analyzed, and the upper and lower limits and probability density information of ground surface vibration displacement are obtained. The results show that the probability density distribution of ground vibration displacement at each time is approximately normal due to the stochastic field of foundation soil. The peak and valley of the vibration displacement curve at the inverted arch of the tunnel are caused by the wheel distance of the metro train. The probability density distribution of velocity and acceleration is more sensitive to the stochastic field of velocity foundation soil and the change in metro train speed. The maximum Z vibration level results under different metro train speeds all meet the requirements of vibration allowable limits in the specification.

Automated summary

Foundation soil plays a significant role in the propagation of vibration waves caused by metro trains. The spatial variability of soil properties has a crucial impact on vibration response. This study establishes a coupling model of the metro train-track-shield tunnel-foundation soil using the probability density evolution method and stochastic field theory. The stochastic field is represented by a series of stochastic variables and deterministic space functions through the Karhunen-Loeve Expansion method. The stochastic parameters of the tunnel-foundation soil cross-section are specified to simulate the stochastic field of foundation soil. The ground surface vibration displacement caused by metro trains in shield tunnels is investigated using the probability density evolution method. The analysis of different metro train speeds reveals the upper and lower limits as well as the probability density distribution of ground surface vibration displacement. The results demonstrate that the probability density distribution of ground vibration displacement follows a normal distribution due to the stochastic field of foundation soil. The vibration displacement curve at the inverted arch of the tunnel exhibits peaks and valleys, which are caused by the wheel distance of the metro train. The probability density distribution of velocity and acceleration is more sensitive to the stochastic field of velocity foundation soil and the change in metro train speed. The maximum Z vibration level results under different metro train speeds satisfy the requirements of vibration allowable limits specified.