Abstract
In this paper, an analytical wave function method was used to calculate the underground train-induced vibrations with the inhomogeneous soils taken into account. The wave function method is suitable for solving dynamic problems of multi-layered soils; therefore, inhomogeneous soils with uncertainty could be achieved by assigning different soil parameters to each soil layer. Based on the method, a half-space dynamic model with a viscoelastic cylinder tunnel was established. The dynamic shear modulus of the soil was the main uncertain variable in this study, and models with different load frequencies are compared to analyze the effect caused by the uncertainty. According to the numerical results, the relationship between the uncertainty of the soil modulus and the dynamic response of the model was given. When the dynamic shear modulus changes randomly with the range of 20%, the vertical displacement of the surface can be from 1.02 to 1.12 times to that in the model where the soil is homogeneous, while the displacement of the tunnel vault is 1.03–1.1 times.
Highlights
The train-induced vibrations, which have caused many disturbances to nearby inhabitants, are attracting more attention due to the wide application of the underground railway lines.1 It may lead to many engineering problems, such as differential settlement at the ground surface and the crack at the tunnel lining
Field tests are based on the local conditions, but it may be unsuitable for the projects somewhere else due to the large amount of property parameters that differ between two locations
The current paper aims to study the influence of the uncertainty of soil properties on the train-induced vibrations, and a threedimensional analytical model is established considering the axialdirection effect of the soil
Summary
The train-induced vibrations, which have caused many disturbances to nearby inhabitants, are attracting more attention due to the wide application of the underground railway lines. It may lead to many engineering problems, such as differential settlement at the ground surface and the crack at the tunnel lining. Schevenels et al. examined the influence of the variations of the dynamic shear modulus on the Green’s functions of a layered soil with random characteristics, while the effect of horizontal soil variability was investigated by Jones and Hunt.24 He developed the thin-layer method (TLM) as an efficient and accurate means of simulating vibration from underground railways in arbitrarily layered half-spaces. The research studies mentioned above have proposed several methods to predict the train-induced vibrations considering the uncertainty of the soil. In the work of Jones and Hunt, the ground part is modeled as a two-dimensional half-plane, which implies that the wave propagation in third direction is not considered They use a fictitious force method to calculate the vibration source at the tunnel-soil interface, which neglects the multi-scattering effects between the ground surface and tunnels. Some representative results including the displacement in the time and frequency domain are presented
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