Analytical modeling for the calculation of underground train-induced vibrations in inhomogeneous soils with uncertainty

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.