Calculation of the wave field in a layered soil foundation using the grid method

Abstract

The article contains a solution to the problem of propagation of waves in a soil massif arising from the movement of subway trains. This problem often arises when predicting vibration levels in buildings located near metro lines. The problem is considered in a two-dimensional formulation, taking into account the actual location of soil layers with different physical and mechanical properties. The soil is modeled using the assumption of its linear deformability, which, to a first approximation, is acceptable due to small vibration displacements. To solve the problem, the finite difference method is used, which allows taking into account the various physical properties of individual soil layers and the structure of subway tunnels and at the same time is one of the simplest numerical methods. To obtain a solution, the direct integration method is used using an explicit scheme, which requires setting sufficiently small time steps. The results are presented as graphs of vibration displacements obtained at various points in time. The graphs illustrate the different nature of the wave field at different load frequencies. The dynamic load is specified in the form of vibrations of the walls of the subway tunnel.