Dynamic stress-strain states in viscoelastic half-spaces from the effects of cylindrical inclusion loads

Vibrations are usually transmitted from a vibration source to a building through the ground, which is rarely uniform. Therefore, the development of methods that allow us to determine and evaluate the vibration levels of a ground mass surface and a building foundation, taking into account the heterogeneous (layered) nature of the soil and any outlines of tunnel lining contours, is an urgent task. In this paper, we developed a calculation method and an algorithm for including a circular cross-section passing near the Earth’s surface in a closed way. The inclusions are circular tunnels. A harmonic load acts inside the tunnels. Mathematical modelling of the stress-strain state of the tunnel lining and the surrounding rock mass is carried out as an element of a single deformed system. This makes possible the obtained analytical solutions to the corresponding problem of the theory of elasticity of the calculation method used as the basis. The aim of this work is to determine the stress-strain state of a cylindrical shell under the influence of harmonic waves. The problem is solved in mixed potentials that satisfy a wave equation with complex parameters. The computer program that implements the developed methodology allows us to clarify the known parameters and establish new formation patterns of the stress-strain state of the linings, taking into account the rheological properties of the environment. The maximum radial stress under the influence of radial loads and the maximum radial stress under the influence of tangential loads, depending on the angle of incidence of waves, are determined.