The impact of normal and tangential loads on a shallow tunnel - Ukrainets В.Н.; Girnis С.Р.; Gorshkova Л.В.; Zhukenova Г.А. (Bulletin of L.N. Gumilyov Eurasian National University. Mathematics, computer science, mechanics series, 2023)
The problem of the action of uniformly moving normal and tangential loads on the inner surface of an elongated thin-walled circular elastic shell along its axis has been solved in moving cylindrical and Cartesian coordinate systems. The shell is located in an elastic half-space (medium) where the horizontal boundary is parallel to the axis of the shell. It is assumed that the moving loads have a lower velocity than the shear wave propagation in the medium. The load functions can be decomposed into a Fourier series by angular coordinate and a Fourier integral by axial coordinate. The motion of the shell is described by the classical equations of shell theory, while the elastic half-space is described by the equations of elasticity theory in displacements, which are expressed in the Lamé potentials. The method of integral Fourier transform is used for solving. In contrast to similar works where the mass is considered as an elastic space, this problem’s solution takes into account the effect of waves reflected from the boundary of the half-space, which arise during the movement of loads. This problem serves as a model for studying the dynamics of a shallowly embedded tunnel with a thin lining under the influence of the specified type of loads. The results of a numerical experiment are presented, which illustrate the stress-strain state (SSS) of the rock mass under the influence of uniformly distributed and steadily moving axisymmetric normal (the action of pressure from a moving object on the tunnel lining) and axial tangential (the action of frictional forces from a moving object on the tunnel lining) loads on the tunnel.