Model of the dynamics of a tunnel and a shallow underground pipeline under the action of traffic loads - Л.А. Алексеева; В.Н. Украинец (Bulletin of L.N. Gumilyov Eurasian National University. Mathematics, computer science, mechanics series, 2020)
A mathematical model has been developed for the effect of transport loads on a tunnel reinforced with a multilayer shell and an underground multilayer pipeline at their shallow location. As a design scheme for these underground structures, an elastic cylindrical multilayer shell located in an elastic half-space (massif) is considered. The displacement of the layers of the shell and the elastic half-space is described by the Lame equations in a moving coordinate system. An analytical solution is obtained for the problem of determining the components of the stress-strain state of a rock mass and a shell at arbitrary loading speeds in the subsonic case, when the transport load moves at a speed lower than the propagation velocities of longitudinal and transverse waves in the rock and shell. The results of computer experiments are presented, which illustrate the stress-strain state of the pipeline and the earth’s surface under moving axisymmetric traffic loads