Stress-Deformed State of the Shallow Tunnels Reinforced by Layered Shells Under the Action of Transport Loads

Abstract

Based on the solution of the problem of the action of a transport loads moving at a constant speed on a three-layer or two-layer shells in an elastic half-space, a comparative analysis was performed for the rock mass in the vicinity of a shallows circular tunnel with various designs of their lining (three-layer and two-layer), along the inner surface of which an axisymmetric normal load moves at a constant speed. The inner layer of the three-layer lining is a thick-walled concrete shell, and the outer layers are thin-walled steel shells of equal thickness. The two-layer lining is structurally different from the considered three-layer lining by the absence of the inner layer of the lining. Dynamic equations of elasticity theory in Lame potentials are used to describe the motion of the half-space and the inner layer of the shell. The vibrations of the outer layers of the shell are described by the classical equations of the theory of thin shells. The equations are represented in a movable coordinate system. The contact between the shell and the array is assumed to be either rigid or sliding. The contact between the layers of the shell is supposed to be rigid. To solve the problem, the method of incomplete separation of variables is used. The solution for potentials is presented in the form of a superposition of Fourier-Bessel series and contour integrals of the Fourier type. Next, the method of decomposition of potentials into plane waves and re-decomposition of plane waves into series according to cylindrical functions is used. The solution is obtained for the case when the velocity of the load is less than its critical velocities. The calculation results are presented in the form of graphs and are analyzed in detail. From the analysis of the calculation results, it follows that the use of a three-layer lining as a building envelope is more efficient than a two-layer lining, since in this case the dynamic effect of the moving loads on the rock mass is significantly less.