Analytical Solutions For Dynamic Response Of Underground Tunnels Under SH Waves

Scattering of wall rocks around underground tunnels subjected to cylindrical SHwaves can affect the ground vibration and dynamic stress concentration, so cylindricalwaves generated by tunnel blasting can lead to the problem of safety of cavities. Thispaper has made quantitative calculations by using the mirror method, and got theanalytical solution. In the process, all wave functions should be transferred to thesame coordinate in which the origin is set in the circle of the underground cavity.Then introducing the boundary conditions, the solution of the problem is reduced tosolving a set of infinite linear algebraic by using Graf’s addition theorem. When noloosing wall rocks, the answer will degrade for known solutions. And its results havebeen compared perfectly. At the same time, the effects of some factors such as thefrequency of the incident waves, the depth of the tunnel and the distance between thewave source and the cavity and the lining’s properties on the hoop stress amplitude onthe the wall of the tunnel are considered. And some useful conclusions are drawed inthis paper.Scattering of plane SH waves in the underground rigid lining cavity hasimportant significance in engineering applications. Similarly with the mirror method,we use the wave function expansion method and dynamic equilibrium equation tosolve the typical case. Researches show that cavity displacement and surfacedisplacement can be influenced by multiple factors. The angle of the incident waves,quality and depth of the cavity and so on have a very significant effect on theamplification.