Dynamic Response of a Lined Tunnel beneath a Truncated Semicircular Canyon Subjected to Plane SH Waves

Abstract

Many underground structures have been constructed beneath irregular topographies, and tunnels traversing canyons are particularly common. Seismic waves propagation is affected by surface irregular topographies and underground tunnels. The stress concentration in tunnels has consistently been a crucial aspect in earthquake engineering designs. Hence, greater attention must be paid to the interaction between irregular topographies and tunnels in contemporary seismic design for subsurface structures. In this study, with the aid of the wave-function expansion approach, a series solution for the scattering issue of shear horizontal (SH) waves induced by a lined tunnel beneath a truncated semicircular canyon in half-space is developed. By adopting the slanted form of Graf’s addition formula and mirror method, wave-function expressions in corresponding subregions in different polar coordinates are unified. According to the continuity conditions of stress and displacement on the auxiliary boundary, the region-matching technique is employed to determine the unknown coefficients of the algebraic equations. Based on the calculated dynamic stress concentration factor (DSCF), the effect of the canyon height, tunnel location, tunnel size, and lining on DSCF is carefully investigated.