Dynamic response of lined circular tunnel to plane harmonic waves

Two dimensional harmonic response of lined circular tunnels in elastic full space medium against plane P–SV waves is investigated. The solution uses hybrid boundary, and finite element methods for modelling of media and lining, respectively. In the proposed ring element used in modelling of lining, the radial and tangential deformations are defined by Fourier series expansion. Therefore, the direct finite element unknowns of the problem are introduced as coefficients of these series. The non-dimensional shear and hoop stresses in the lining, and the same parameters in its interface with surrounding media are presented.