ANALYTICAL SOLUTIONS OF DYNAMIC RESPONSES OF A LINED TUNNEL IN VISCOELASTIC SOIL

Using an analytical method, the harmonic vibration characteristics of viscoelastic soil and lining structure are presented in the frequency domain. Firstly, the soil skeleton is treated as a viscoelastic medium with the fractional derivative constitutive relations. By the viscoelastic theory, the analytical solutions for the displacement and stress of the fractional derivative type viscoelastic soil are obtained, subject to a harmonic axisymmetric load. Secondly, the lining is treated as a homogeneous elastic medium. The lining is equivalent for a thin shell structure. The motion equation of the lining structure is established by the Flügge theory of a thin shell. The dynamic interactions of fractional derivative viscoelastic soil and the shell are analyzed. The expressions of undetermined coefficients are based on continuity conditions. Thirdly, the analytical results are compared with the analytical solutions from current existing literatures. Finally, the system dynamic characteristics are analyzed for different parameters of the soil and the lining by the numerical examples. It is shown that the system dynamic responses with a thin shell are greater than those with homogeneous elastic lining conditions; the response amplitudes decrease gradually as the modulus ratio between soil and lining increases. The parameters of fractional derivative constitutive have great influences on the system dynamic characteristics.