DYNAMIC CHARACTERISTICS OF SATURATED FRACTIONAL DERIVATIVE TYPE VISCOELASTIC SOIL AND LINING SYSTEM WITH A DEEPLY EMBEDDED CIRCULAR TUNNEL

The coupled harmonic vibration of the saturated fractional derivative type viscoelastic soil and elastic lining of a deeply embedded circular tunnel is investigated in the frequency domain. Regarding the soil skeleton as a viscoelastic medium with a fractional derivative constitutive relation and based on the theory of saturated porous medium and plane elasticity, analytical solutions of the harmonic vibrations of the saturated viscoelastic soil and the elastic lining are presented, respectively. The steady-state dynamic responses of the saturated viscoelastic soil and lining system are obtained by the inner boundary conditions of the lining and the continuity conditions on the interface between the saturated soil and the lining, and the analytical expressions of the displacements, stresses and the pore water pressures for the saturated viscoelastic soil and lining are given. Then, the parameter study is conducted, and the influences of the physical and geometry parameter on the dynamic characteristics of the system are examined. It is revealed that there exist remarkable differences for the dynamic responses between the saturated fractional derivative type viscoelastic soil-lining system and the classical saturated elastic/viscoelastic soil-lining system.