Dynamic response of an eccentrically lined circular tunnel in poroelastic soil under seismic excitation

An exact analysis for two-dimensional dynamic interaction of monochromatic progressive plane compressional and shear seismic waves with a permeable circular tunnel lining of circumferentially varying wall thickness buried in a boundless porous elastic fluid-saturated formation is presented. The novel features of Biot dynamic theory of poroelasticity in conjunction with the translational addition theorems for cylindrical wave functions, along with the appropriate wave field expansions and the pertinent boundary conditions are employed to develop a closed-form solution in form of infinite series. The analytical results are illustrated with numerical examples in which an air-filled and water-saturated permeable tunnel lining of variable wall thickness, embedded within water-saturated surrounding formations of distinct frame properties (soft, stiff, and stiff viscoelastic soil), is insonified by fast compressional or shear waves at selected angles of incidence. The effects of liner eccentricity, interface permeability, formation material type, incident wave frequency, and angle of incidence on the hoop stress amplitude are evaluated and discussed for representative values of the parameters characterizing the system. Limiting cases are considered and good agreements with the solutions available in the literature are obtained.