Dynamic stress concentrations in lined twin tunnels within fluid-saturated soil

An exact analysis for three-dimensional dynamic interaction of monochromatic seismic plane waves with two lined circular parallel tunnels within a boundless fluid-saturated porous elastic medium is presented. The novel features of Biot dynamic theory of poroelasticity along with the appropriate wave field expansions, the pertinent boundary conditions, and the translational addition theorems for cylindrical wave functions are employed to obtain a closed-form solution in the form of infinite series. The analytical results are illustrated with numerical examples in which two identical tunnels, lined with concrete and embedded within water-saturated soils of distinct frame properties (i.e., soft or stiff soils), are insonified by plane fast compressional or shear waves at end-on incidence. The basic dynamic field quantities such as the hoop and axial stress amplitudes are evaluated and discussed for representative values of the parameters characterizing the system. The effects of formation material type, angle of incidence, incident wave frequency, and the proximity of the two tunnels on the liner stresses are examined. Particular attention is paid to the influence of bonding and drainage conditions at the liner/soil interface on the dynamic stress concentrations. Limiting cases are considered and good agreement with the solutions available in the literature is obtained.