Analytical Solution for Circular Tunnel under Obliquely Incident P Waves considering Different Contact Conditions

An analytical solution for the seismic-induced thrust and moment of the circular tunnel in half-space under obliquely incident P waves is developed in this study, which is the superposition of the solution for deep tunnels under incident and reflected P waves and the reflected SV waves. To consider tangential contact stiffness at the ground-tunnel interface, a spring-type stiffness coefficient is introduced into the force-displacement relationship. Moreover, the tunnel lining is treated as the thick-wall cylinder, providing more precise forecasts than beam or shell models used in previous analytical solution, especially for tunnels with thick lining. The reliability of the proposed analytical solution is assessed by comparing with the dynamic numerical results. Based on the proposed analytical solution, parametrical studies are conducted to investigate the effect of some critical factors on the tunnel’s seismic response, including the incident angles, the tangential contact stiffness at the ground-tunnel interface, and the relative stiffness between the ground and the tunnel. The results demonstrate that the proposed analytical solution performs well and can be adopted to predict the internal forces of circular tunnels under obliquely incident P waves in seismic design.

Polarization Properties of Obliquely Incident EM Waves in Nonuniform Weakly Ionized Dusty Plasma

Effects of nonuniform weakly ionized dusty plasma on the polarization properties of obliquely incident electromagnetic (EM) waves were theoretically investigated in this paper. The dielectric coefficient of magnetized dusty plasma is obtained based on the Bhatnagar–Gross–Krook collision model. Then, the effects of external magnetic field, dust radii, and density on the polarization mismatch loss of obliquely incident EM waves in the L-band were analyzed using the equivalent impedance method. Results indicate that the larger the external magnetic field, the greater the polarization mismatch loss. In addition, we also found that dusty particles alleviate the deterioration of the polarization state significantly; regulating and controlling dust radius and density can avoid polarization reversal and reduce the polarization mismatch loss. We further analyzed the variation of the polarization state under different reentry heights. Our analysis reveals interesting features concerning polarization properties of obliquely incident EM waves, which provide an important theoretical basis for information reception in the plasma sheath containing ablative particles.