Nonmonotonic traveling waves in an unsaturated medium induced by a solid force and fluid mass sources. (August 2020) - Zhang, Yu; Ping, Ping
Highlights: Spatiotemporal wave signatures induced by solid and fluid sources in an unsaturated porous medium are predicted. The traveling waves are sensitive to the excited sources. The waves show nonmonotonic feature about the water saturation. Abstract: The traveling wave responses in an unsaturated medium induced by a solid force and fluid mass sources are derived in 3D Green's functions using the Dirac Delta function decompositions. The wave behaviors are described in pore fluid pressures and solid frame displacement along with fluctuations of capillary pressure in response to time variant fluid injections and solid force loadings. These solutions are numerically calculated and analyzed for unconsolidated sands as a function of water saturation as representative examples. Our results reveal and validate four wave modes, a fast compressional wave (P1), two slow compressional waves (P2 and P3), and a shear wave. The P1 wave and shear wave can be effectively observed. The slow waves with diffusive characters bear low amplitudes and low velocities. The traveling waves in the pore fluid pressures and solid displacement are sensitive to the different sources and the water saturation. The solid force induces the total stress perturbation while the fluid mass sources directly make the volume strains in the fluid phases. This fluid-solid coupling difference causes the distinct traveling wave signature contrasts in the pore-fluid and solid-frame response amplitudes and tendencies with water retention. For the variation of water saturation, the traveling wave shows a nonmonotonic feature. The fluctuation of capillary pressure exhibits a concave upward relationship, which can further interpret the changes of wave amplitude with water saturation. A solid force may enhance the fluctuation. However, for high water saturation, the interactive fluid-solid effect by the solid force may break the fluid contact due to the extremely compressible air.