Characterization of wave propagation in unsaturated thermo-viscoelastic porous media

Based on the wave theory of unsaturated porous elastic media, a wave equation for unsaturated porous thermo-viscoelastic media is established by considering the viscosity of the soil skeleton and thermal effects, and utilizing the Kelvin-Voigt viscoelastic model, the equations of motion for unsaturated porous viscoelastic media, and the generalized thermoelasticity theory. By introducing displacement potential functions for each constituent phase, the dispersion characteristic equations for body waves in unsaturated porous thermo-viscoelastic media are derived. Numerical calculations are performed to analyze the influence of thermophysical parameters, such as relaxation time, thermal conductivity, medium temperature, specific heat capacity of the solid phase, and saturation, on the wave velocity and attenuation coefficient of thermo-viscoelastic waves. The results show that for every 0.5×10-3 s increase in relaxation time, the velocities and attenuation coefficients of the P1 wave increase by up to 2.93% and 44.51%, respectively; those of the S wave increase by up to 17.49% and 51.32%, respectively; while the velocity and attenuation coefficient of the T wave decrease by up to 25.4% and 20.3%, respectively. The thermal conductivity coefficient only affects the T-wave velocity and attenuation coefficient. For every 1 J/(m·s·K) increase in thermal conductivity, the T-wave velocity increases by 21.62% and its attenuation coefficient decreases by 6.83%. For every 20 K increase in medium temperature, the P1-wave velocity increases by approximately 0.3% and its attenuation coefficient decreases by approximately 0.2%. An increase in the specific heat of the solid phase causes the wave velocities of both the P1-wave and the T-wave to gradually increase. Saturation has a significant effect on the wave velocities of P1, P3, and S waves. When the saturation decreases from 0.99 to 0.4, the wave velocities of the P1 and S waves increase by up to 15.6% and 6.5%, respectively, and the wave velocity of the P3 wave increases by up to 4.4 times.