REFLECTION CHARACTERISTICS OF P-WAVE INCIDENT ON THE FREE SURFACE OF NONLOCAL THERMO-VISCOELASTIC SATURATED SOILS

To investigate the reflection of a plane incident P-wave at the free surface of a nonlocal thermo-viscoelastic saturated soil, this study formulates governing wave equations for a nonlocal thermo-viscoelastic saturated porous medium that simultaneously incorporate thermal effects, pore-scale effects (including pore-scale variations and dynamic pore pressure), and the viscoelastic behavior of the soil skeleton. On this basis, a computational framework is developed to evaluate the amplitude ratios and energy reflection coefficients of the reflected P₁-wave, reflected P₂-wave, reflected T-wave, and reflected S-wave. Numerical examples are then used to examine how relaxation time, thermal conductivity, medium temperature, and the nonlocal parameter influence the amplitude reflection coefficients and energy reflection coefficients, thereby further elucidating the mechanistic roles of nonlocality and thermos-viscoelastic coupling in shaping the propagation characteristics of reflected waves. The results indicate that reflection is most sensitive and dissipation is strongest within a moderate range of incident angles. The combined action of nonlocality and thermos-viscoelastic coupling weakens P₁-wave reflection and induces a shift in the extremum angle; moreover, nonlocality suppresses T-wave reflection. Under the nonlocal thermo-viscoelastic model, the S-wave reflection exhibits a “single-peak” pattern. Incorporating skeleton viscosity redistributes reflected-wave energy: the energy reflection coefficient of the P₁-wave decreases, whereas those of the P₂ and T waves increase, and the P₂-wave is more sensitive to the relaxation time. With respect to thermophysical parameters, the reflection coefficient of the P₁-wave increases with increasing thermal conductivity and medium temperature, while that of the P₂-wave decreases as temperature rises. The amplitude reflection coefficient of the T-wave is positively correlated with thermal conductivity; however, its energy reflection coefficient decreases with increasing thermal conductivity and temperature. The S-wave reflection coefficient decreases as temperature increases. The coupled effect of the nonlocal parameter and incident angle also exerts a pronounced regulatory influence on the reflection behavior of all reflected waves: the reflected P₁-wave follows a “U-shaped” trend and weakens overall as τ increases; increasing τ suppresses the amplitude reflection coefficient of the reflected P₂-wave but increases its energy reflection coefficient; the energy reflection coefficient of the reflected T-wave increases first and then decreases with τ; and the S-wave reflection coefficient decays monotonically with τ, with the peak angle remaining essentially unchanged.