Mechanical Association between Pressure Wave Propagation Time and Constitutive Parameter Damage in Porous Media: Theoretical Derivation and Sensitivity Analysis

Hongxing Li

The propagation time of pressure waves in porous media carries critical information about the constitutive parameters of the medium. This study rigorously derives the mechanical relationship between the lag time of pressure wave and the hydraulic parameters of porous media based on the diffusion wave equation. The lag time is shown to be a direct functional of the hydraulic conductivity and specific yield, with sensitivity analysis demonstrating that internal erosion—through simultaneous increase of hydraulic conductivity and decrease of specific yield—causes an accelerated shortening of the lag time. Based on the Kozeny-Carman equation, connecting fine particle loss to changes in porosity and specific surface area, and subsequently to changes in hydraulic conductivity and lag time, A mechanical transfer function is established. Parametric sensitivity analysis on typical earth dam materials reveals shows that a five-percentage-point reduction in fine content can increase hydraulic conductivity by fifty to four hundred percent, and reduce the lag time by fifteen to fifty percent. To remove the interference of geometric boundary effects caused by reservoir water level fluctuations, a medium baseline function method is proposed. By constructing a geometric effect response function using lag time versus reservoir water level data from a stable baseline period, enabling the rigorous separation of the net medium effect from geometric effects. The theoretical framework built in this study, provides a mechanical foundation for characterizing constitutive parameter damage in porous media through pressure wave propagation time, and puts forward five quantitative predictions for subsequent experimental verification.