Derivation and validation of the motion equation for seepage in unsaturated soils

Starting from the balance differential equation of pore water in unsaturated soils, this study transcends the traditional empirical model framework predicated on Darcy’s law. The equation of motion for unsaturated soil seepage was derived through rigorous mathematical derivation of the pore water balance differential equation. By introducing the condition that flow resistance is proportional to velocity during laminar seepage, a theoretical formula for permeability coefficient was established, revealing the physical essence of soil-water interaction mechanisms in seepage dynamics. To validate the theoretical model, an improved apparatus for simultaneous measurement of soil-water characteristic curve (SWCC) and permeability coefficient was employed. Multi-step seepage tests were conducted on various soil types, with transient seepage velocity and moisture content parameters obtained synchronously. Experimental results demonstrate that the calculated seepage velocities from the theoretical formula show excellent agreement with measured data across the effective saturation variation range, preliminarily verifying the applicability of the derived equation of motion for unsaturated soil seepage.