An Unsteady Seepage Calculation Method Based on an Improved Voronoi Pipe-Domain Mesh and ADE Finite Difference Scheme

Cracking of water diversion channel linings can induce localized unsteady seepage, and the resulting soil deformation process may seriously affect engineering safety. This paper proposes an unsteady seepage calculation method based on a Voronoi pipe-domain mesh and an ADE finite difference scheme. To address the limitation of the conventional pipe-domain method, in which boundary particles cannot be completely enclosed by the fluid computational domain, a Voronoi flow network construction method based on the relationships among adjacent particles is adopted to establish an irregular seepage spatial discretization model, providing a spatial basis for particle-scale seepage calculations. On this basis, to overcome the difficulty of directly applying the finite difference method to Voronoi irregular meshes, a local regular virtual grid is constructed, and a permeability coefficient-weighted interpolation method is employed to reconstruct pore-water pressures at virtual nodes, thereby establishing an unsteady seepage difference calculation method applicable to irregular meshes. Furthermore, an analytical hydraulic head field is used to evaluate the interpolation accuracy of virtual nodes, and the variation and convergence characteristics of interpolation errors under different mesh resolutions are analyzed. The stability condition of the difference scheme is derived based on Fourier analysis, and the relationships among the time step, spatial step, and permeability coefficient are clarified. The one-dimensional seepage validation in homogeneous soil demonstrates that the proposed method can reasonably describe the evolution of pore-water pressure, and the pore-water pressure exhibits an approximately linear relationship with the hydraulic gradient. Parameter analysis indicates that the time step, spatial step, and permeability coefficient jointly influence computational accuracy, stability, and efficiency. The two-dimensional simulation of seepage through a cracked water diversion channel shows that crack-induced localized seepage concentration causes rapid adjustment of pore-water pressure near cracks and corresponds well with regions of high particle velocity, revealing the controlling mechanism of localized seepage on particle migration and soil deformation development. The proposed method provides an effective numerical tool for analyzing unsteady seepage and seepage-induced deformation processes in channels under complex crack conditions.