A simple and efficient three-dimensional spring element model for pore seepage problems

Abstract

This study introduces a novel spring element model for efficient simulation of nonlinear seepage in porous media. The model discretizes the simulation domain into tetrahedral elements and constructs orthogonal Three-dimensional permeability networks within each element, establishing a quantitative relationship between pipe flow and nodal pressure differences. By developing a mathematical model linking network flow to nodal pressure differences, the method enables precise allocation of pipe flow in the local coordinate system and accurate transformation to the global coordinate system, thereby determining nodal flow and velocity. The Three-Dimensional Seepage Spring Element Method (3D-SSEM) simplifies the element flow matrix in finite element analysis to three essential pipe permeability stiffness values, thereby reducing computational complexity. Coupled with parallel computing strategies, the algorithm achieves significant improvements in computational efficiency and memory usage. The method is validated through four numerical examples, demonstrating high efficiency and accuracy in solving saturated-unsaturated seepage problems. Compared with analytical solutions and other numerical methods, it exhibits superior convergence and reduced solution time while maintaining precision. Additionally, the method effectively simulates complex coupled processes in large-scale real-world environments, offering robust support for practical engineering design optimization.