Transparent Python Framework for <img src=image/14843115_01.gif> Reduction Slope Stability Analysis: Implementation and Validation

This study presents a comprehensive implementation of the <img src=image/14843115_02.gif> reduction method coupled with the Finite Element Method for slope stability analysis, using a transparent Python-based framework. While traditional Limit Equilibrium Methods cannot capture actual deformation distributions or progressive failure mechanisms, this work addresses the gap in available transparent numerical tools. The theoretical foundation encompasses rigorous mathematical formulation using <img src=image/14843115_03.gif> triangular elements with Delaunay triangulation and Lax–Milgram convergence analysis. A benchmark slope with 40◦ inclination achieves convergence to a critical factor of safety <img src=image/14843115_04.gif> within 15 iterations using an improved Newton–Raphson algorithm. Validation against Plaxis software shows excellent agreement with displacement patterns differing by less than 5% and identical failure surface locations. Key contributions include the first fully documented <img src=image/14843115_02.gif> reduction FEM implementation in Python, automated mesh generation achieving element quality > 0.8, computational efficiency with analysis completion under 2 minutes, and professional-grade accuracy at zero licensing cost. The framework successfully validated an example of slope configurations, demonstrating versatility and robustness. This establishes a valuable educational platform promoting reproducibility in computational geomechanics while achieving commercial software accuracy. Future extensions include three-dimensional analysis with applications in landslide risk assessment and geotechnical education.