Relative Particle Motion–Based Discrete Element Method (RPM–DEM) for Analyzing Soil Arching Effects

During tunnel excavation, complex soil arch structures often form due to the redistribution of in situ stresses, and their evolution and stability significantly influence the deformation of surrounding rock and the risk of geological instability. Most existing studies are based on continuum mechanics or experimental methods, which struggle to capture particle‐scale discontinuities and microscopic failure mechanisms, and often overlook the influence of tunnel cross‐sectional geometry on the development and failure of soil arch structures. This study proposes a relative particle motion (RPM)–discrete element method (DEM) that integrates both interparticle sliding and rotation to reflect the discontinuous nature of granular media and complex boundary interactions. The method is implemented within the particle flow code (PFC) platform and applied to investigate the soil arching effect and stratum stability of three typical tunnel cross‐sections (Standard, QYB, and QYD) from the An–An segment of Beijing Metro Line 12 under varying burial depths. Simulation results reveal that tunnel geometry significantly affects soil arch morphology and failure characteristics. For the Standard and QYB sections, soil arching primarily localizes at the arch shoulders, where disturbance is most intense. In contrast, the QYD section exhibits arching extending from shoulder to sidewall, with the widest disturbance range. As the formation loss rate increases, ground settlement intensifies, with the QYD section inducing the greatest impact and the Standard section the least. This research advances the micromechanical understanding of tunnel‐induced soil arching and offers a robust numerical tool for optimizing tunnel cross‐section design and assessing stratum stability under complex geological conditions.