• An improved 3D model accurately calculates backfill vertical stress at varying mine depths and positions along stope length, with error rates below 4% versus numerical simulation.
• Maximum vertical stress σzz,max is positively correlated with rock-backfill closure; it increases with mine depth and backfill elastic modulus, but decreases with stope width, stope inclination, backfill friction angle, and rock mass elastic modulus.
• σzz,max peaks at a stope length of 150 m and remains insensitive to rock-backfill interface parameters.
• Reducing σzz,max improves backfill stability, providing direct guidance for backfill strength design and safe deep-mining pillar recovery.