Analytical solution and experimental validation for roof deformation of pier-column-type partial backfilling under variable-stiffness support via initial parameter method

To investigate roof deformation and overburden failure, this study combines theoretical modeling with physical simulation to compare full and partial backfilling. Results show that, based on elastic foundation beam theory and the initial parameter method, roof subsidence increases and then stabilizes, reaching 0.52 m for partial backfilling and 0.38 m for full backfilling. In the simulation, full backfilling results in one overburden fracture and minor roof caving with a maximum displacement of 3 mm, indicating good integrity. In contrast, partial backfilling leads to multiple fracture and caving events, with a maximum roof displacement of 5.5 mm. Delayed filling may induce localized roof collapse and more developed fractures; however, the backfill body effectively restricts overburden rotation and prevents overall cutting failure. Overall, partial backfilling presents favorable surrounding rock control performance, with advantages in backfilling cost and mining efficiency, and possesses broad application prospects.