<p>Determining the optimal filling height for multi-mid-section goafs is essential for sustainable mine development and safe operations. The present study investigates the optimal filling height using the central mining area of the Daxin Manganese Mine in Guangxi as a case study. It examines the morphological characteristics of the goaf post-filling, explores the instability and failure mechanisms of the roof beneath the filling body, and establishes a mechanical model for roof stability. Through numerical simulations of goaf behaviour at different filling heights and the application of cusp catastrophe theory, the study derives the necessary and sufficient conditions for roof failure beneath the filling body, validating the reliability of the simulation results. Key findings include: (1) As the filling height increases, the roof’s controlling factor shifts from the extrusion effect of the intervening pillar to the gravitational influence of the filling body. (2) Tensile stress distribution initially decreases and then increases, with roof stability gradually deteriorating once the filling height exceeds a critical threshold. (3) Stress concentration decreases significantly in the upper goaf but increases gradually in the lower goaf. (4) The maximum vertical displacement of the roof plate shows a continuous upward trend. Considering both economic and safety factors, a filling height of 21&#xa0;m is identified as optimal for the study area. The application of cusp catastrophe theory confirms that the numerical simulation results meet safety production requirements. These findings provide valuable insights for determining optimal filling heights in similar mining scenarios.</p>