In urban regions with karst developments, grouting is commonly utilized to fill cavities. However, the extent and control standards of grouting reinforcement are primarily determined through experience and field testing, which poses challenges in ensuring its effectiveness. Based on the instability mechanism of surrounding rocks in underwater karst shield tunnels, this study develops a mechanical model for analyzing the grouting reinforcement extent of such tunnels using strength theory. The reinforcement range for karst formations at various tunnel locations is clarified, and corresponding grouting reinforcement control standards are proposed based on cusp catastrophe theory. The findings indicate the following: the primary cause of surrounding rock instability in underwater karst shield tunnels is that the reduction in surrounding rock thickness during shield tunneling modifies the original constraints and boundary conditions and disrupts the initial equilibrium state. These changes influence the water content of the surrounding rocks and disturb the surrounding rock and soil mass, leading to surrounding rock instability. When grouting causes damage to the surrounding rocks between the karst and tunnel, the system is simplified into cantilever beam and plate models for analysis. It is determined that the grouting reinforcement extent is primarily influenced by factors such as karst size, properties of the karst filling material, and tunnel span. The total potential energy of the rock mass between the karst and tunnel is calculated, leading to the development of an instability and catastrophe model for the surrounding rocks. The proposed grouting reinforcement control standards are mainly dependent on factors such as the distance of the karst, characteristics of the reinforced surrounding rocks, shield machine support force, material properties post-reinforcement, and karst size.

Backfill is often employed in mining operations for ground support, with its positive impact on ground stability acknowledged in many underground mines. However, existing studies have predominantly focused only on the stress development within the backfill material, leaving the influence of stope backfilling on stress distribution in surrounding rock mass and ground stability largely unexplored. Therefore, this paper presents numerical models in FLAC3D to investigate, for the first time, the timedependent stress redistribution around a vertical backfilled stope and its implications on ground stability, considering the creep of surrounding rock mass. Using the Soft Soil constitutive model, the compressibility of backfill under large pressure was captured. It is found that the creep deformation of rock mass exercises compression on backfill and results in a less void ratio and increased modulus for fill material. The compacted backfill conversely influenced the stress distribution and ground stability of rock mass which was a combined effect of wall creep and compressibility of backfill. With the increase of time or/and creep deformation, the minimum principal stress in the rocks surrounding the backfilled stope increased towards the pre-mining stress state, while the deviatoric stress reduces leading to an increased factor of safety and improved ground stability. This improvement effect of backfill on ground stability increased with the increase of mine depth and stope height, while it is also more pronounced for the narrow stope, the backfill with a smaller compression index, and the soft rocks with a smaller viscosity coefficient. Furthermore, the results emphasize the importance of minimizing empty time and backfilling extracted stope as soon as possible for ground control. Reduction of filling gap height enhances the local stability around the roof of stope. (c) 2025 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/ 4.0/).