Methodology for Determining the Optimal Support Control Distance Based on the Deformation Increment Rate of Surrounding Rock and Its Engineering Application

The stability of surrounding rock after tunnel excavation is the result of the combined interaction between the rock mass and the support structure. The timing of support installation significantly influences the self-stabilizing capacity of the surrounding rock and the safety of the structure. However, there has been a persistent lack of well-defined methods for determining the optimal timing of support installation. Building upon the theoretical framework of collaborative interaction between surrounding rock and support, this paper proposes a novel approach that identifies the critical point of rock stability based on the maximum deformation increment rate of the surrounding rock. By establishing the coordinated deformation relationship between the support and surrounding rock, the initial deformation of the rock can be determined, and subsequently, the optimal timing for support installation can be identified using the corresponding working face control distance. Leveraging the parameters of a tunnel in Xinjiang, this study employs the FLAC^3D numerical simulation software to ascertain the optimal timing of support installation under the given conditions. Through a comparative analysis, the rationality of the proposed method is validated. The research findings can offer practical methods and theoretical insights for similar engineering projects.