Semi‐analytical solution for the stability of deep vertical shaft considering time‐dependent rock‐structure interaction

This study focuses on the stability of deep vertical shafts in underground construction, addressing critical concerns in mining and geotechnical engineering. A semi‐analytical approach is proposed to capture the time‐dependent ground response during shaft excavation in an elasto‐visco‐brittle‐plastic medium. This solution accounts for variations in internal cavity pressure and the time elapsed since excavation, providing a more accurate representation of rock‐structure interactions. Parametric studies based on a typical deep vertical shaft in western China reveal several key insights. An increase in the viscosity of surrounding rock leads to decreased total rock displacement upon stabilization. The ultimate interaction pressure increases nonlinearly with factors including the strength grade and thickness of the supporting shaft wall structure. Deeper embedment depths lead to slower convergence of ground characteristic response curves, increased cavity displacements, and higher interaction pressures. Additionally, a versatile multilayer composite model for shaft wall structures is introduced, considering heterogeneity and nonlinearity of shaft materials for more accurate simulations. The predictive capability of the proposed method is validated through a case study in Hulusu Coal Mine, demonstrating its potential for real‐world applications. This study enhances our understanding of the time‐dependent mechanisms governing deep vertical shafts and provides significant insights for the safety and efficiency of underground construction endeavors.