In-depth Consideration of the Application of Whole-Space Stereographic Projection in Block Stability Analysis

This paper presents a systematic investigation of whole-space stereographic projection applications in block theory through representative case studies. Despite its proven utility in engineering rock stability analysis, comprehensive studies on this method within block theory remain scarce. Through representative case studies, this study systematically investigates the method's application in block stability analysis, elucidating its fundamental principles, operational procedures, limitations, and implementation processes for block identification and stability assessment. Comparative case analyses demonstrate the method's unique advantages in enhancing analytical accuracy, optimizing engineering designs, and preventing geological hazards. The method proves particularly effective in scenarios involving multiple structural planes or complex block movements, underscoring its critical role in practical engineering applications. The investigation further reveals its superior capability in comprehensively characterizing rock mass stability compared to conventional approaches. The paper concludes by outlining future research directions and potential applications, offering valuable insights for advancing rock mechanics analysis and geohazard prevention technologies.