An improved vector method for simultaneous analysis of removability and kinematics in block theory

Block theory is an important and commonly used method for addressing stability problems in rock engineering, and it is very meaningful to simplify its analysis procedure and improve its computational efficiency. In this paper, an improved vector method capable of simultaneously analyzing block removability and kinematics that works well for both convex and concave blocks is proposed. This improved approach is based on rigorously proven theorems. Compared to the original vector method in block theory, it is simpler and more efficient because it skips the removability analysis and simplifies some of the judgment conditions in kinematic analysis. With the results of kinematic analysis, the improved vector method can also determine the removability of the block. The validity of the improved vector method is verified by analyzing a series of individual convex or concave blocks with different removability and failure modes. Finally, the improved vector method is applied to the block progressive failure analysis of an engineering slope, which again validates the effectiveness of the improved vector method. The advantages of the improved vector method are highlighted through a comparison with existing methods, especially its high computational efficiency, ease of understanding and implementation.