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.

中文翻译：

---

一种改进的矢量方法，用于块理论中可移动性和运动学的同时分析


块体理论是解决岩石工程中稳定性问题的重要常用方法，简化其分析程序，提高其计算效率具有重要意义。在本文中，提出了一种改进的矢量方法，能够同时分析块的可移动性和运动学，该方法对凸块和凹块都适用。这种改进的方法基于经过严格验证的定理。与块论中的原始向量方法相比，它更简单、更高效，因为它跳过了可移动性分析，简化了运动学分析中的一些判断条件。根据运动学分析的结果，改进的矢量方法还可以确定块的可移动性。通过分析一系列具有不同可移动性和失效模式的单个凸或凹块，验证了改进向量方法的有效性。最后，将改进的矢量方法应用于工程边坡的块体渐进破坏分析，再次验证了改进矢量方法的有效性。通过与现有方法的比较，突出了改进的矢量方法的优势，特别是其计算效率高、易于理解和实现。