In rock engineering, block theory is a fundamental theory that aims to analyze the finiteness, removability, and mechanical stability of convex blocks under different engineering conditions. In practice, the possible combinations of the fractures and joint sets that may generate key blocks can be identified by stereographic projection graphs of block theory. However, classic key block theory does not provide solutions for nonconvex blocks, which are very common in civil projects, such as those with underground edges, corners, and portals. To enhance the availability of block theory, a general algorithm that can analyze the removability and stability of blocks of arbitrary shapes is proposed in this paper. In the proposed algorithm, the joint pyramid for blocks of arbitrary shapes can be computed, and the faces of the blocks are grouped according to their normal vectors such that parallel or nonadjacent sliding faces with the same normal vector can be immediately identified when the sliding mode is determined. With this algorithm, blocks of arbitrary shapes can be analyzed, and users do not need to have experience interpreting graphs of block theory to take advantage of its accuracy and effectiveness. The proposed algorithm was verified by several benchmarking examples, and it was further applied to investigate the stability of the left bank rock slope of a dam. The results showed that the proposed algorithm is correct, effective, and feasible for use in the design and support of excavation in complex rock masses.

中文翻译：

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任意块形状的通用块稳定性分析算法

在岩石工程中，块体理论是一门基础理论，旨在分析不同工程条件下凸块的有限性、可移性和力学稳定性。在实践中，可以通过块体理论的立体投影图来识别可能产生关键块体的裂缝和节理组的可能组合。然而，经典的关键块体理论并没有为非凸块提供解决方案，非凸块在土木工程中非常常见，例如具有地下边缘、拐角和入口的那些。为了提高块理论的可用性，本文提出了一种可以分析任意形状块的可移除性和稳定性的通用算法。在提出的算法中，可以计算任意形状块的联合金字塔，并且块的面根据其法向量进行分组，使得具有相同法向量的平行或不相邻的滑动面在滑动模式确定时可以立即被识别。使用该算法，可以分析任意形状的块，用户无需具有解释块理论图的经验即可利用其准确性和有效性。所提算法通过若干基准实例验证，并进一步应用于大坝左岸岩质边坡稳定性研究。结果表明，该算法正确、有效、可行，可用于复杂岩体开挖的设计与支护。