Abstract The two-dimensional discontinuous deformation analysis (DDA), as a discrete numerical method, has been successfully used to simulate many rock mechanics and rock engineering problems. However, for the development of the three-dimensional DDA (3D-DDA), the contact detection between polyhedral blocks has long been one of the key difficulties awaited to be solved. A universal Contact Theory was proposed by Shi in 2015, in which the complicated contact relationship of two any-shaped blocks is represented by a simple relationship between a reference point and an entrance block, along with a concept of the contact cover. In the present study, a robust contact detection algorithm in the 3D-DDA for convex polyhedral blocks based on the Contact Theory is proposed. In this algorithm, all the six basic contact types of polyhedral blocks are functionally treated as two contact types, namely, the vertex-to-face contact and the non-parallel edge-to-edge contact; meanwhile, the vertex-to-vertex and vertex-to-edge contacts are specially handled to guarantee the effectiveness and efficiency of the algorithm. Two special contact cases with the parallel edge-to-edge contact and the vertex-to-vertex contact, respectively, and two multi-block cases, in which various contact types and the transition between them are involved, are simulated to verify the effectiveness and robustness of the proposed contact detection algorithm. Moreover, failure simulations of sliding and toppling slopes with massive rock blocks are conducted and in the sliding case the effect of a retaining wall is also simulated. Results indicate that, the proposed algorithm can handle the contact detections of convex polyhedral blocks effectively under critical and complex conditions, which builds a good precondition for the successful development and practical application of the 3D-DDA method.

中文翻译：

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三维不连续变形分析中基于接触理论的鲁棒接触检测算法

摘要 二维不连续变形分析(DDA)作为一种离散数值方法，已成功地用于模拟许多岩石力学和岩石工程问题。然而，对于三维DDA（3D-DDA）的发展，多面体块之间的接触检测一直是等待解决的关键难点之一。施于2015年提出了一种通用接触理论，将两个任意形状块的复杂接触关系用参考点和入口块之间的简单关系来表示，并提出了接触盖的概念。在本研究中，提出了一种基于接触理论的凸多面体块的 3D-DDA 中的鲁棒接触检测算法。在这个算法中，多面体块的所有六种基本接触类型在功能上都被视为两种接触类型，即顶点对面接触和非平行边对边接触；同时，对顶点到顶点和顶点到边缘的接触进行了特殊处理，以保证算法的有效性和效率。分别模拟平行边到边接触和顶点到顶点接触的两种特殊接触情况，以及涉及各种接触类型及其之间的过渡的两种多块情况，以验证有效性和所提出的接触检测算法的鲁棒性。此外，还进行了具有大量岩块的滑动和倾倒边坡的破坏模拟，并且在滑动情况下还模拟了挡土墙的影响。结果表明，