A split three-characteristics method was proposed that can be used to analyze the stress wave propagation through a rock mass with double-scale discontinuities (micro-defect (MD) and macro-joint (MJ)). The mechanisms of the effects of MDs and MJs on stress wave propagation were investigated. The characteristic lines were divided into the three basic elements of triangle, diamond and separated diamond elements to calculate the stress, strain and velocity of the stress wave propagation through a rock mass with double-scale discontinuities (MD-MJ). The results show that the effects of MJ on stress wave propagation are related to the macro-joint stiffness, while the effects of MDs on stress wave propagation are related to the viscous coefficient and propagation distance. The comparison of the stress wave propagation through MJs and MD-MJs shows that the traditional MJ model can be regarded as a special case of the present MD-MJ model and the effects of MDs can be neglected when the propagation distance is sufficiently short. However, when the propagation distance is long, the effects of MDs must be considered. The results also show that the present characteristics method can be used to investigate the stress wave propagation through double-scale discontinuities efficiently.

中文翻译：

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双尺度不连续岩体应力波传播的分裂三特征法

提出了一种分裂三特征方法，可用于分析应力波在具有双尺度不连续性（微缺陷（MD）和宏观节理（MJ））的岩体中的传播。研究了 MDs 和 MJs 对应力波传播的影响机制。将特征线分为三角形、菱形和分离菱形三个基本元素，计算应力波在具有双尺度不连续性(MD-MJ)岩体中传播的应力、应变和速度。结果表明，MJ对应力波传播的影响与宏观关节刚度有关，而MD对应力波传播的影响与粘性系数和传播距离有关。应力波通过 MJ 和 MD-MJ 传播的比较表明，传统的 MJ 模型可以看作是当前 MD-MJ 模型的一个特例，当传播距离足够短时，可以忽略 MD 的影响。但是，当传播距离较长时，必须考虑 MD 的影响。结果还表明，本特征方法可以有效地研究应力波通过双尺度不连续性的传播。