Abstract In rock excavating and mining, blasting a row of circular holes is a common practice. It is often observed that cracks emanating from two adjacent holes tend to avoid each other when closely approached and form a hooked or butterfly-shaped loops. Five crack models were designed in this paper to study the propensity of forming the hook pattern. The five models are to simulate geometric imperfection in the field or laboratory for the two borehole case. Using the T-stress at the crack tip, the incremental crack growth method is adopted to simulate the crack propagation paths. The results showed that: (1) the T-stress values calculated from the first two models are negative, indicating curving (or hooking) cannot occur, (2) the T-stress at the crack tip is positive in the third model, and therefore crack curving (or hooking) may occur, (3) unlike the first three models, the fourth and fifth models are mixed mode I/II crack geometries and the mode II stress intensity factor dictates the crack curving direction, (4) the hook pattern would indeed happen under certain conditions.

中文翻译：

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爆破载荷作用下两个圆孔裂纹扩展的断裂路径

摘要 在岩石开挖和采矿中，爆破一排圆孔是一种常见的做法。经常观察到，从两个相邻孔发出的裂缝在靠近时往往会相互避开并形成钩状或蝴蝶形环。本文设计了五种裂纹模型来研究形成钩纹的倾向。这五个模型用于模拟现场或实验室中两个钻孔情况下的几何缺陷。利用裂纹尖端的T应力，采用增量裂纹扩展法模拟裂纹扩展路径。结果表明：（1）前两个模型计算的 T 应力值为负，表明不会发生弯曲（或钩状），（2）第三个模型中裂纹尖端的 ​​T 应力为正值，并且因此可能会出现裂纹弯曲（或钩住），