The crack stress thresholds of rocks have remained a focus in rock mechanics and engineering. Herein, a novel observation method uses Hooke's law to evaluate crack stress thresholds based on transition points in the equivalent elastic modulus. Unlike previous studies, this method considers confining pressure as a variable and involves a differential method to handle the variation of discrete data. To test the method, we compare it with the volumetric strain method and another observation method with respect to the crack stress thresholds of sandstone and granite. The results are within the boundary values presented in the literatures. For the sandstone and granite samples, the proposed method performs better than the other two methods. In summary, the results indicate that the proposed method can be practically applied with that a promising performance. In the future, we will further improve the method by considering more types of rocks with various confining pressures.

中文翻译：

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基于胡克定律确定岩石裂缝应力阈值的新观测方法

岩石的裂纹应力阈值一直是岩石力学和工程学的重点。在本文中，一种新颖的观察方法使用胡克定律基于等效弹性模量中的过渡点来评估裂纹应力阈值。与以前的研究不同，此方法将围压视为变量，并涉及一种差分方法来处理离散数据的变化。为了测试该方法，我们将其与体积应变方法和另一种观察方法在砂岩和花岗岩的裂缝应力阈值方面进行了比较。结果在文献中给出的边界值之内。对于砂岩和花岗岩样品，该方法的性能优于其他两种方法。综上所述，结果表明，所提出的方法可以在实际应用中获得令人满意的性能。将来，我们将通过考虑更多具有各种围压的岩石类型来进一步改进该方法。