The crack initiation stress threshold (σci/σp) is an important parameter in the process of brittle failure of rocks, and it plays a significant role in assessing the macroscopic deformation and micro-fracture characteristics of rocks. In this study, the rock system during loading stage is equivalently modeled as a viscoelastic system undergoing light damping vibration, and the bifurcation characteristics of the vibration period are analyzed based on chaos theory. The stress corresponding to first bifurcation of the iterative growth factor of self-vibration period is chosen as the crack initiation stress (σci), and the analytical solution is σci=49σp+59ν(σ2+σ3). The existing experimental results were employed to validate the feasibility and efficacy of the proposed method. Additionally, the proposed method was compared with results obtained by energy-based method, strain-based methods and the Acoustic Emission (AE) method. Compared to energy-based method, the proposed method is more consistent with existing results. Compared to strain-based methods and the AE method, the proposed method is effective and rapid in determining the crack initiation stress σci, and it also reduces the subjectivity associated with parameter determination.

中文翻译：

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基于自振动周期混沌特性的岩石压缩初裂应力估算新方法

裂纹起裂应力阈值 （σci/σp） 是岩石脆性破坏过程中的重要参数，在评价岩石的宏观变形和微观断裂特性中起着重要作用。本研究将加载阶段的岩石系统等效建模为承受轻阻尼振动的粘弹性系统，并基于混沌理论分析了振动周期的分叉特征。选择自振周期迭代增长因子第一次分岔对应的应力作为裂纹起裂应力 （σci），解析解为 σci=49σp+59ν（σ2+σ3）。利用现有的实验结果验证了所提方法的可行性和有效性。此外，将所提出的方法与基于能量的方法、基于应变的方法和声发射 （AE） 方法获得的结果进行了比较。与基于能量的方法相比，所提方法与现有结果更加一致。与基于应变的方法和 AE 方法相比，所提出的方法在确定裂纹起裂应力 σci 方面有效且快速，并且还减少了与参数确定相关的主观性。