基于改进尖点突变理论的裂隙砂岩破裂预警模型研究

doi:10.3724/1000-6915.jrme.2025.0050

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摘要为探究裂隙岩石变形破坏过程中的关键前兆信息特征及损伤状态预警模型，对含不同几何构型的预制裂隙砂岩开展一系列单轴压缩试验，分析裂隙砂岩声发射参量及能量演化机制，建立基于多指标融合的尖点突变预警模型，从控制因子和判别函数响应特征角度对试样破坏突变过程进行分析。采用最大似然估计法（MLE）和Davidon-Fletcher-Powell（DFP）算法求解模型，并引入前兆响应系数和前兆响应应力比对比分析基于声发射能量方差、声发射b值、弹性能耗散比等单一指标模型和多指标融合模型的预警效果。结果表明：耗散能呈现出非线性缓慢上升→缓慢下降→骤然上升3个演变阶段；试样趋近失稳破坏前，声发射b值急剧减小，声发射参量方差突增，弹性能耗散比曲线由上升迅速转为下降，这些突变过程可作为岩石破坏的早期预警指标；对比基于声发射能量方差、声发射b值和弹性能耗散比的破裂前兆信息，其平均前兆响应系数分别为9.19%，8.26%和6.72%；另外，平均前兆响应应力比分别为92.54%，92.70%和95.84%；改进后的综合指标预警模型比单一指标模型的预警区间明显变小，并减少了误报和漏报的可能性；多指标融合预警模型具有良好的鲁棒性，预警区间位于（0.96～0.98）??，前兆响应系数在5.55%～10.20%范围，前兆响应应力比在93.62%～97.75%范围。

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	雷瑞德1
	2
	3
	周林森1
	顾清恒2
	郭伟耀4
	马庆5
	胡超1
	李怀宾2

关键词 ：岩石力学, 尖点突变理论, 声发射, 弹性能耗散比, 预警模型

Abstract：To investigate the key precursor information characteristics and damage state early warning model in the deformation and failure process of fractured rock, a series of uniaxial compression tests were carried out on prefabricated fractured sandstone samples with different geometric configurations. Also, the acoustic emission (AE) and energy mechanism of fractured sandstone were analyzed, and a catastrophe mutation early warning model based on multi-index fusion was established. The failure and mutation process of the sample were analyzed from the perspective of control factor and discriminant function response characteristics. The maximum likelihood estimation (MLE) and Davidon-Fletcher Powell (DFP) algorithm methods were adopted to solve the model. The precursor response coefficient and the precursor response stress ratio were introduced to comparatively analyze the early warning effect of the single-index model based on AE energy variance, AE b-value, elastic energy dissipation ratio, and the multi-index fusion model. The results show that the dissipative energy presents three stages: slow rise, slow decline and sudden rise. Before the sample approaches instability failure, the AE b-value decreases sharply, the AE parameter variance increases abruptly, and the elastic energy dissipation ratio curve changes rapidly from rising to falling. These sudden changes can be regarded as early warning indicators of rock failure. The average precursory response coefficients defined by AE energy variance, AE b-value and elastic energy consumption ratio are 9.19%, 8.26% and 6.72%, respectively. In addition, the corresponding average response stress ratios are 92.54%, 92.70% and 95.84%, respectively. The early warning range of the improved multi-index early warning model is smaller than that of the single index model, and the possibility of false alarms and missing alarms is reduced. The multi-index fusion warning model has good robustness. The early warning interval is within (0.96–0.98)??, the precursory response coefficient is between 5.55% and 10.20%, and the precursory response stress ratio ranges from 93.62% to 97.75%.

Key words： rock mechanics cusp mutation theory acoustic emission elastic energy dissipation ratio warning model

引用本文:

雷瑞德1，2，3，周林森1，顾清恒2，郭伟耀4，马庆5，胡超1，李怀宾2. 基于改进尖点突变理论的裂隙砂岩破裂预警模型研究[J]. 岩石力学与工程学报, 2025, 44(10): 2638-2653.
LEI Ruide1,2,3, ZHOU Linsen1, GU Qingheng2, GUO Weiyao4, MA Qing5, HU Chao1, LI Huaibin2. Catastrophe warning model in flawed sandstone based on improved cusp mutation theory. , 2025, 44(10): 2638-2653.

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https://rockmech.whrsm.ac.cn/CN/10.3724/1000-6915.jrme.2025.0050 或 https://rockmech.whrsm.ac.cn/CN/Y2025/V44/I10/2638

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