孙光华, 齐育珠, 刘志义,等.基于k-均值聚类的红砂岩循环加卸载下破坏前兆研究[J].河南理工大学学报（自然科学版）,2026,45(2):120-128.

SUN G H, QI Y Z, LIU Z Y ,et al. Study on failure precursors in red sandstone under cyclic loading and unloading based on k-means clustering[J].Journal of Henan Polytechnic University(Natural Science) ,2026,45(2):120-128.

基于k-均值聚类的红砂岩循环加卸载下破坏前兆研究

孙光华1,2,3, 齐育珠1,2, 刘志义1,2,3, 韩凯明1,2, 郭将1,2, 吴柄纬1,2

1.华北理工大学 矿业工程学院，河北 唐山  063210；2.华北理工大学 唐山市矿业开采与安全技术重点实验室，河北 唐山  063210；3.华北理工大学 河北省矿业开发与安全技术实验室，河北 唐山  063210

摘要: 目的 实际工程中岩石常处于循环加卸载状态，需要探究循环加卸载下红砂岩的破坏前兆问题。  方法 开展循环加卸载下红砂岩声发射力学监测试验，采用k-均值聚类算法，进行声发射特征参数聚类分析，研究岩石损伤破裂模式。  结果 结果表明：声发射事件主要发生在循环加载中，卸载阶段声发射事件极少并进入“间歇期”；随着循环次数积累，峰值应力逐步增高，声发射事件数量突增并进入“活跃期”；循环加卸载初期声发射b值最大，随着循环次数增加，声发射b值逐级降低并稳定在0.75~1.25，在岩石进入破裂阶段前声发射b值出现骤降，但每次循环加载开始前声发射b值也出现大幅骤降现象而岩石并未破裂，将声发射b值骤降作为岩石破坏前兆的判断依据存在局限性，需结合其他现象研究岩石破裂前兆；根据k-均值聚类将岩石损伤破裂过程的声发射信号分为3类即聚类1，聚类2和聚类3，每个聚类对应不同损伤阶段，循环加卸载末期，聚类3声发射事件能量陡然上升，反映出加载末期砂岩破裂尺度明显增大直至破坏，可以作为岩石的破坏前兆特征。  结论 聚类3声发射信号在岩石弹性变形阶段零星出现，随着循环积累，在岩石完全破坏阶段前聚类3声发射信号持续密集出现，将声发射b值和聚类信号结合分析可提升预测岩石损伤破裂的准确率。

关键词:循环加卸载;声发射;值分析;-均值聚类;岩石破坏前兆

doi:10.16186/j.cnki.1673-9787.2024070082

基金项目:国家自然科学基金资助项目（52204134）； 河北省自然科学基金资助项目（E2024209129）

收稿日期:2024/07/24

修回日期:2024/10/20

出版日期:2026/01/28

Study on failure precursors in red sandstone under cyclic loading and unloading based on k-means clustering

Sun Guanghua1,2,3, Qi Yuzhu1,2, Liu Zhiyi1,2,3, Han Kaiming1,2, Guo Jiang1,2, Wu Bingwei1,2

1.School of Mining Engineering， North China University of Science and Technology， Tangshan  063210， Hebei， China；2.School of Mining Engineering， Tangshan City Key Laboratory of Mining Development and Security Technology， Tangshan  063210， Hebei， China；3.School of Mining Engineering， Hebei Provincial Mining Development and Safety Technology Laboratory， Tangshan  063210， Hebei， China

Abstract: Objectives In engineering practice， rocks are often subjected to cyclic loading and unloading conditions， making it essential to investigate the failure precursors in red sandstone under such conditions.  Methods Mechanical monitoring tests with acoustic emission （AE） measurement were conducted on red sandstone under cyclic loading and unloading. The k-means clustering algorithm was employed to perform cluster analysis on AE characteristic parameters， aiming to investigate the rock damage and fracture patterns.  Results The results indicate that acoustic emission （AE） events occur predominantly during the cyclic loading phase， while very few events are recorded during the unloading phase， marking an “intermittent period”. As the number of cycles increases， the peak stress gradually rises， and the number of AE events surges abruptly， entering an “active period”. At the initial stage of cyclic loading and unloading， the AE b-value is the highest. As the number of cycles increases， the AE b-value gradually decreases and stabilizes within the range of 0.75~1.25. Before the rock enters the fracture stage， the AE b-value shows a sharp drop. However， a similar sharp decline in the AE b-value is also observed at the beginning of each loading cycle， even though the rock does not fracture. This suggests that using a sharp drop in the AE b-value as a precursor indicator for rock failure has limitations， and it is necessary to combine other phenomena to study rock fracture precursors. Based on k-means clustering， the AE signals during the rock damage and fracture process are classified into three categories： cluster 1， cluster 2， and cluster 3. Each cluster corresponds to different damage stages. In the late stage of cyclic loading and unloading， the energy of AE events in cluster 3 increases sharply， reflecting a significant enlargement of fracture scale in the sandstone during the final loading stage until failure. This can serve as a characteristic precursor to rock failure.  Conclusions Cluster 3 acoustic emission signals sporadically appear during the elastic deformation stage of the rock. As cycling accumulates， these signals become continuously and densely concentrated prior to the complete failure stage of the rock. Integrating the analysis of the AE b-value with the cluster-based signals can enhance the accuracy of predicting rock damage and fracture.

Key words: cyclic loading and unloading; acoustic emission; b-value analysis; k-means clustering; rock failure precursor