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.

doi:10.16186/j.cnki.1673-9787.2024070082

Received:2024/07/24

Revised:2024/10/20

Published: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