<p>The failure of rock material is an instability process caused by progressive accumulation of internal damage. The damage state and evolution pattern of rocks are crucial for early warning of its failure time. Red sandstone was selected as the study object, this study quantitatively revealed its damage acceleration behavior and the key transitional points of the evolution stages under uniaxial compression. By integrating acoustic emission (AE) signals to construct damage variables, a method for predicting and early warning of rocks failure time was established. The results demonstrated that during the critical instability stage, red sandstone exhibited a clear damage acceleration phenomenon, which accompanied by the rapid initiation and propagation of tensile cracks. The key threshold points of the damage response could be determined based on the stress state and damage variables of the specimens. At the first key damage point B, the damage variable defined by AE ringing counts was approximately 0.28 for specimen a, and 0.31 for specimen b. The damage threshold at this first critical point reached about 30% of the peak damage variable. Subsequently, the point C corresponded to the damage acceleration point, which served as a critical node distinguishing different stages of damage evolution. After this point, its damage growth began to accelerate, and the damage response intensified noticeably. This study further proposed a quantitative method for identifying the damage acceleration point. The method demonstrated good robustness when the parameter <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> <EquationSource Format="TEX">$\alpha $</EquationSource> </InlineEquation> ranged from 2 to 4. The coefficient of variation for the stress level corresponding to the acceleration point was less than 8%. Moreover, it exhibited highly consistent relative stress levels across different specimens, validating its effectiveness as a universal precursor to failure. A stress-damage evolution model based on the Boltzmann function was developed. It accurately described the entire damage process of red sandstone. The coefficient of determination R<sup>2</sup> for the fitted pre-peak stress curve reached 99%. Based on the damage acceleration onset point and the critical point, the initial and critical damage warning thresholds for rocks failure were established. Then, the linear regression was performed on the data between the damage acceleration point and the failure point. It enabled high-precision prediction of the failure time of rocks. For the tested specimens, the prediction errors for the damage acceleration response time were 1.24% and 2.83%, respectively, and both errors fell within 3%. This meets the accuracy requirements for damage identification and instability warning in engineering rock masses. This study established an integrated analytical method for rock failure behaviors, and it combined the damage evolution modeling, the damage acceleration threshold identification, and the instability time prediction. It provided a theoretical basis for the time-dependent warning of rockburst disasters. It also offered methodological support for the stability assessment of deep engineering rock masses.</p>

Time-to-failure prediction and early warning method for red sandstone failure-instability based on damage acceleration behavior and acoustic emission technique

期刊论文
发表日期：

2026年5月11日

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Ansen Gao,
Xinyuan Jing,
Chengzhi Qi,
Kuan Jiang,
Jinglong Li,
Chunlai Wang,
Genshui Wu,
Zhen Wei

摘要

The failure of rock material is an instability process caused by progressive accumulation of internal damage. The damage state and evolution pattern of rocks are crucial for early warning of its failure time. Red sandstone was selected as the study object, this study quantitatively revealed its damage acceleration behavior and the key transitional points of the evolution stages under uniaxial compression. By integrating acoustic emission (AE) signals to construct damage variables, a method for predicting and early warning of rocks failure time was established. The results demonstrated that during the critical instability stage, red sandstone exhibited a clear damage acceleration phenomenon, which accompanied by the rapid initiation and propagation of tensile cracks. The key threshold points of the damage response could be determined based on the stress state and damage variables of the specimens. At the first key damage point B, the damage variable defined by AE ringing counts was approximately 0.28 for specimen a, and 0.31 for specimen b. The damage threshold at this first critical point reached about 30% of the peak damage variable. Subsequently, the point C corresponded to the damage acceleration point, which served as a critical node distinguishing different stages of damage evolution. After this point, its damage growth began to accelerate, and the damage response intensified noticeably. This study further proposed a quantitative method for identifying the damage acceleration point. The method demonstrated good robustness when the parameter $α$ $\alpha $ ranged from 2 to 4. The coefficient of variation for the stress level corresponding to the acceleration point was less than 8%. Moreover, it exhibited highly consistent relative stress levels across different specimens, validating its effectiveness as a universal precursor to failure. A stress-damage evolution model based on the Boltzmann function was developed. It accurately described the entire damage process of red sandstone. The coefficient of determination R² for the fitted pre-peak stress curve reached 99%. Based on the damage acceleration onset point and the critical point, the initial and critical damage warning thresholds for rocks failure were established. Then, the linear regression was performed on the data between the damage acceleration point and the failure point. It enabled high-precision prediction of the failure time of rocks. For the tested specimens, the prediction errors for the damage acceleration response time were 1.24% and 2.83%, respectively, and both errors fell within 3%. This meets the accuracy requirements for damage identification and instability warning in engineering rock masses. This study established an integrated analytical method for rock failure behaviors, and it combined the damage evolution modeling, the damage acceleration threshold identification, and the instability time prediction. It provided a theoretical basis for the time-dependent warning of rockburst disasters. It also offered methodological support for the stability assessment of deep engineering rock masses.