Catastrophe warning model in flawed sandstone based on improved cusp mutation theory

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 <italic>b</italic>-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 <italic>b</italic>-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 <italic>b</italic>-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)<italic>σ</italic>_p, the precursory response coefficient is between 5.55% and 10.20%, and the precursory response stress ratio ranges from 93.62% to 97.75%.