The accuracy of the threshold is very important for early warning of slopes. However, the existing slope failure threshold criteria are insufficiently accurate and have limited applicability. This paper proposes three dimensionless parameters based on slope deformation displacement, velocity, and acceleration and statistically analyzes 80 slope deformation monitoring examples. The second-order dimensionless failure threshold is obtained using probability and statistics theory. The dimensionless threshold is applied in the early warning analysis of landslide #2 in Jiangxi Province's copper mine. The results show that: (1) the "two-sample heteroscedasticity t-test" method shows that the dimensionless parameters in the failure case are significantly greater than the dimensionless parameters in the non-failure case. (2) A dimensionless threshold can eliminate the influence of vector parameters, which are physical in nature. (3) The "ROC curve" approach is used to validate the reliability and accuracy of the dimensionless threshold model, and it is theoretically explained that the prediction accuracy of the dimensionless threshold of acceleration is relatively the highest. (4) In this situation, the corresponding warning time of the three dimensionless thresholds is not the same, with the secondary dimensionless threshold of acceleration having the earliest time.
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