A Total Displacement Catastrophe Criterion for Assessing Open‐Pit Slope Stability Under Rainfall Conditions

Abstract

The aim of the present study is to address the challenge of accurately assessing the stability of open‐pit mine slopes under rainfall infiltration. This study innovatively combines total displacement theory with the cusp catastrophe model. A slope instability criterion based on total displacement mutation is proposed. The MATLAB platform was used for model validation and comparative analysis. Firstly, a quartic polynomial model was developed to characterize the relationship between the total displacement and the reduction coefficient based on the strength reduction method and total displacement theory. The equilibrium and discriminant equations for the cusp catastrophe model were then derived. Secondly, a typical mine slope in Guizhou Province, China, was selected as a case study to assess the applicability and accuracy of three instability criteria: the plastic zone penetration criterion, the key point displacement catastrophe criterion, and the total displacement catastrophe criterion (TDCC). The results indicate that the slope safety factor calculated by the TDCC is 1.201. This criterion is objective and independent of the monitoring point location, significantly reducing human errors. The criterion's accuracy was further verified by varying the cohesion and the internal friction angle. The results obtained from the TDCC were stable and central, aligning with the variation trends of the other two criteria, thereby confirming its reliability and accuracy. This work provides a quantitative, operational method for identifying instability in slope rainfall‐infiltration stability analysis. It is of theoretical and engineering guidance significance for the prevention and control of slope disasters in open‐pit mines.