Stability Evaluation of Rock Slope–Anchoring Systems Based on Catastrophe Theory

With the rapid development of China’s economy, the number and scale of infrastructure projects in energy, water conservancy, and transportation have expanded significantly. Anchoring technology has been widely applied, resulting in the formation of numerous rock slope–anchoring systems. This study proposes a novel method for evaluating the stability of rock slope–anchoring systems by introducing catastrophe theory into the stability assessment framework. Based on the characteristics of the rock slope–anchoring system and its stability-influencing factors, a hierarchical analytic structure for catastrophe-level evaluation is constructed, and relevant indicator data are collected. Catastrophe models are selected according to the identified state and control variables, and catastrophe levels are computed to establish a sample dataset. The relationship between catastrophe levels and the stability coefficients of rock slope–anchoring systems is verified to define stability grade intervals. Stability evaluation is then performed by calculating the catastrophe level of each system. The results indicate that: (1) the proposed method effectively considers the influence of multiple factors on the stability of rock slope–anchoring systems, ensuring high accuracy in the evaluation. (2) The method allows for the automatic quantification of the relative importance of indicators within the same hierarchy, reducing subjectivity caused by manual weighting. (3) By standardizing state variables and computing catastrophe levels, the method couples qualitative descriptions with mechanical parameters, enhancing the objectivity of the assessment. (4) The stability evaluation method for rock slope–anchorage systems based on mathematical catastrophe theory determines system stability through catastrophe-order analysis, featuring a concise process and clear results. It enables rapid evaluation of the stability of similar rock slope–anchorage systems and offers high efficiency for cluster assessments.