Stability evaluation of karst roof of pile foundation based on variable weight fuzzy comprehensive theory

Regarding the lower accuracy of the Analytic Hierarchy Process (AHP) in assessing the stability of karst cave roof under pile foundations, an improved structural model of evaluation indicators based on variable weight theory was developed to establish an effective mathematical assessment method for stability determination. Focusing on the parking lot of Shenzhen Rail Transit Line 3 within a karst development area, the main factors influencing the stability of the karst cave roof under pile foundations were identified utilizing Fault Tree Analysis theory. The structural model of stability assessment indicators was delineated through theoretical analysis. Subsequently, based on Fuzzy Mathematics, a comprehensive evaluation method of stability integrated the AHP and the assessment method under variable weights was conducted to contrast the outcomes with stability assessment results under constant weights. Results indicate: (1) Factors obtained from Fault Tree Analysis theory can be used to evaluate stability systematically, identify potential event pathways, and mitigate incomplete evaluation factors. (2) The comprehensive evaluation method introduced variable weight fuzzy, employing a “penalty” mechanism for weight variation to determine the need for weight variation in assessment factors, achieves accurate on-site assessments through amplifying their influences. (3) The stability grade within the study area under the variable weight model was “unstable”, contrasting the evaluation of “relatively unstable” under the constant weight model, demonstrating that the variable weight fuzzy comprehensive evaluation model aligns more closely with on-site survey results. This study underscores that the variable weight theory-based assessment method for karst cave roof stability under pile foundations reflects the overall stability level within the research area, offering crucial insights for preliminary stability assessment in similar karst engineering endeavors.