Risk assessment of karst collapse using an integrated fuzzy analytic hierarchy process and grey relational analysis model

A karst collapse, as a natural hazard, is totally different to a normal collapse. In recent years, karst collapses have caused substantial economic losses and even threatened human safety. A risk assessment model for karst collapse was developed based on the fuzzy analytic hierarchy process (FAHP) and grey relational analysis (GRA), which is a simple and effective mathematical algorithm. An evaluation index played an important role in the process of completing the risk assessment model. In this study, the proposed model was applied to Jiaobai village in southwest China. First, the main controlling factors were summarized as an evaluation index of the model based on an investigation and statistical analysis of the natural formation law of karst collapse. Second, the FAHP was used to determine the relative weights and GRA was used to calculate the grey relational coefficient among the indices. Finally, the relational sequence of evaluation objects was established by calculating the grey weighted relational degree. According to the maximum relational rule, the greater the relational degree the better the relational degree with the hierarchy set. The results showed that the model accurately simulated the field condition. It is also demonstrated the contribution of various control factors to the process of karst collapse and the degree of collapse in the study area.