Stability evaluation of karst cave roof under pile in karst areas based on the interval non-probabilistic reliability method

The uncertainty and finiteness of the factors affecting the stability of karst cave roof under pile in karst areas bring about some difficulties to the evaluation of the stability of karst cave roof under pile. According to the existing research results, the punching, shearing and bending mechanical simplified models of karst cave roof under pile tip are established, and the corresponding stability checking formulas are derived. Combined with the interval analysis theory and structural non-probabilistic reliability measurement method, the stability evaluation method of karst cave roof under pile tip based on interval non-probabilistic reliability method is proposed. This method uses the INTLAB toolbox in MATLAB to perform interval operations, and then uses the truncation method to eliminate the interval expansion phenomenon in the process. The stability of karst cave roof under pile is judged by comparing the relationship between the non-probabilistic reliability index η and 1. The karst cave under the D ramp 2# pile in the Danxia grade separation area is taken as an example, and the non-probabilistic reliability index η of the karst cave roof under 2# pile is calculated to be 7.95. η greater than 1 indicates that the karst cave roof under 2# pile is in a stable state. The evaluation result is consistent with the actual situation, indicating the rationality and feasibility of the method. The three performance functions are used as the unit to study the variation law of the non-probabilistic reliability index η when the coefficient of variation C of the interval variable is different (C increases from 0.01 to 0.1). The results show that with the increase of the coefficient of variation C of each interval variable, the corresponding non-probabilistic reliability indexes are reduced to varying degrees. The variability of the thickness of karst cave roof h has the greatest influence on the evaluation results, followed by the sharing ratio of pile tip resistance T, and the counterforce of pile tip F has the least influence.