Bearing capacity of karst roof based on lower bound method

Based on the existing solution format of lower bound analysis method, stress boundary is directly divided into overload boundary and non-overload boundary by taking the overload coefficient as the objective function. A nonlinear programming model is established to solve the lower bound solution of bearing capacity of karst roof ultimate, and the internal point method is used to solve the optimal solution. The accuracy of the method and program is verified by simulating triaxial tests, and then the program is used to study the bearing capacity of karst roof. The influences of horizontal ground stress on the bearing capacity of karst roof are further considered based on the studies on the bearing capacity of karst roof using the lower bound method. The results show that the karst span has a significant effect on the bearing capacity of karst roof, regardless of whether the karst horizontal and the stress boundary conditions are the same. When the karst size is the same, the thickness of the karst roof has a great influence on the ultimate bearing capacity in a certain range, and the effect is not significant after exceeding this range. Considering the horizontal ground stress has a great influence on the bearing capacity when the thickness of the roof is large and the height of the span is relatively small, the influences of horizontal ground stress can not be neglected when the ultimate bearing capacity of the karst roof is calculated using the lower bound method.