Stability analysis of the karst roof under the non-uniform subgrade load

According to the Boussinesq solution, the additional stress on the karst roof under the non-uniform subgrade load is obtained. The MATLAB is used to fit the distribution of the additional stress on the roof with a high order function. The maximum bending moment and shearing force of the karst roof that is treated as a simply supported beam, fixed beam and cantilever beam are obtained by superimposing the calculated results with the self-weight effect of the soil and the roof. The bending and shearing stability of the roof is determined by calculating the maximum tensile stress and shear stress on the karst roof, and a stability assessment method of the karst roof under the uneven embankment load is put forward. The stability factor is introduced to carry out the parameter analysis from four aspects: the distribution of subgrade load, the relative position of the cave and the subgrade load, the thickness of the roof, and the span of the roof. The feasibility and rationality of the method are verified with the comparative analysis of the engineering example.