Reliability analysis of slopes reinforced by frame-anchor structures under earthquake conditions

Earthquakes often cause slope collapse, which poses a serious threat to people's lives and property. Therefore, it is important to study slope stability under earthquake conditions. The limit element upper bound method was improved and applied to the stability analysis of the slope reinforced by frame-anchor structures under earthquake action. The influences of anchor prestress and seismic force on the stability of slope were analysed comprehensively, and the soil was regarded as a heterogeneous material in its natural state under the action of weathering, deposition and historical stress. The rationality of the slope's safety factor and failure mode obtained by this method was verified by an example. Based on the Monte Carlo method, considering the random distribution of soil parameters in space and the autocorrelation between any two points, the midpoint method based on Cholesky decomposition was used to simulate the relevant Gaussian random field. The solution program was compiled in MATLAB. The influence of several commonly used autocorrelation function types on the failure probability of slopes was analysed. The influence of the anchor rod prestress, anchor rod inclination angle and seismic force on the slope's safety factor was discussed, and the failure mode of the slopes under a random field was studied. The results show that the velocity field boundary obtained by the reliability analysis method proposed in this paper is close to the sliding surface obtained by the traditional methods and the deviation of the slope's safety factors between the proposed method and the traditional methods is small. The probability density functions of the slope's safety factors under different autocorrelation functions are approximately normally distributed. Increasing the seismic force will increase the probability of slope failure, while the increase in anchor rod prestress and the decrease in anchor rod inclination angle have positive effects on the slope stability. The failure modes of slopes under different random distribution of soil parameters change significantly. The method proposed in this paper, which does not require to assume the failure model, can realistically and intuitively display the actual failure of slopes.