Point estimation method: Validation, efficiency improvement, and application to embankment slope stability reliability analysis

•Use of binary bits of integers to allocate the sign array in the Rosenbueth method (PEM).•Application of PEM in slope stability analysis by confirming normal or lognormal distribution of the factors of safety.•Successful application of PEM in a 165 m high rockfill dam. Calculating the reliability index is a common approach used in structural reliability analysis. It typically involves a procedure for determining the reliability index of a performance function. The method developed by Rosenblueth only requires calculating the objective functions at selected weighting points. The method is easily implemented and free of numerical iteration. However, it requires large storage space for sign information during coding. In the present study, the problem of large storage space is easily solved by taking the binary bits of integers, which can be achieved with most commercial compilers. By conducting an extensive numerical investigation based of the chi-squared goodness test, it is found that the factors of safety obtained in slope stability analysis follow normal distributions if the uncertainty variables are normally distributed. Meanwhile, the factors of safety obtained in retaining-wall stability analysis follow lognormal distributions. Therefore, the conventional slope stability analysis methods are confirmed not substantially change the distribution form of the performance function, which is a condition that makes the Rosenblueth method applicable. In conjunction with other reliability analysis methods (Monte Carlo and FORM), the Rosenblueth method is shown to be useful for the reliability analysis of slopes and retaining walls with satisfactory accuracy. This study applies the proposed method to the analysis of the 165-m-high earth core rockfill Xiaolangdi Dam in China.