Slope Reliability Analysis Using Generalized Method of Slices

Chen and Morgenstern extended Morgenstern and Price's method of slices by expressing force and moment equilibrium in two equations involving multiple integrals. In the present study a practical nested quadrature integration procedure is proposed and implemented in a spreadsheet, to obtain the factor of safety and side force inclinations that satisfy the Chen-Morgenstern equations. Since the deterministic factor-of-safety analysis does not explicitly reflect the uncertainties of the parameters that affect performance, the paper next considers the Hasofer-Lind second moment reliability index. It is shown that extending from the deterministic analysis—a demanding task in its own right, traditionally—to the hitherto equally complicated reliability index computation requires little extra effort. The spreadsheet approach is powerful and versatile, yet practical, and it affords the user an appreciation of what is being implemented.