Reliability Analysis of Slopes

摘要

The Spencer (1973) limit equilibrium method of slices is recast to enhance practicality and extended to a hitherto complicated reliability analysis. The method allows varying side force inclination. The search for the noncircular critical slip surface is accomplished using spreadsheet cell-object-oriented constrained optimization. The extension to probabilistic approach is done by computing the Hasofer-Lind reliability index via constrained optimization of the dispersion hyperellipsoid in the original space of the random variables. Reliability analyses involving spatially correlated normal and lognormal random variables are illustrated for an embankment on soft ground, with search for the reliability-based noncircular critical slip surface. The probabilities of failure and the probability density functions inferred from reliability indices are compared with Monte Carlo simulations. It is shown that the hitherto complicated problems of locating noncircular critical surface and reliability analysis involving implicit functions and correlated nonnormals can be solved with relative ease and transparency using cell-object-oriented constrained optimization in the ubiquitous spreadsheet platform.