FORM, SORM, and spatial modeling in geotechnical engineering

• Expanding equivalent dispersion ellipsoid perspective for FORM.
• Spreadsheet-automated constrained optimization FORM procedures.
• Geotechnical SORM analysis after FORM analysis.
• Slope reliability analysis for spatially autocorrelated shear strength.
• Reformulated Spencer method for slope reliability analysis.

An intuitive ellipsoidal perspective is described together with three spreadsheet-automated constrained optimizational FORM procedures and a SORM approach. The three FORM procedures are then compared in the context of geotechnical examples of a confined soil element, a rock slope, and an embankment on soft ground with spatially autocorrelated undrained shear strength in the soft clay foundation, the performance function of which is based on a reformulated Spencer method with search for reliability-based critical noncircular slip surface. Two methods of modeling spatial autocorrelations are presented, and the merits and limitations of the three constrained optimizational FORM procedures are studied. The complementary roles and interconnections among the three constrained optimizational FORM procedures and SORM approach are emphasized. Comparisons are also made with Monte Carlo simulations.