Comparison and Use of Failure Envelope Forms for Slope Stability Analyses

This paper reviews and compares different mathematical forms for representing the effective stress failure envelope in the context of slope stability analysis. Although commonly assumed to be linear, the effective stress failure envelope for many soils is non-linear, at least when considered over a wide range of normal stresses. Multiple studies have considered the effects of including non-linearity in slope stability calculations, but little guidance is available for selecting an appropriate envelope form. Differences between six mathematical forms are examined by analyzing four real data sets, each with different characteristics. Statistical descriptors are used to evaluate the goodness of fit for each form. Two simple slopes are analyzed with each data set to ascertain the impact that the envelope form has on the calculated factor of safety. The envelope form is shown to have a relatively small impact on the predicted shear strength and calculated factor of safety for slope stability, provided that (1) the failure envelopes are fit to the test data using a robust regression procedure and (2) the effective normal stresses acting on the critical failure surface are mostly within the range tested by the laboratory shear strength program. The largest differences in predicted shear strength occurred when the failure envelopes were extrapolated to stresses below the laboratory test stress range. In this low stress range, a practical engineering solution is obtained by drawing a linear failure envelope from the origin to the “best-fit” failure envelope at the lowest effective normal stress indicated by the test data.