Interpretation of shear strength uncertainty and reliability analyses of slopes

The variance of the friction angle or friction coefficient (tan ?) is often considered in geotechnical reliability analyses, which implies that the variance of the shear strength as defined by a Mohr-Coulomb envelope increases as the normal stress on the shearing surface increases. However, shear strength data sometimes has approximately constant variance, and most simple regression techniques assume constant variance. Four effective stress shear strength data sets are evaluated using both the constant variance (homoscedastic) and constant coefficient of variation (heteroscedastic) interpretations. The impact of the variance interpretation on slope stability is evaluated using infinite slope, homogeneous dam, and zoned dam examples. For relatively shallow infinite slope surfaces, the reliability index for the heteroscedastic interpretation of shear strength variance was about twice the reliability index obtained using the homoscedastic approach. In the dam examples, the difference in the reliability indices resulting from the heteroscedastic and homoscedastic interpretations was about one, indicating a tenfold increase in the probability of failure. The typical assumption of constant coefficient of variation of shear strength may result in unconservative estimates of the reliability of shallow failure surfaces and overly conservative results for deeper failure surfaces.