Liquefied Strength and Its Relationship to Effective Stress

The residual strength of liquefied soil ($s_{u,r}$) is a large-strain strength variable often used for forecasting the seismic stability of dams, embankments, and mine tailings. This variable is usually arrived at by back-analysis of failure case histories and through laboratory experiments. Over the last few decades, there has been debate about whether the liquefied strength should be normalized by the prefailure vertical effective stress (${\sigma }_v^{\prime }$). Normalizing a variable is usually done for two reasons; (1) to render the variable dimensionless, and/or (2) to improve the relationship between the independent and dependent variables. The first objective has obvious benefits for engineering practice in the United States, where two unit systems are commonly used. For the second objective, the benefits of normalizing can be measured by the reduced uncertainty in the statistical relationship. In this study, it is shown that normalizing the residual strength by the prefailure vertical effective stress ($s_{u,r}/{\sigma }_v^{\prime }$) increases the scatter and uncertainty in the relationship between blow count and residual strength for flow failures. This increase in scatter means that the process of normalizing generates additional uncertainty, thereby making the statistical relationship more ambiguous (measured using R-squared and mean squared error). However, for lateral spreads, the opposite is true, and normalizing the liquefied strength reduces uncertainty and improves predictive power. The differences between the two types of seismic soil failures from a critical state perspective, and how these relate to the prefailure vertical effective stress conditions, are discussed.