Recommended b-Value for Computing Number of Equivalent Stress Cycles and Magnitude Scaling Factors for Simplified Liquefaction Triggering Evaluation Procedures

Abstract

Magnitude scaling factors (MSFs) account for the influence of ground motion duration on liquefaction triggering in simplified stress-based models in which the duration of the motion is quantified in terms of number of equivalent stress cycles (Neq). Central to computing Neq and MSF is the relationship relating the amplitude of applied loading and the corresponding number of cycles to trigger liquefaction, that is, cyclic stress ratio (CSR)-NL curves. Based on empirical evidence (and mathematical convenience), CSR-NL curves are commonly assumed to plot as straight lines on log-log scales, with the line having a slope of −b. As such, the b-value is central to computing Neq and MSF and has a significant influence on computed normalized seismic demand in simplified liquefaction evaluations. It is widely assumed that the b-value varies significantly as a function of soil density. However, in this study a review of published laboratory data and analysis of constant-volume cyclic direct simple shear tests performed as part of this study were used to assess the dependency of the b-value on soil density and other factors. We show that the criterion used to define liquefaction triggering in laboratory tests and the nonlinearity of the CSR-NL curves can result in the apparent dependency of the b-value on soil density. However, using a consistent liquefaction criterion based on the cumulative dissipated energy in a unit volume of soil yields b-values that are relatively insensitive to changes in soil density. Published modulus reduction and damping (MRD) curves can be used to compute b-values using an energy-based framework; this yields more generalized and less test- and soil-specific b-values. As a result of these efforts, a b-value of 0.28 is recommended for computing Neq and MSF, independent of soil density.