Recommended -Value for Computing Number of Equivalent Stress Cycles and Magnitude Scaling Factors for Simplified Liquefaction Triggering Evaluation Procedures
Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 148, Issue 12
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 (). Central to computing 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 curves. Based on empirical evidence (and mathematical convenience), curves are commonly assumed to plot as straight lines on log-log scales, with the line having a slope of . As such, the -value is central to computing and MSF and has a significant influence on computed normalized seismic demand in simplified liquefaction evaluations. It is widely assumed that the -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 -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 curves can result in the apparent dependency of the -value on soil density. However, using a consistent liquefaction criterion based on the cumulative dissipated energy in a unit volume of soil yields -values that are relatively insensitive to changes in soil density. Published modulus reduction and damping (MRD) curves can be used to compute -values using an energy-based framework; this yields more generalized and less test- and soil-specific -values. As a result of these efforts, a -value of 0.28 is recommended for computing and MSF, independent of soil density.
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Data Availability Statement
Some or all data, models, or code that support the findings of this paper are available from the corresponding author upon reasonable request.
Acknowledgments
The authors would like to thank Mr. Alex Osuchowski and Mr. Prakash Ghimire for their help in running the CV-CDSS tests and improving the testing procedures. This research was partially funded by the National Science Foundation (NSF) (Grant Nos. CMMI-1825189 and CMMI-1937984). This support is gratefully acknowledged. However, any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the NSF.
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Journal of Geotechnical and Geoenvironmental Engineering
Volume 148 • Issue 12 • December 2022
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© 2022 American Society of Civil Engineers.
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Received: Jun 16, 2021
Accepted: Aug 1, 2022
Published online: Oct 8, 2022
Published in print: Dec 1, 2022
Discussion open until: Mar 8, 2023
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