Performance-Based Assessment of Magnitude (Duration) Scaling Factors

More pronounced at relatively smaller magnitude events, significant variations to an extent of a factor of two in magnitude (duration) scaling factors (MSFs) explain the need to further study this issue, which is also recognized and recommended by the National Center for Earthquake Engineering Research Group. Inspired from this gap, the main motivation of this study is defined as to (1) comparatively assess the validity of existing magnitude scaling models and the accuracy of their predictions; (2) develop robust and practical to use semiempirical magnitude scaling models applied on CRR: separate sets for strain (cyclic mobility) or excess pore pressure (cyclic or flow liquefaction) problems. The writers’ excess pore water pressure and shear strain accumulation models were used for the assessment of magnitude (duration) scaling factors. On the basis of the proposed framework, it is concluded that (1) MSFs are not only a function of number of equivalent loading cycles but increase with increasing $r_u$ or ${\gamma }_{\max }$ thresholds and decreasing dilational response (i.e., decreasing relative density and/or increasing effective stress states) of soil layers, (2) significantly different set of MSFs than the NCEER recommendations can be estimated for different combinations of ${\gamma }_{\max }$ (or $r_u$), $N_{1,60,CS}$, ${\sigma }_{v,0}^{\prime }$, (3) for the assessment of critical structures (e.g.,  nuclear power plants), where significantly smaller shear strain performance targets are needed, use of existing models may produce significantly higher MSFs, leading to unconservative estimates of cyclic mobility potential.