Probability-based assessment of number of equivalent uniform stress cycles

For seismic soil liquefaction triggering and performance assessments, durational effects in field-based evaluations are mostly represented by the magnitude of the seismic event. However, in the laboratory, the equivalent number of uniform shear stress cycle concept is used. Benefitting from the findings of both case history- and laboratory-based research streams requires the conversion of earthquake-induced transient shear stresses to equivalent uniform (harmonic) stress cycles, or vice versa. A critical review of currently existing studies has revealed that; i) significantly extended earthquake catalogs are now available, which enable improved assessment of the conversion scheme, ii) based on the findings of Cetin and Bilge, weighting factors (m values) of stress conversions are now known to be stress, strain and density state dependent, and iii) these weighting factors extend to ranges that exceed the limits of earlier studies. Inspired by these, a semi-empirical probability-based model for the estimation of equivalent number of uniform stress cycles as functions of earthquake, site and performance (either strain or pore pressure-based) parameters is proposed. The proposed predictive relationship is shown to be more accurate and precise, evident by higher R-2 and smaller model error standard deviations. However, despite significant improvement to an R-2 value of 0.30, it is concluded to be still low, which addresses the uncertainties involved in duration assessments of earthquake shaking, and the need for further research. The probabilistic use of the proposed model is illustrated for a sandy soil layer at a soil site, which is expected to be shaken by a scenario earthquake event.