Empirical estimation of the Newmark displacement from the Arias intensity and critical acceleration

This study employs strong-motion data from the 1999 Chi-Chi earthquake, the 1999 Kocaeli earthquake, the 1999 Duzce earthquake, the 1995 Kobe earthquake, the 1994 Northridge earthquake and the 1989 Loma Prieta earthquake to refine the relationship among critical acceleration (Ac), Arias intensity (Ia), and Newmark displacement (Dn). The results reveal that, as expected, logDn is proportional to logIa when Ac is large. As Ac gets smaller however, the linearity becomes less. We also found that logDn is proportional to Ac, and that the linearity is very stable through all Ia values. These features are common to all six sets of data. Therefore, we add a third term in addition to the Jibson's form which covers the aforementioned problem, and propose a new form for the relationship among Ia, Ac and Dn. Two alternative forms were tested using each of the six data sets, before a final form was selected.The final analyses grouped the data into a worldwide data set and a Taiwanese data set. Coefficients for the selected form were derived from regression with the data, and two final empirical formulas, one for global, the other for local, proposed. Site conditions are also considered in this study with empirical formulas being developed for soil and rock sites, respectively. The estimation error is smaller and the goodness of fit is higher for both the local soil-site and rock-site formulas. Since landslides are more likely to occur on hillsides, the rock site formula may be more applicable for the landslide cases, whereas the soil site formula should be used for side slope of landfills.

Research Highlights
► Logarithmic Newmark displacement is proportional to logarithmic Arias intensity logIa.
► Logarithmic Newmark displacement is also proportional to critical acceleration Ac.
► We add an new term - AclogIa in our empirical formula.
► We provide a global formula and a local formula for use.