Probabilistic Model for the Assessment of Cyclically Induced Reconsolidation (Volumetric) Settlements

A maximum likelihood framework for the probabilistic assessment of cyclically induced reconsolidation settlements of saturated cohesionless soil sites is described. For this purpose, over 200 case history sites were carefully studied. After screening for data quality and completeness, the resulting database is composed of 49 high-quality, cyclically induced ground settlement case histories from seven different earthquakes. For these case history sites, settlement predictions by currently available methods of Tokimatsu and Seed (1984), Ishihara and Yoshimine (1992), Shamoto (1998), and Wu and Seed (2004) are presented comparatively, along with the predictions of the proposed probabilistic model. As an integral part of the proposed model, the volumetric strain correlation presented in the companion paper is used. The accuracy of the mean predictions as well as their uncertainty is assessed by both linear regression and maximum likelihood methodologies. The analyses results revealed that (1) the predictions of Shamoto and Tokimatsu and Seed are smaller than the actual settlements and need to be calibrated by a factor of 1.93 and 1.45, respectively; and (2) Ishihara and Yoshimine, and Wu and Seed predictions are higher than the actual settlements and need to be calibrated by a factor of 0.90 and 0.98, respectively. The Wu and Seed procedure produced the most unbiased estimates of mean settlements [i.e., their calibration coefficient (0.98) is the closest to unity], but the uncertainty (scatter) of their predictions remains high as revealed by the second to last smaller R(2) value, or relatively higher standard deviation (sigma(epsilon)) of the model error. In addition to superior model predictions, the main advantage of the proposed methodology is the probabilistic nature of the calibration scheme, which enables incorporation of the model uncertainty into mean settlement predictions. To illustrate the potential use of the proposed model, the probability of cyclically induced reconsolidation settlement of a site after a scenario earthquake to be less than a threshold settlement level is assessed