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Assessment of earthquake-induced liquefaction is an important topic in geotechnical engineering due to the significant potential for damage to infrastructure. Some of the most significant infrastructure damage occurs due to differential settlement of the ground, including due to liquefaction. Postliquefaction deformations commonly are assessed using one-dimensional empirical models, which inherently assume laterally homogeneous soil layers. Numerical models offer the potential to examine the effects of ground motion variability and spatially variable soil properties on liquefaction-induced deformations. This study explored the postliquefaction reconsolidation settlement for a site in Hollywood, South Carolina, which was characterized using a three-dimensional (3D) geostatistical model and simulated using the numerical platform FLAC and constitutive model PM4Sand. The effects of ground motion characteristics on mean and maximum differential settlements were investigated. The physical mechanisms associated with postliquefaction responses such as excess pore pressures, shear strains, and volumetric strains also were examined. The efficacy of uniform models assuming representative percentile soil properties to represent the stochastic mean settlement was investigated. The inherent inability of uniform models to capture differential settlements and therefore the need for using stochastic models is discussed. 

In a previous work, the first two authors proposed a data-driven method that can construct a site specific multivariate probability density function model for soil properties using sparse, incomplete, and spatially variable site investigation data. The spatial variability was limited to the depth direction (horizontal variability was not considered). This data-driven method is referred to as GPR-MUSIC-X. In the current paper, two improvements with respect to GPRMUSIC-X are made. First, the one-dimensional spatial variability considered by GPR-MUSIC-X is extended to three-dimensional spatial variability (denoted by GPR-MUSIC-3X). Second, a hierarchical Bayesian model (HBM) is adopted to learn the cross-correlation (correlation among different soil parameters) behaviour of generic sites in a soil database accounting for site differences (or uniqueness), and the learning outcome is incorporated into GPR-MUSIC-3X. The resulting model is a quasi-site-specific model (denoted by HBM-MUSIC-3X) because it not only is based on site-specific data but also is informed by the soil database in a manner sensitive to site uniqueness. A case history is used to illustrate the effectiveness of the proposed HBM MUSIC-3X.