A probabilistic energy-based framework for performance-based liquefaction hazard assessment: From triggering to consequence

Liquefaction-induced ground settlement is a critical engineering demand parameter for performance-based seismic design, yet conventional stress-based simplified procedures primarily focus on liquefaction triggering. This paper presents a probabilistic energy-based framework that bridges the gap between liquefaction triggering assessment and ground settlement estimation. The framework consists of four integrated components: (1) a strain-dependent normalized cumulative energy capacity model with a strain-dependent overburden correction factor (C σ ) developed from numerically simulated cyclic simple shear tests using the advanced soil constitutive model, (2) a seismic demand model developed from a series of nonlinear site response analyses that correlated normalized cumulative dissipated energy with surface Arias Intensity ( I a ), standard penetration resistance of sandy soil, and depth, (3) a maximum shear strain prediction model linking energy demand to earthquake-induced shear strains, and (4) a simplified ground settlement estimation framework following the empirical relationship. The total model uncertainty was calibrated using Maximum Likelihood Estimation (MLE) against a database of 215 field case histories. The framework achieved an overall classification accuracy of 83.3% for liquefaction triggering prediction. Monte Carlo simulation was employed to propagate uncertainties through the settlement estimation for performance-based design. For a given level of seismic demand, the framework provides the full distribution of liquefaction-induced ground settlement rather than a binary triggering outcome, enabling direct evaluation of the probability of exceeding a specified settlement threshold. This output format aligns with performance goals specified by acceptable ground settlement limits.