Liquefaction-induced ground settlement remains notoriously difficult to predict using empirical or single-stage machine learning (ML) models, which often ignore event-to-event variability and the hierarchical physics of seismic energy transmission. In this study, we present a two-stage, physics-guided ML framework that first predicts site amplification (lnPGA) and then, using that predicted demand, estimates post-liquefaction settlement (Sp). The term "physics-guided" is adopted throughout in preference to "physics-informed," as the ML models are standard data-driven architectures (XGBoost, Ridge, Lasso, etc.) whose feature space is constructed from physically motivated predictors, rather than architectures embedding governing partial differential equations into the learning objective (as in physics-informed neural networks, PINNs, in the strict sense). A critical methodological advance is the adoption of Leave-One-Event-Out cross-validation (LOEO-CV), which prevents intra-event data leakage and provides truly out-of-sample performance estimates across distinct earthquake sequences. From a global database of 100 case histories spanning five seismotectonic settings, 33 physically grounded features are engineered—including a Basin Effect Index (BEI, physically grounded in site period and impedance contrast theory) and a Gutenberg-Richter-based seismic energy density. Stage 1 (lnPGA prediction) achieves LOEO-CV R2 = 0.961 (95% CI: 0.941–0.975). Stage 2 (settlement prediction), using hybrid XGBoost, attains LOEO-CV R2 = 0.239 (95% CI: 0.18–0.30), consistent with the predictive ceiling imposed by aleatory field variability (benchmark ceiling range: 0.18–0.28). Per-event LOEO-CV R2 values are: Tohoku fold: 0.31; Chi-Chi fold: 0.22; Loma Prieta fold: 0.19; Hyogoken-Nambu fold: 0.24; Supplementary Events fold: 0.21. The two-stage framework improves upon single-stage regression by ΔR2 approximately + 0.03 (consistent directional trend; bootstrap CIs partially overlap) and reduces RMSE by 27% relative to the Tokimatsu-Seed empirical procedure. Basin sites exhibit 63% higher mean settlement than non-basin sites. SHAP-based interpretability (correlational, not causal) identifies seismic travel time (lnt) as the dominant predictor, consistent with its role as a shaking-duration proxy in geomechanical theory. Bootstrap and Bayesian uncertainty quantification provide probabilistic prediction bounds for performance-based design applications.

Physics-Guided Machine Learning for Liquefaction-Induced Settlement Prediction

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发表日期：

2026年6月25日

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Ajay Pratap Singh Rathor,
Deepika Khandelwal

摘要

Liquefaction-induced ground settlement remains notoriously difficult to predict using empirical or single-stage machine learning (ML) models, which often ignore event-to-event variability and the hierarchical physics of seismic energy transmission. In this study, we present a two-stage, physics-guided ML framework that first predicts site amplification (lnPGA) and then, using that predicted demand, estimates post-liquefaction settlement (Sp). The term "physics-guided" is adopted throughout in preference to "physics-informed," as the ML models are standard data-driven architectures (XGBoost, Ridge, Lasso, etc.) whose feature space is constructed from physically motivated predictors, rather than architectures embedding governing partial differential equations into the learning objective (as in physics-informed neural networks, PINNs, in the strict sense). A critical methodological advance is the adoption of Leave-One-Event-Out cross-validation (LOEO-CV), which prevents intra-event data leakage and provides truly out-of-sample performance estimates across distinct earthquake sequences. From a global database of 100 case histories spanning five seismotectonic settings, 33 physically grounded features are engineered—including a Basin Effect Index (BEI, physically grounded in site period and impedance contrast theory) and a Gutenberg-Richter-based seismic energy density. Stage 1 (lnPGA prediction) achieves LOEO-CV R² = 0.961 (95% CI: 0.941–0.975). Stage 2 (settlement prediction), using hybrid XGBoost, attains LOEO-CV R² = 0.239 (95% CI: 0.18–0.30), consistent with the predictive ceiling imposed by aleatory field variability (benchmark ceiling range: 0.18–0.28). Per-event LOEO-CV R² values are: Tohoku fold: 0.31; Chi-Chi fold: 0.22; Loma Prieta fold: 0.19; Hyogoken-Nambu fold: 0.24; Supplementary Events fold: 0.21. The two-stage framework improves upon single-stage regression by ΔR² approximately + 0.03 (consistent directional trend; bootstrap CIs partially overlap) and reduces RMSE by 27% relative to the Tokimatsu-Seed empirical procedure. Basin sites exhibit 63% higher mean settlement than non-basin sites. SHAP-based interpretability (correlational, not causal) identifies seismic travel time (lnt) as the dominant predictor, consistent with its role as a shaking-duration proxy in geomechanical theory. Bootstrap and Bayesian uncertainty quantification provide probabilistic prediction bounds for performance-based design applications.