Liquefaction Hazard Forecasts

• Liquefaction hazard forecasts are predictive frameworks that combine physical criteria, high-resolution geospatial data, and advanced numerical methods to assess soil liquefaction risks.
• They integrate techniques such as FEM, MPM, and hybrid schemes, calibrated with seismic and remote sensing data, to simulate pore pressure evolution and critical ground deformations.
• These forecasts support infrastructure risk assessment, urban planning, and emergency preparedness by delivering probabilistic maps that guide effective mitigation strategies.

Liquefaction hazard forecasts predict the spatial and probabilistic occurrence of soil liquefaction and its induced deformations under dynamic or static loading, most notably earthquakes. Liquefaction transforms saturated or near-saturated granular soils into a fluid-like state, reducing their shear strength and rigidity, and underpins diverse geotechnical hazards including foundation failure, lateral spreading, dam and embankment collapse, and flow slides. Accurate forecasting requires integrating advanced physical criteria, sophisticated numerical modeling, high-resolution geospatial data, remote sensing, and, increasingly, ML and explainable AI.

1. Physical Criteria and Foundational Advances

Classical liquefaction assessment follows Terzaghi’s effective stress principle, stipulating that liquefaction occurs when pore pressure $P$ equals applied normal stress $\sigma_n$ ($\sigma' = \sigma_n - P = 0$). However, real soils under dynamic forcing rarely satisfy the assumption of spatially uniform pressure. A revised and general criterion has been formulated for granular and porous layers with spatially heterogeneous pore pressure fields (Goren et al., 2013):

• The necessary and sufficient condition for liquefaction is that the average pore pressure along a continuous surface (typically horizontal), $⟨P⟩_h(z)$, equals the applied normal stress:

$⟨P⟩_h(z) = \sigma_n^T,$

where $⟨P⟩_h(z)$ denotes horizontal averaging. This generalizes Terzaghi’s classical rule by explicitly accounting for pressure heterogeneity and is critical for mechanistic and site-resolved hazard assessment.

• Simulation results confirm that in low-permeability (drained) scenarios, localized zones can liquefy transiently even when the bulk-averaged pore pressure is below the threshold, while undrained cases conform to the uniform pressure assumption.

This criterion enables granular identification of vulnerable slip surfaces and informs experimental and field monitoring strategies, shifting the focus from single-point or bulk-averaged measurements to spatially explicit mapping.

2. Mechanics Beyond Pore Pressure: Buoyancy and Acceleration Thresholds

Recent research has established that classical pore-pressure-driven mechanisms are not sufficient to describe all forms of liquefaction, especially under conditions of moderate or fully drained loading (Clément et al., 2018, Clément et al., 2018). Key findings include:

• Buoyancy-mediated liquefaction: Seismic shaking imparts inertial stresses that may overwhelm the reduced frictional resistance of saturated grains, even in the absence of increased pore pressure. The criterion for sliding among grains is:

$$\Gamma = \frac{A\omega^2}{g} > \mu \left(1 - \frac{\rho_w}{\rho_s}\right),$$

where $\Gamma$ is the normalized peak ground acceleration, $A$ and $\omega$ are shaking amplitude and angular frequency, $\mu$ is the friction coefficient, $\rho_w, \rho_s$ are water and grain densities.

• Phase diagrams constructed from model, experiment, and discrete element simulations delineate three regimes: rigid, “heterogeneous liquefaction” (partial fluidization, critical for structural sinking), and “globally excited liquefaction” (pervasive grain sliding).
• The equilibrium response for structures (intruders) on liquefied soils follows an isostatic relation:

$V_{im}^{eq} = \frac{\rho_B V_B}{\rho_{eff}},$

with $\rho_B, V_B$ being the intruder’s density and volume, and $\rho_{eff}$ the effective density of the saturated granular mixture.

Hazard forecasts calibrated by such critical acceleration criteria reliably predict the onset and spatial variability of liquefaction, including in well-compacted, previously densified, or drained soils where classical models fail.

3. Numerical Modeling: FE, MPM, and Hybrid Schemes

Accurate quantification of liquefaction-triggered deformations and runout is achieved using advanced numerical methods:

• Finite Element Method (FEM): Proven effective for simulating triggering (pore pressure evolution, strain localization) and probabilistic settlement fragility curves (Khalil et al., 2020, Sottile et al., 2020). For example:
  • Embankment crest settlement under 76 real earthquake records, modeled using FE/ElastoPlastic multi-mechanism soil models, reveals that peak ground acceleration (PGA) and soil permeability anisotropy are critical determinants of damage probability.
  • Fragility functions relate the probability of exceeding damage thresholds to seismic severity ($a_{max_{out}}$), adopting lognormal formulations, e.g.,

  $$P[u/H > \delta] = \frac{1}{2} \left[1 + \operatorname{erf} \left( \frac{\ln a_{max_{out}} - \mu}{\sigma \sqrt{2}} \right) \right].$$

• Material Point Method (MPM): Handles very large deformations and history-dependent constitutive responses, eliminating mesh distortion limitations inherent in FE methods. In simulations of the San Fernando Dam failure, MPM predicts the observed runout and final dam geometry with high fidelity (Tjung et al., 2021).

• Hybrid Sequential FEM–MPM Schemes: State-of-the-art hazard forecasts now deploy a two-phase approach: FEM precisely models initiation and critical state transitions up to substantial deformation; at a critical timestep, MPM takes over, capturing the unbounded flow and runout characteristics vital for downstream hazard assessment (Sordo et al., 24 Apr 2024).

A summary of physical, numerical, and calibration modeling approaches and their application focus is provided below:

Approach	Focus Phase	Key Application
FE (ElastoPlastic)	Initiation, fragility	Dam/embankment settlement
MPM	Large deformation, runout	Dam failure, flow slides
Hybrid (FEM→MPM)	Full life-cycle	Tailings dam runout

Proper calibration of constitutive models (e.g., Hardening Soil with small-strain stiffness) is essential for robust forecasts, especially under scenarios of progressive static liquefaction (Sottile et al., 2020).

4. Geospatial, Remote Sensing, and Knowledge Graphs

Forecasting at regional and urban scales now exploits remote sensing, satellite-derived indices, and data-intensive analytics:

• Water Content Mapping with NDWI: The Normalized Difference Water Index (NDWI) derived from Sentinel-2 bands (NIR/SWIR) provides a quantitative, spatially resolved proxy for soil saturation—critical for liquefaction susceptibility. NDWI is calculated as:

$NDWI = \frac{B08 - B11}{B08 + B11}$

where $B08$ and $B11$ are the reflectances in NIR and SWIR bands (Razi et al., 4 Jan 2025). High NDWI zones correlate with liquefaction vulnerability and, when merged with geological and seismic data, yield actionable urban scale hazard maps.

• Bayesian Causal Graphical Models: Causal networks integrate coarse geospatial susceptibility proxies (e.g., soil type, water depth) and high-resolution remote sensing (such as SAR-derived damage proxy maps) via Bayesian updating. Variational inference is used to estimate posterior probabilities of liquefaction occurrence, leading to a marked improvement in positive prediction rates and spatial resolution over prior maps (Xu et al., 2022).

• Knowledge Graphs for Scientific Data: Domain knowledge and automated metadata extraction, implemented as knowledge graphs, enable discovery of latent correlations (e.g., linking relative density to pore pressure evolution) in large experimental datasets. This approach improves both phenomenological understanding and forecasting precision by supporting complex multi-parameter queries (Mehta et al., 2023).

5. Machine Learning, Explainable AI, and Mechanics-Informed Surrogates

Recent progress in ML-driven hazard forecasting includes both site-specific and geospatially extensive models:

• Mechanics-informed Surrogates: Bagged decision trees and ensemble ML models trained on ~37,000 CPTs, surrogating state-of-practice geotechnical models for liquefaction indices (LPI, LPIISH, LSN), produce rapid, spatially continuous hazard forecasts over regional/global scales (Sanger et al., 13 Sep 2025, Sanger et al., 13 Sep 2025). These models:

  • Fit site-specific response parameters ($A$, $B$) that encode susceptibility and sensitivity to ground shaking ($MI(PGAM) = A \cdot \tan^{-1}[B(PGAM - T)]$).
  • Are geostatistically updated using regression kriging, wherein spatial interpolation of residuals anchors predictions to ground-truth CPT data.
  • Quantify variance products, thereby providing a spatial confidence metric for forecast users.
• Explainable AI (XAI): Approaches such as SHAP (Shapley Additive exPlanations) are integrated into both tree-based and deep transformer frameworks (Hsiao et al., 24 Apr 2024, Youwai et al., 11 Feb 2025). These methods:
  • Provide local and global attribution of features (e.g., proximity to rivers, groundwater depth, CPT-derived soil parameters) for predicted hazard, ensuring model transparency and interpretability.
  • Match or exceed conventional model accuracy on cross-regional validation (e.g., transformer models achieving 93.75% accuracy) and facilitate interactive, user-facing deployment with real-time site assessment capabilities.
• LSTM Neural Networks: Data-driven models that learn pore pressure evolution under cyclic loading (and capture shielding effects) outperform traditional constitutive models, particularly in replicating history-sensitive responses (Choi et al., 2022).
• Critical Appraisal: Reviews show that most published AI/ML models for liquefaction are underutilized due to shortcomings in validation, benchmarking against state-of-practice models, small or imbalanced datasets, lack of transparency, and insufficient code sharing. Best practice entails rigorous statistical testing, explicit comparison to classical models, and clear, actionable deployment (Maurer et al., 13 Sep 2025).

6. Applications, Fragility Assessment, and Future Directions

Liquefaction hazard forecasts are critical for:

• Infrastructure Risk and Fragility Analysis: Probabilistic fragility curves (e.g., for embankment crest settlements) relate the probability of exceeding defined damage thresholds to seismic intensity measures. These inform engineering design, retrofitting, and emergency preparedness (Khalil et al., 2020).
• Urban and Regional Planning: GIS-ready hazard maps support land-use planning, disaster simulations, evacuation routing, insurance loss modeling, and public investment prioritization (Sanger et al., 13 Sep 2025).
• Tailings and Dam Safety: Advanced intensity measures, calibrated via nonlinear FE simulations and validated against observed disaster cases, enable more reliable prediction of liquefaction-induced runout and deformation in critical structures (Labanda et al., 2022, Sordo et al., 24 Apr 2024).
• Uncertainty Quantification and Communication: Models accompanied by variance products and SHAP/XAI diagnostics allow practitioners to assess forecast reliability and sources of sensitivity, fostering informed decision-making.

A plausible implication is that integration of mechanics-informed ML, explainable AI, comprehensive geospatial data, and multi-method validation will form the basis of future high-reliability liquefaction hazard forecasting frameworks.

7. Ongoing Challenges and Research Frontiers

Key areas for further research and improvement include:

• Full coupling of pressure-driven and buoyancy-controlled mechanisms, including their dynamic interplay under variable saturation, non-uniform friction, and complex earthquake loading (Clément et al., 2018, Clément et al., 2018).
• Benchmarking and transparency for AI/ML models, particularly in geotechnical contexts where interpretability and statistical rigor remain priorities for practitioner trust and code adoption (Maurer et al., 13 Sep 2025).
• Refinement of numerical–physical hybrid schemes, especially for three-dimensional, multi-phase, and domain-scale simulations to accurately predict runout and cascading failure processes (Sordo et al., 24 Apr 2024, Tjung et al., 2021).
• Global scaling of data-driven hazard maps, using cloud computing, satellite imagery, and harmonized geotechnical databases, to provide high-fidelity, near-real-time forecasts adaptable to diverse regional geologies and infrastructure (Sanger et al., 13 Sep 2025, Sanger et al., 13 Sep 2025, Razi et al., 4 Jan 2025).

Advancements in sensor networks, remote sensing analytics, and real-time seismic data integration are expected to further enhance the precision, spatial fidelity, and utility of liquefaction hazard forecasting in multidisciplinary engineering and risk management contexts.