Probabilistic risk assessment of a flood-damaged river levee using SPH with Nyström-based heterogeneous soil fields

This study develops a probabilistic framework for assessing the failure risk of a flood-damaged river levee. The framework incorporates spatial heterogeneity of soil properties into large-deformation analysis using the Smoothed Particle Hydrodynamics (SPH) method. Spatially correlated random fields of density, stiffness, cohesion, and friction angle are generated directly at SPH particle locations through the Nyström approximation, enabling assignment of multi-property and cross-correlated variability to a particle-based model. Failure risk is evaluated using a deformation-based criterion defined in terms of crest settlement relative to the available freeboard, which governs the potential for overtopping. To quantify the risk, 1000 Monte Carlo SPH simulations were performed using heterogeneous soil fields. The ensemble simulations reproduced deformation features observed in the field, including sliding deformation, sand-boils, toe heaving, and localized subsidence. The probabilistic results indicated that deformation sufficient to induce overtopping was unlikely under the hydraulic conditions of the event, consistent with field observations. A comparison with a homogeneous (deterministic) model indicated that neglecting spatial heterogeneity may underestimate localized deformation and associated failure risk. These results indicate that spatial soil variability influences the localization of deformation in river levees. Incorporating heterogeneous soil fields into particle-based analysis enables probabilistic assessment of levee performance under extreme hydraulic loading. The case study shows that the framework is applicable to real flood-induced deformation problems in river levees.