Comparative modelling of retrogressive landslide runout: 2D and 3D random large-deformation analyses using coupled Eulerian-Lagrangian method

Retrogressive landslides in sensitive clays pose significant risks to nearby infrastructure, as natural toe erosion or localized disturbances can trigger progressive block failures. While prior studies have largely relied on two-dimensional (2D) large-deformation analyses, such models overlook key three-dimensional (3D) failure mechanisms and variability effects. This study develops a 3D probabilistic framework by integrating the Coupled Eulerian–Lagrangian (CEL) method with random field theory to simulate retrogressive landslides in spatially variable clay. Using Monte Carlo simulations, we compare 2D and 3D random large-deformation models to evaluate failure modes, runout distances, sliding velocities, and influence zones. The 3D analyses captured more complex failure modes—such as lateral retrogression and asynchronous block mobilization across slope width. Additionally, the 3D analyses predict longer mean runout distances (13.76 vs. 11.92 m), wider mean influence distance (11.35 vs. 8.73 m), and higher mean sliding velocities (4.66 vs. 3.94 m/s) than their 2D counterparts. Moreover, 3D models exhibit lower coefficients of variation (e.g., 0.10 for runout distance) due to spatial averaging across slope width. Probabilistic hazard assessment shows that 2D models significantly underpredict near-field failure probabilities (e.g., 48.8% vs. 89.9% at 12 m from the slope toe). These findings highlight the limitations of 2D analyses and the importance of multi-directional spatial variability for robust geohazard assessments. The proposed 3D framework enables more realistic prediction of landslide mobility and supports the design of safer, risk-informed infrastructure.