Slope deformation poses significant risks to infrastructure, ecosystems, and human safety, making early and accurate predictions essential for mitigating slope failures and landslides. In this study, we propose a novel approach that integrates a fractional-order grey model (FOGM) with particle swarm optimization (PSO) to determine the optimal fractional order, thereby enhancing the model’s accuracy, even with limited and fluctuating data. Additionally, we employ a k-means clustering technique to account for both temporal and spatial variations in multi-point monitoring data, which improves the model’s ability to capture the relationships between monitoring points and increases prediction relevance. The model was validated using displacement data collected from 12 monitoring points on a slope located in Qinghai Province near the Yellow River, China. The results demonstrate that the proposed model outperforms the traditional statistical model and artificial neural networks, achieving a significantly higher coefficient of determination $R^2$ up to 0.9998 for some monitoring points. Our findings highlight that the model maintains robust performance even when confronted with data of varying quality—a notable advantage over conventional approaches that typically struggle under such conditions. Overall, the proposed model offers a robust and data-efficient solution for slope deformation prediction, providing substantial potential for early warning systems and risk management.

Landslide-generated waves occur as a result of the intrusion of landslides such as mud flows and debris flows into bodies of water such as lakes and reservoirs. The objective of this study was to determine how the momentum is transferred from the sliding mass to the body of water on the basis of theoretical analysis and physical model experiments. Considering the viscoplastic idealization of natural landslides, the theoretical model was established based on the momentum and mass conservation of a two-phase flow in a control volume. To close the theoretical equations, slide thickness and velocity passing through the left boundary of the control volume were estimated by lubrication theory, and the interaction forces between the slide phase and water phase, including hydrostatic force and drag force, were given by semiempirical equations fitted with experimental data obtained using the particle image velocimetry (PIV) technique. The near-field velocity fields of both the sliding mass and the body of water, as well as the air–water–slide interfaces, were determined from the experiments. The theoretical model was validated by comparing the theoretical and experimental data of the slide thickness and slide velocity, as well as the momentum variations of the two phases in the control volume.

Engineering constructions in coastal areas not only affect existing landslides, but also induce new landslides. Variation of the water level makes the coastal area a geological hazard-prone. Prediction of the slope displacement based on monitoring data plays an important role in early warning of potential landslide and slope failure, and supports the risk management of hazards. Given the complex characteristic of the slope deformation, we proposed a prediction model using random coefficient model under the frame of panel data analysis, so as to take the correlation among monitoring points into consideration. In addition, we classified the monitoring data using Gaussian mixture model, to take the temporal-spatial characteristics into consideration. Monitoring data of Guobu slope was used to validate the model. Results indicated that the proposed model have a better performance in prediction accuracy. We also compared the proposed model with the BP neural network model and temporal – temperature model, and found that the prediction accuracy of the proposed model is better than those of the two control models.

A key scientific challenge in landslide-generated impulse-wave research is to determine how initial slide conditions are translated into wave responses through the intermediate water-entry process. Existing data-driven studies generally focus on direct prediction or variable-importance ranking and therefore provide limited insight into the pathways linking slide release, water entry, and wave generation. To address this issue, a three-stage process-chain framework was developed using 290 laboratory test cases, integrating initial slide conditions, water-entry dynamics, and wave responses. Cross-stage correlation analysis, standardized path modeling, mediation-effect decomposition, cascade prediction, bootstrap resampling, and diagnostic analyses were jointly applied. The results show that relative effective entry mass M is strongly correlated with relative wave amplitude A and relative wave height H, with Spearman coefficients of 0.96 and 0.91, respectively, while the corresponding coefficients for the entry Froude number $Fr$ are 0.71 and 0.80. Within the present dataset and fitted model, mediation analysis indicates that the pathways through M have the largest modeled indirect contributions: the indirect effects of initial slide mass through M are 0.652 for A and 0.600 for H, whereas the corresponding effects of the Bingham number are $-0.669$ and $-0.615$. The cascade framework further shows that the realized entry state can be systematically reconstructed from the initial conditions and used as an explicit intermediate layer for wave-response prediction. Prediction comparisons further show that the observed entry-state model is best interpreted as an explanatory or diagnostic benchmark because it uses measured entry-state variables, whereas the direct initial-condition and cascade models address prospective prediction from prescribed initial-condition information. The main advantage of the cascade framework therefore lies in its physical interpretability rather than a substantial gain in predictive accuracy. Within the present dataset and fitted model, the associations between the initial slide conditions and wave responses are expressed mainly through mass-related and inertia-related pathways involving the realized entry state.