Coastal regions are increasingly vulnerable to sea-level rise and extreme storm events, making the accurate prediction of wave run-up on seawalls crucial for effective flood and erosion protection. This study presents a novel hybrid approach combining K-means clustering with artificial neural networks (ANNs) to predict wave run-up distance. The method begins with dimensionless analysis to scale all the variables, followed by data segmentation using K-means clustering to group wave characteristics such as the Froude number, scaled distance from the wave front to the shoreline, and wave nonlinearity. These clusters help to focus the ANN on more homogeneous wave conditions, significantly improving prediction accuracy. Two-dimensional flume experiments systematically varied wave height, period, and steepness, producing a robust dataset that accounts for a range of wave conditions. The model’s performance is demonstrated through a high $R^2$ value of 0.97 and low mean squared error (MSE) of 0.0092, surpassing traditional ANN models in its ability to capture complex wave dynamics.

Predicting wave run-up on seawalls is essential for assessing coastal flood risk and guiding resilient design. In this study, we combine physical model experiments with a hybrid data driven method to forecast wave run-up distance. Laboratory tests generated a nonlinear data set spanning a wide range of wave amplitudes, wavelengths, Froude numbers. To capture the underlying physical regimes, the records were first classified using a Gaussian Mixture Model (GMM), which automatically grouped waves of similar hydrodynamic character. Within each cluster a Gradient Boosting Regressor (GBR) was then trained, allowing the model to learn tailored input–output relationships instead of forcing a single global fit. Results demonstrate that the GMM-GBR combined model achieves a coefficient of determination $R^2$ greater than 0.91, outperforming a conventional, non-clustered GBR model. This approach offers a reliable tool for predicting seawall performance under varying wave conditions, contributing to better coastal management and resilience strategies.

Monte Carlo simulation (MCS) is widely applied to slope system reliability analysis, but it is often criticized for the drawback of the heavy computational burden involved in deterministic evaluations of slope systems. To address this issue, this paper proposes a novel method for efficient system reliability analysis of soil slope based on MCS, which incorporates the physical information of a soil slope to enhance computational efficiency. The method employs strength reduction sampling to identify a limited number of critical slope samples in a limit state, and considers the intrinsic relationship between soil shear strength parameters and the slope stability to determine the safety or failure of a slope sample based on the obtained critical samples without extra calculations of safety factor. As byproducts, the failure slope samples obtained are further utilized to identify the most probable points (MPPs) of failure, which are essential for determining the significant failure modes and understanding the slope failure mechanisms. A soil slope example is provided to validate the method.

《地球科学》(ISSN 1000-2383;CN42-1874/P) (原刊名《地球科学——中国地质大学学报》ISSN 1000-2383;CN42-1233/P)，创刊于1957年，是由教育部主管、中国地质大学主办的综合性地学学术理论期刊，月刊，2015年改名为《地球科学》,她以反映中国地质大学教学与科研最新的、高水平的基础地质、应用地质、资源与环境地质及地学工程技术研究成果为主要任务。