Depth to bedrock (DTB) is a critical factor for rainfall-induced slope failures. However, the influence of uncertainties in these measurements, particularly at a small-scale, has not been fully understood. Numerical modeling was conducted to assess the impact of a variable bedrock topography on the stability of a real-world unsaturated slope. The simulations included a three-dimensional pore-water pressure estimation, derived from the numerical solution of the Richards equation, coupled with a slope stability assessment using numerical limit analysis. The study explored the potential of incorporating random fields (RFs) into an established DTB model to improve the understanding of rainfall-triggered landslides. The proposed methodology was applied to the analysis of a small watershed within the Papagaio River basin in Brazil, an area historically subjected to landslides triggered by rainfall events. Our main findings reveal that small variations in DTB can significantly impact the safety factor and probability of failure estimations. Furthermore, they influence the shape, location and failure volume associated to predicted landslides. The incorporation of RFs effectively addresses small- scale uncertainty in DTB, controls bedrock morphology, and enhances the assessment of probabilistic numerical modeling for landslide susceptibility. This study highlights the importance of accurate and comprehensive DTB characterization for assessing rainfall-induced landslides at local slope scale.

The influencing mechanism of the spatial variability in concrete materials on the seismic damage of concrete gravity dams is still unclear, and existing methods for evaluating the seismic damage are insufficient. In this work, the effects of concrete's spatial variability on the seismic damage distribution, energy dissipation, and deformation in concrete gravity dams are performed based on the damaged plastic model of concrete. Prior to the seismic damage analysis, the method for seismic inputting and the correlation function for realizing random fields of concrete materials are carefully determined. Based on the seismic damage analysis of the Koyna gravity dam, the tensile strength has the greatest influence on the seismic damage, followed by the elastic modulus and fracture energy. Aiming at the parameter of tensile strength, the decrease of correlation distance and the increase of the coefficient of variation increase the damage degree and complicate the damage distribution. A convenient and comprehensive damage profiling indicator is proposed to avoid the one-sidedness and evaluation error caused by using a single scalar damage value. The triangular area enclosed by the three individual damage indexes represents the comprehensive damage degree, and the shape change of the damage triangle indicates the change in the damage pattern of the dam. This damage profiling indicator is specifically designed to quantitatively distinguish and evaluate the damage degrees between a series of damage cases.

The aim of this study is to investigate the influence of the anisotropic variability in soil on the failure mechanism and the ultimate bearing capacity of foundations that are placed near slopes. A random adaptive finite-element limit analysis (RAFELA) with anisotropic random field modeling and the Monte Carlo simulation technique are combined. The stochastic ultimate bearing capacity for various undrained shear strengths, slope angles, normalized slope heights, distances from the slope crest, and horizontal and vertical correlation distances are analyzed. The quantitative identification and characterization of failure mechanisms, which are determined by the failure slip and passive wedge contribution, are achieved through the digital image processing of realizations from anisotropic random soil. This study showcases the diverse failure mechanisms and sliding surface sizes that arise from distinct soil patterns, which are influenced by alterations in slope geometry and soil anisotropic spatial variability. The quantitative findings highlight that alterations in failure mechanisms and slip surface sizes lead to heightened failure probabilities and significant variations in bearing capacity.

Desiccation crack is a prevalent natural phenomenon that plays a significant role in the stability of soil slopes. In this study, a hydromechanical coupling model incorporating a layer of stochastic cracks is developed for analyzing cracked soil slopes. To properly consider the anisotropy and spatial variability of desiccation cracks, three crack indices are generated through cross-correlated random fields via Cholesky decomposition. The seepage and mechanical behavior of a cracked slope are analyzed by adjusting stochastic parameters and rainfall conditions. Applied to the Ningzhen Mountains area in China, the model investigates the stability of slopes under various annual meteorological conditions. The results indicate that neglecting the spatial variability of cracked layer properties can lead to inaccurate assessments of instability risks at the base and water accumulation at the top of slopes. During heavy rainfall, slopes with deeper (up to 5 m) and weaker cracked layers often show a roughly planar sliding morphology. Moreover, the uncertainties in crack depth have the most pronounced influence on the uncertainties of the slope stability, more than horizontal permeability or crack aperture. The average crack aperture's influence on slope stability depends on the relationship between crack infiltration rate and rainfall intensity.