Evaluating the temporal stability and risk of unsaturated soil slopes during rainfall is essential for early warning and emergency response to landslides. However, limited research has been conducted on the transition timing of sliding mechanisms, instability/failure time and the integration of sliding consequences into quantitative risk assessment. In order to extend the research in this field, the Random Finite Element Method (RFEM) is used in this paper to investigate the influence of spatial variability of hydraulic properties (related to the fundamental parameter porosity) on the temporal stability and risk of soil slopes subject to rainfall. The findings indicate that the advancing speed of the wetting front is more rapidly in zones with low porosity than that in zones with high porosity. As rainfall progresses, the sliding mechanism of the slope shifts from deep sliding to shallow sliding. The homogeneous case tends to underestimate the rise in groundwater levels, leading to an overestimation of slope stability. Hydraulic boundary conditions significantly affect slope stability, making it crucial to consider horizontal (or near the toe of the slope) drainage conditions in practical applications. Additionally, the time of instability/failure predicted in the homogeneous case may be delayed compared to the actual conditions. Both probability of instability/failure and risk increase with continued rainfall. Compared to scenarios where the spatial variability of internal friction angle is not considered, the probability of instability/failure and risk will be higher when the spatial variability of internal friction angle is additionally considered. Risk-based assessment can define the risk levels, reflecting the severity of sliding consequences. Furthermore, the Malin slope failure record from the Chibo region of India is used to validate the effectiveness of the proposed approach. The probabilities of slope failure align well with actual observations, and the risk-based assessment provides additional information into the Malin landslide. This paper proposes a general model for studying the performance of heterogeneous slopes subject to rainfall, providing valuable guidance for landslide early warning systems and the scope and timing of emergency measures taken.

Correlation length or scale of fluctuation (SOF) is often used as a primary parameter in defining the spatial correlation characteristics of varying soil properties. However, geotechnical site investigations are rather limited so that proper determination of correlation length is not always possible. The concept of a worst-case correlation length thus has important implications in reliability-based designs. In the case of insufficient information, the worst-case correlation length can be used to conservatively estimate the reliability or probability of failure of geotechnical structures. However, the definition of the worst-case correlation length in the literature is not very clear and has been seen in some investigations to not exist. This paper, in the context of bearing capacity of 3D spatially varying soils, investigates the worst-case correlation length based on different definitions to clarify past findings. Further analyses provide insight into practical applications, where the impact of site sampled data and realistic uncertainties are considered. Using realistic values of the coefficient of variation, and taking account of the distance at which site investigation is likely to occur from the loaded area, a worst-case SOF is identified and found to be similar using all definitions.

The bearing capacity of square and/or rectangular footings in geotechnical foundation designs traditionally is determined based on experimental observations and/or deterministic analysis assuming uniform soil profiles. However, soils are spatially varying, and this spatial variability can significantly affect the bearing capacity of the foundation soils. Probability-based design methods can address this problem explicitly. However, a full three-dimensional (3D) probabilistic simulation, such as that involving the random finite-element method, generally is prohibitive, because it involves numerous Monte Carlo runs of a complicated nonlinear elastoplastic algorithm. This paper developed and validated an approximate analytical method based on local averaging theory and geometric averages of soil properties directly under the footing. It was found that the theoretical prediction of the first two moments of a square footing bearing capacity agrees very well with crude Monte Carlo simulation. The analytical prediction of the probability of a design failure was validated through simulation and can be used directly in reliability-based designs against bearing failure.