The influence of soil variability on the probabilistic bearing capacity of strip footings near slopes has been extensively studied, particularly under short-term undrained conditions. However, these investigations, predominantly based on the plane-strain assumption, fall short in accurately estimating the bearing capacity of square and rectangular footings and in capturing the spatial variability of soils. This study focuses on short-term undrained conditions and employs the random finite element method (RFEM) and Monte Carlo simulation (MCS) techniques to explore the effect of rotational anisotropy on the bearing capacity response and failure probability of a square and rectangular footing-cohesive slope system under a three-dimensional (3D) framework. The findings reveal that the rotation angles of soil strata significantly impact both the mean and coefficient of variation of the bearing capacity, with distinct variation patterns emerging for different footing orientations and aspect ratios. Typical failure patterns are identified, illustrating the correlation between the bearing capacity response, the footing orientations and aspect ratios, and the extension direction of plasticity. The probabilistic results are presented as probability density functions (PDF) and cumulative distribution functions (CDF) for various rotation angles around the x-axis and y-axis and for different L/B ratios of the footings. Additionally, detailed design tables, including failure probability results and corresponding safety factors for specific target failure probabilities, are provided to guide engineering applications.

The spatial distributions of hydraulic conductivity and shear strength parameters are influenced by the soil structure, property and mineral composition. However, hydraulic conductivity is not only determined by the intrinsic soil property but also influenced by external factors such as fractures and interlayers. This study investigates the impact of the asynchronism between the spatial distribution of hydraulic conductivity and shear strength parameters on the reliability assessment and failure mechanism of unsaturated soil slopes with different titled stratifications under rainfall conditions. The results indicate that the asynchronism in the rotational angles (alpha) of hydraulic conductivity and shear strength parameters shows the greatest impact on the probability of failure (Pf) of slopes. By contrast, the asynchronism in the scales of fluctuation of hydraulic conductivity and shear strength parameters and employing different autocorrelation functions (ACFs) show minor impact on the Pf. The impact of using different ACFs, alpha, and scales of fluctuation to characterise the spatial variability of hydraulic conductivity on sliding mass and failure modes is minimal.

Natural slopes often exhibit tilted stratification with rotated transverse anisotropy in multiple soil properties, including the mechanical (e.g., friction angle phi and cohesion c) and hydraulic properties (e.g., saturated hydraulic conductivity ks). This phenomenon indicates that to achieve an accurate assessment of slope reliability under rainfall infiltration, the anisotropic spatial variation of the shear strength parameters and ks should be incorporated in a combined manner. Thus, this paper discusses the combined influence of rotated transverse anisotropy in the shear strength parameters and ks on the reliability and failure mechanism of an unsaturated slope under rainfalls. It is found that for a slope with tilted stratification, the failure mechanism and reliability estimator are dominantly influenced by the rotated transverse anisotropy in the shear strength parameters, while the influence induced by that in ks is slight. In particular, only incorporating the rotated transverse anisotropy in ks may lead to an incorrect reliability estimator of a slope with tilted stratification. Herein, the reliability index beta would be estimated to be dramatically higher, and beta of a slope with horizontal bedding would be higher than that of an anti-dip slope, which is inconsistent with the engineering experiences. Nonetheless, the rotated transverse anisotropy in ks should not be ignored in slope reliability assessment, because ignoring the rotated transverse anisotropy in ks would lead to overestimation of the reliability index beta, which is adverse to the safety design of a slope.