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 underground concrete silo, designed as a hollow cylinder with a large aspect ratio and thin walls, is highly susceptible to failure caused by intentional or accidental soil explosions. To enhance its protection, this study investigates the dynamic tensile responses and failure mechanisms of underground concrete silos subjected to high-yield soil explosions. The concept of nominal crack width is proposed to quantitatively describe the degree of overall bending-induced tensile responses and failure of the concrete silo. The influences of explosive weights, standoff distances, and the aspect ratios and thicknesses of the underground concrete silo are quantitatively explored first. On this basis, a dimensionless number combining these major influencing factors is derived using dimensional analysis. The derived dimensionless number has a clear physical meaning, reflecting three aspects: the inertia of the blast loading, the resistance ability of concrete material to bending responses and failure, and the resistance ability of silo structure to bending responses and failure. The results demonstrate that the proposed dimensionless number effectively correlates with the overall bending-induced tensile responses and failure of silo structures across various geometries and explosion scenarios, exhibiting a good linear relation with the dimensionless nominal crack width of the concrete silo. With its solid physical foundation, the dimensionless number offers practical applications in scaling analysis and fast damage assessment. Specific examples of these applications are presented and discussed in this study.

This paper examines the thermo-hydro-mechanical (THM) coupling behavior of layered transversely isotropic media under axisymmetric and plane strain conditions by utilizing the transformed differential quadrature method (TDQM), taking groundwater into consideration. Initially, the coupled governing equations of layered transversely isotropic media in multi-dimensional coordinate systems are established with considering the influence of groundwater levels. Subsequently, appropriate integral transform methods are applied to derive ordinary differential equations under different coordinate systems. It can be seen that the equations in different coordinate systems after the discretization are similar. Boundary conditions and internal continuity conditions are defined through the stress-strain relationship in the transformed domains, which are integrated into the discretized equations to form the global matrix equations. After solving the matrix equations, this study verifies the solution and investigates the impact of groundwater levels and the key parameters of transverse isotropy, and compares the behaviors of the media in different coordinate systems.

The freezing index (FI) is an important index used in investigations of climate change, frozen ground degradation and frost heave resistance engineering design. In view of the fact that the deterministic effects of latitude and elevation are not considered in the frequency calculation of FI, we proposed an index-freezing method that considers the certainty effects of both elevation and latitude by referring to the index-flood method in this paper. The correlations between the FI and certainty factors (elevation and latitude) were obtained by multiple regression analysis. The effects of latitude and elevation were then removed by nondimensionalisation, and dimensionless FI sequences were subsequently obtained. Finally, the index-freezing method was verified by regional probability analysis. Using the daily average temperature data recorded at 10 major meteorological stations over the 1960-2020 period in Ningxia, the calculation process of the FI and its frequency distribution were provided. The results showed that the proposed FI method can not only remove the certainty effects of elevation and latitude but can also consider the uncertainty associated with interannual FI variations, thus providing more scientific, reasonable and accurate results. The generalised extreme value (GEV) distribution is the optimal frequency distribution of the nondimensional regional FI. The estimation errors of the missing data tests were mostly within 10%, and the residual sum of squares (RSS) and root-mean-square error (RMSE) values were also lower than those obtained through spatial interpolation, thus indicating that the interpolation preci-sion of the proposed FI method was optimal.