The bearing capacity of offshore single pile composite foundations can be significantly affected by the spatially variable soil properties and the different soil layers installing the pile. The previous research mainly focuses on effects of isotropy or transverse anisotropy spatial variable soil on the bearing capacity and failure mechanism of piles embedded in a single soil layer. The practical sites generally contain multiple soil layers and the soil properties may exhibit strong rotated anisotropy characteristics due to the complex geological movements. However, how the rotated anisotropy spatial variability of soil property affects the bearing capacity of the offshore single pile composite foundation embedded into multiple soil layers remains unclear. This study aims to systematically investigate the effects of rotated anisotropy three-dimensional spatial variability of soil properties on the vertical bearing capacity of the offshore single pile composite foundation embedded into two soil layers. The three-dimensional random finite element is used to simulate the pile-soil response of the offshore single pile composite foundations under vertical static loads. The influence of the scale of fluctuation delta, rotated angle of anisotropy, and coefficient of variation of different soil parameters including elastic modulus E, cohesion c, and internal friction angle phi are investigated. The results show that the COV of E and c have a larger influence than that of phi. The rotated anisotropy of the upper-layer soil generally has a prominent effect on the bearing capacity of the pile compared with the lower-layer soil especially when the horizontal scale of fluctuation is large. These findings underscore the importance of accounting for rotated anisotropy spatial variability in the design of offshore single pile composite foundations.

Strength anisotropy and heterogeneous rotated anisotropy are prevalent phenomena in natural slopes. Previous studies have underscored their significance in slope stability analysis. However, in previous slope stability analyses, the effects of strength anisotropy and heterogeneous rotated anisotropy on slope stability were studied separately, without considering their coupled effect. This paper aims to propose a probabilistic analysis framework of slope stability considering the coupled effect of strength anisotropy and heterogeneous rotated anisotropy. Through an undrained clay slope case, the proposed probabilistic analysis framework is examined. The influence of strength anisotropy and heterogeneous rotated anisotropy on slope stability is investigated. The results show that the proposed probabilistic analysis framework of slope stability considering the coupled effect of strength anisotropy and heterogeneous rotated anisotropy is effective. Both strength anisotropy and heterogeneous rotated anisotropy have an important influence on slope stability. Furthermore, the statistics of safety factor including mean value, coefficient of variation, and reliability index, vary with the strength anisotropy coefficient, the heterogeneous anisotropy coefficient, and the rotational angle. The smaller the strength anisotropy coefficient, the larger the heterogeneous anisotropy coefficient, and the smaller the reliability index. The rotational angle of strata corresponding to the minimum and maximum values of the slope reliability index is sensitive to the strength anisotropy coefficient, but not to the heterogeneous anisotropy coefficient.

Soil-rock mixture (SRM) slopes consist of soils and rocks and are widely distributed globally. In addition to heterogeneity and discontinuity within SRM slopes, the inherent spatial variability can be observed in soil and rock properties. However, spatial variability in rock and soil properties and layouts has not been well considered in the stability analysis of SRM slopes. Additionally, SRM slopes commonly show a rotated anisotropic fabric pattern, while such fabric has rarely been accounted for in SRM slope stability analysis. In this study, a two-phase rotated anisotropy random field simulation method is proposed to model these spatial variations simultaneously. The proposed approach is then integrated with the finite element method (FEM) to study the impacts of soil volume fraction and bedding dip angle (i.e., rotated anisotropy) on the probability of failure (pf) and failure mode of SRM slopes. It is found that considering only spatially varying layouts can underestimate pf by up to 97% compared to considering both spatially variable properties and layouts. The increase in soil volume fraction significantly improves pf and the likelihood of deep failure. The bedding dip angle greatly influences pf, yet deep failure remains dominant across different bedding dip angles. Furthermore, the failure mode of SRM slopes is more sensitive to the changes in soil volume fraction than to bedding dip angle.

By incorporating the bedding orientation of soil, this paper numerically investigates the effects of soil's anisotropic and heterogeneous behavior on strip footing under eccentric loading. The lower bound finite element limit analysis in association with second order cone programming is implemented to carry out the analysis by modeling cohesive soil as spatially random field. In order to generate the spatially random discretized soil domain, the well-known Cholesky decomposition technique is utilized. The probabilistic response is obtained by using the Monte Carlo simulation technique. The mean bearing capacity factor, failure probability of the footing for wide ranges of eccentricity, and soil heterogeneity are provided in design charts with respect to different bedding orientations. With the increase of eccentricity, the magnitude of the bearing capacity factor decreases in deterministic as well as probabilistic cases. At lower magnitudes of correlation lengths and eccentricity having different bedding orientations, significant variations are observed both in the magnitudes of mean bearing capacity factor and probability of failure; however, the variations are found to be minimized with the increase in the magnitudes of correlation lengths and eccentricity. Based on the obtained results, required factor of safety is evaluated for corresponding target probability by varying different bedding orientations.

The construction of the 'Dayangyun' Expressway has generated a large number of engineering landslide disaster chains, mainly due to the lack of consideration of the influence of soil sediment anisotropy and slope geometric characteristics on slope stability, instability risk, and failure characteristics. It is urgent to propose a reasonable geometric optimization design method for slopes to prevent the occurrence of such disasters. This study established a random field model that incorporates rotational anisotropy-related structures of strength parameters. Subsequently, the slope reliability index(beta) was computed to evaluate slope stability. Additionally, failure modes were classified, introducing the shallow failure probability (PL) to assess failure risk. Finally, a comprehensive probability analysis framework with two indexes(the beta and PL) was designed to determine the optimal platform width of the slope(Lopt), and two slope cases were utilized for research and application purposes. The results indicate that rotation angles(theta) and platform width (L) significantly impact slope stability and instability risk. As the theta increases, the beta and PL exhibit S and M shaped trends, respectively. Specifically, the beta and PL display a logarithmic and exponential increasing trend with the increase of the L, respectively, this trend determines the Lopt. The dual-index comprehensive probability analysis framework can be employed to assess slope excavation stability and risk, as well as optimize slope geometry design. The research results can be used to prevent the occurrence of excavation slope disasters.

The stratigraphic uncertainty and rotated anisotropy of soil properties exist widely in nature. Recent studies have shown that the slope stability was significantly influenced by these two uncertainties. However, there is no proper method for simulating these two uncertainties at the same time, and the influence of the two uncertainties has not been considered in previous unsaturated soil slope stability analysis. This paper aims to propose a coupled method for characterizing the stratigraphic uncertainty and rotated anisotropy of soil properties, and investigate the unsaturated soil slope stability considering the two uncertainties. Through a slope case, the proposed method for characterizing the two uncertainties is examined. The effect of rotational angle on the slope stability and groundwater table is studied. In addition, four different uncertainty considerations are chosen to compare their influence on the slope stability and groundwater table. The results show that the proposed method can well characterize the two uncertainties at the same time. The rotational anisotropy of soil properties has a substantial impact on the slope stability and groundwater table. The rotational angles corresponding to the maximum and minimum reliability index of slope depend on the uncertainty considerations in the slope stability analysis. The slope reliability index only considering stratigraphic uncertainty is the highest, and the slope reliability index considering stratigraphic uncertainty and rotated anisotropy of soil properties is the lowest.