This paper presents a method for analyzing slope stability in anisotropic and heterogeneous clay using a strength reduction finite element method (SRFEM) integrated with the level set method (LSM). Anisotropy refers to the inherent anisotropy in the clay's strength, while heterogeneity describes the spatial variability in strength parameters. The static LSM uses a zero level set function to model heterogeneous clay slopes. The method is validated through undrained slope stability analyses on different types of anisotropic clay and heterogeneous fields, showing its effectiveness in modeling anisotropic shear strength and capturing the characteristics of heterogeneous regions. The results indicate that the proposed method accurately predicts factors of safety and slip surfaces across various soil conditions, accounting for both anisotropic and heterogeneous characteristics.

The study presents a comprehensive study on the assessment of the bearing capacity of closely spaced strip footings on c-& oslash; soil, considering spatial variability in soil properties. A linear elastic model is employed for footings and elastic-perfect plastic soil behaviour via the Mohr-Coulomb yield criterion. Soil properties obtained from extensive field investigations of Taranto Blue Clay (TBC) in Italy are modelled as stationary random fields (RFs) generated using the Fourier series method. The cohesion and friction angle RFs are integrated with the Z-soil FE code. The final results are obtained according to the random finite element method (RFEM). The study investigates the influence of spacing distances between footings and spatial correlation lengths of soil parameters on the bearing capacity. Results show how spacing distance affects bearing capacity. Moreover, it indicates that neighbouring footing bearing capacity is strongly correlated with investigated parameters. In the case of small spatial correlation lengths, the patterns were obtained as non-symmetrical, transitioning to more symmetrical patterns at larger lengths. The manuscript concludes by presenting reliability-based design considerations for the ultimate bearing capacity, considering the horizontal spatial scale of fluctuation (SOF). The findings emphasize the importance of evaluating allowable design bearing capacity for proximity structures using RFEM and provide valuable insights into the interplay between spacing distances and spatial variability in soil properties. To this end, the study underscores the critical interplay between spacing distance, spatial correlation lengths, and random soil properties in assessing neighbouring footing-bearing capacities.

This study aimed to emphasize the significance of spatial variability in soil strength parameters on the behavior of nailed walls, highlighting the necessity of probabilistic design approaches. The investigation involved a 7.2-m nailed wall reinforced with five nails, simulated using the local average subdivision random field theory combined with the limit equilibrium method and the FEM, known as the random limit equilibrium method (RLEM) and the random finite-element method (RFEM) approaches. Initially, the wall stability was evaluated by RLEM using 10,000 Latin hypercube sampling realizations. The wall was globally stable among all samples for a correlation length equal to its height (7.2 m). The wall behavior, associated displacements, moments, wall shear forces, nail axial forces, and ground settlements were examined using RFEM. The RFEM analysis reveals that different random fields influence the maximum displacement (H-max), maximum moment (M-max), and maximum shear force (Vmax) experienced by the wall. The cumulative distribution function plots were generated for the wall critical parameters, including H-max, M-max, and V-max. Leveraging the simple weighted averaging and ordered weighted averaging techniques, different combinations of H-max, M-max, and Vmax were assessed with varying weight assumptions. This allowed us to identify critical random field realizations and estimate the level of risk using a newly introduced parameter, the decision index. Finally, the effect of different correlation lengths (isotropic and anisotropic) for two different coefficients of variation of soil strength parameters on the distribution of H-max, M-max, and Vmax was studied. The findings highlight the importance of considering the spatial variability of soil properties to achieve a reliable design of nailed walls.

The spatial variability of soil properties is pervasive, and can affect the propagation of seismic waves and the dynamic responses of soil-structure interaction (SSI) systems. This uncertainty is likely to increase the damage state of a structure and its risk of collapse. Additionally, conducting multiscale simulations efficiently in the presence of uncertainties is a pressing concern that must be addressed. In this work, a 3D probabilistic analysis framework for an SSI system considering site effects and spatial variability of soil property (i.e., elastic modulus, E) has been proposed. This framework is based on the random finite element method (RFEM) and domain reduction method (DRM). A multiscale model of a five-story reinforced concrete (RC) frame structure was developed on an ideal 3D slope to verify the effectiveness of the proposed framework. The dynamic responses of the structure were analyzed, and the peak floor acceleration (PFA) and peak interstory drift ratio (PSDR) were selected to estimate the damage state of structures. It was found that the proposed method significantly improves computational efficiency approximately 20 times compared with the direct method. In the regional models, with the increase of the coefficient of variation (COV) of E, the energy of seismic waves becomes more concentrated at the crest and the response spectrum value of medium and long periods increases. In the local SSI model, the soil variability increases the mean value of PSDR, resulting in a more severe damage state compared to the results from the deterministic analysis. Consequently, this study provides some suggestions for engineering practice, and the importance of probabilistic analysis considering spatially variable soils in the SSI problem is highlighted.