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.

Sudden and unforeseen seismic failures of coal mine overburden (OB) dump slopes interrupt mining operations, cause loss of lives and delay the production of coal. Consideration of the spatial heterogeneity of OB dump materials is imperative for an adequate evaluation of the seismic stability of OB dump slopes. In this study, pseudo-static seismic stability analyses are carried out for an OB dump slope by considering the material parameters obtained from an in-situ field investigation. Spatial heterogeneity is simulated through use of the random finite element method (RFEM) and the random limit equilibrium method (RLEM) and a comparative study is presented. Combinations of horizontal and vertical spatial correlation lengths were considered for simulating isotropic and anisotropic random fields within the OB dump slope. Seismic performances of the slope have been reported through the probability of failure and reliability index. It was observed that the RLEM approach overestimates failure probability (Pf) by considering seismic stability with spatial heterogeneity. The Pf was observed to increase with an increase in the coefficient of variation of friction angle of the dump materials. Further, it was inferred that the RLEM approach may not be adequately applicable for assessing the seismic stability of an OB dump slope for a horizontal seismic coefficient that is more than or equal to 0.1.

This study aims to develop hazard curves to assess the reliability of shallow foundation design on sandy soils. The random finite element method was employed to analyze the elastoplastic behavior of soils with spatially varying deformation modulus and angle of shearing resistance, which were generated as random fields and assigned to the analysis models. The output distributions were fitted with a corresponding probability density function (PDF), and the probability of exceedance (Pf) for determined damage limits was estimated from these PDFs, forming the proposed hazard curves for the determined anisotropy ratios. The method proposed in the study was validated by a database containing field test measurements, and a sample problem was presented to exemplify the application of hazard curves. The significant contribution of this study is to form the hazard curves for superficial foundations on sandy soils by considering both the elastoplastic behavior of soil and the influence of all effecting parameters, which satisfy the serviceability limits in the foundation design codes. The curves proposed in this study provide an approach for probabilistic investigation of superficial foundations taking the variability of sands into account and robust technique for the reliability-based design of strip footings with a serviceability limit state.

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.

The amplification of seismic waves due to surface topography and subsurface soils is a significant factor contributing to seismic site amplification and consequent damage. However, conventional deterministic analysis methods can hardly account for the impact of inherent spatial variability of subsurface soil properties. This study employs a random finite element method (RFEM) to address this limitation and investigate the amplification of ground acceleration in time and frequency domains for 2D slope models with varying magnitudes of soil elastic modulus (E) and coefficients of variation (COVs). Comprehensive insights are provided through the analysis of amplification indicators related to peak ground acceleration, Fourier spectrum ratio, and response spectra of input motion. It is found that the spatial variability of E reduces the maximum amplification factor (AF) at the slope crest. Frequency domain analyses show that considering spatially variable E leads to decreasing trends in Fourier spectra and mean values of the transfer function, especially in the mid-to-high-frequency range. However, transfer functions for topographic effects exhibit high-frequency amplification in models with a higher impedance ratio. For the response spectra, the topographic amplification factor (TAF) and spectra amplification factor (SAF) at longer periods gradually increase in random simulations, indicating the potential risk for long-period structures. The findings emphasize the significance of spatial variability in soil properties for seismic amplification, providing probabilistic insights for seismic design and optimization in complex site conditions.