Iron pipes connected by bell-spigot joints are utilized in buried pipeline systems for urban water and gas supply networks. The joints are the weak points of buried iron pipelines, which are particularly vulnerable to damage from excessive axial opening during seismic motion. The axial joint opening, resulting from the relative soil displacement surrounding the pipeline, is an important indicator for the seismic response of buried iron pipelines. The spatial variability of soil properties has a significant influence on the seismic response of the site soil, which subsequently affects the seismic response of the buried iron pipeline. In this study, two-dimensional finite element models of a generic site with explicit consideration of random soil properties and random mechanical properties of pipeline joints were established to investigate the seismic response of the site soil and the buried pipeline, respectively. The numerical results show that with consideration of the spatial variability of soil properties, the maximum axial opening of pipeline joints increases by at least 61.7 %, compared to the deterministic case. Moreover, in the case considering the variability of pipeline-soil interactions and joint resistance, the spatial variability of soil properties remains the dominant factor influencing the seismic response of buried iron pipelines.

Investigations of seismic response of underground structures often assume homogeneous or layered homogeneous sites. However, significant spatial variability in soil parameters may lead to vastly different underground structure performance from that obtained for homogeneous sites. Based on random field theory, this study models the spatial variability of the soil elastic modulus, cohesion, and friction angle using the Karhunen-Loe`ve (K-L) expansion method. Target acceleration response spectra are generated according to standards, and the trigonometric series method is employed to create artificial seismic waves of four different intensities. Nonlinear dynamic analyses of underground structures under deterministic and random field conditions are conducted using ABAQUS software. The study comprehensively analyzes the structural damage state, internal forces, interstory displacement, and drift ratio to evaluate the station structure's performance under different seismic intensities. Results show that the spatial variability of soil parameters significantly impacts the dynamic response of underground structures, especially for stronger earthquakes. The variability of soil stiffness and strength parameters leads to greater fluctuations and uncertainties in displacement and internal force responses, exacerbating structural damage. It is recommended that when the peak ground acceleration (PGA) reaches or exceeds 0.5 g, the spatial variability of soil parameters should be incorporated into the analysis to ensure a reliable assessment of the structural seismic performance.

Soil-water characteristics, which vary with hydrological events such as rainfall, significantly influence soil strength properties. These properties are crucial determinants of the bearing capacity of foundations. Moreover, shear strength characteristics of soils are inherently spatially variable, and considering them as homogeneous parameters can result in unreliable design. This paper presents a probabilistic study of the two-dimensional bearing capacity of a strip footing on spatially random, unsaturated fine-grained soil using Monte Carlo simulation. The study employs the hydro-mechanical random finite difference method through MATLAB programming along with FLAC2D software. The undrained shear strength under saturated conditions is modelled as random fields using a log-normal distribution. The generated random values are then made depth-dependent by correlating them with matric suction. Initially, matric suction is assumed to be under a hydrostatic condition and decreases linearly with depth to zero at the groundwater level. Afterward, unsaturated soil is subjected to rainfall with different durations, resulting in the non-linear distribution of matric suction and, consequently, the mean value of undrained shear strength in depth. The results showed that rainfall infiltration impacts the strength characteristics of near-surface heterogeneous strata, leading to significant effects on the bearing capacity and failure mechanism of footing.

Frost damage on infrastructure in seasonally frozen regions is mainly caused by the coupled water-heat transfer during freeze-thaw processes. Because of complex geological deposition and weathering, the properties of seasonally frozen soil are spatially variable. In this study, based on random field theory, heat transfer process, and frozen soil physics, a water-heat coupling model is developed to explore the impact of non-uniform thermal parameters on soil water-heat behavior. The statistical characteristics of the water-heat behavior and frozen depth of a slope are analyzed. The simulation results show that the water-heat coupling process of the soil exhibits obvious seasonal differences. The uncertainty in thermal conductivity has a greater effect on soil waterheat state than the uncertainty in volumetric heat capacity. The maximum frozen depth (MFD) from the traditional deterministic analysis is slightly smaller than the mean value of analysis result considering the nonuniformity of thermal parameters; as such, the deterministic analysis is likely to underestimate the MFD, which may result in local frost damage to infrastructure in cold regions. To ensure the safety of infrastructure in cold regions, the most unfavorable conditions need to be considered, and the upper bound of the MFD based on the random analysis can serve as the guideline for frost protection design.

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.

The slope has an adverse effect on the ultimate bearing capacity of shallow foundations. Due to inherent variability in soil properties and geometric factors of slopes, designing a foundation on slopes is a perplexing and challenging task. The spatial variation in the soil's shear strength property is commonly ignored by the designers to avoid complexity in design. Shear strength property in real scenarios increases along the depth and simultaneously it poses spatial variability. This kind of randomness is modelled using a non-stationary random field. The proposed study aims to evaluate the probabilistic bearing capacity of strip footing on spatially varying slopes. The probabilistic bearing capacity factor is analyzed for different influential factors like geometry and footing placements, correlation distances and coefficient of variation of soil properties. Slopes exhibiting nonstationary characteristics contribute to remarkable differences in the bearing capacity of footing as compared to the stationary condition. The study highlights that the geometry factors, footing placements, soil spatial variability and most importantly the increasing trend of soil strength play a critical role in the bearing capacity and risk of failure of a footing. High variations in the failure probability can be observed even after considering safety factors.

The study deals with reliability analysis of strip foundation on spatially variable c - phi soil. The spatial variability of soil strength parameters, namely cohesion c and friction angle phi is modelled using anisotropic uncorrelated random fields, generated with the Fourier series method. Random finite element limit analysis (RFELA) providing a rigorous lower and upper bound for bearing capacity for individual Monte-Carlo simulations is employed. Additional use of adaptive meshing refinement algorithm leads to a significant reduction of the relative difference between statistical moments of obtained lower and upper bound results. The influence of the horizontal and vertical scales of fluctuation and foundation depths on the mean and standard deviation of the obtained bound moments is investigated. Additionally, the rigorousness of the mean and standard deviation of both considered bounds estimation is checked. As a result of the analysis, a novel approach based on a mixed distribution that combines lower and upper bound moments is introduced. As shown, this approach offers significant benefits by providing conservative and relatively precise measures of reliability which can be obtained in reasonable computation time. The proposed method seems to be adequate for practical engineering reliability analysis of foundation bearing capacity and other limits states problems.

Depth to bedrock (DTB) is a critical factor for rainfall-induced slope failures. However, the influence of uncertainties in these measurements, particularly at a small-scale, has not been fully understood. Numerical modeling was conducted to assess the impact of a variable bedrock topography on the stability of a real-world unsaturated slope. The simulations included a three-dimensional pore-water pressure estimation, derived from the numerical solution of the Richards equation, coupled with a slope stability assessment using numerical limit analysis. The study explored the potential of incorporating random fields (RFs) into an established DTB model to improve the understanding of rainfall-triggered landslides. The proposed methodology was applied to the analysis of a small watershed within the Papagaio River basin in Brazil, an area historically subjected to landslides triggered by rainfall events. Our main findings reveal that small variations in DTB can significantly impact the safety factor and probability of failure estimations. Furthermore, they influence the shape, location and failure volume associated to predicted landslides. The incorporation of RFs effectively addresses small- scale uncertainty in DTB, controls bedrock morphology, and enhances the assessment of probabilistic numerical modeling for landslide susceptibility. This study highlights the importance of accurate and comprehensive DTB characterization for assessing rainfall-induced landslides at local slope scale.

The in-situ stress can significant influence the damage caused to rock. A comprehensive analysis of the in-situ stress field is essential for tunnel design, construction and geological monitoring. This study establishes a 3D geologic model using the finite difference method, explicit considering material heterogeneity through random field theory. After conducting 300 simulations, the distribution pattern of the in-situ stress field was statistically analyzed. The inversion accuracy, considering material heterogeneity, is superior to that for homogeneous materials at the measurement points, with smaller relative errors. The extent of in-situ stresses in both the horizontal and vertical directions of the model depend not only the burial depth but also on the physico-mechanical properties of the material. In particular, the distribution of the in-situ stress field exhibits heterogeneity in localized regions, influenced by the material's variability. In the river valley area, the river valley bank slopes are divided into three zones based on the stress force values: the stress release zone, the stress concentration zone, and the virgin rock stress zone. The stress distribution around the tunnel shows significant non-uniformity and irregular fluctuations, with alternating high-stress and low-stress regions. Notably, stress concentration occurs at the crown, sidewalls, and both sides of the tunnel bottom. These in-situ stress fields, which account for the spatial variability of rock parameters, provide a more realistic and accurate reference for engineering practice.

The aim of this study is to investigate the influence of rock variability on the failure mechanism and bearing capacity of strip footings. A probabilistic analysis of the bearing capacity of footings on rock masses is conducted in this paper, where random adaptive finite-element limit analysis (RAFELA) with the Hoek-Brown yield criterion and the Monte Carlo simulation technique are combined. The stochastic bearing capacity is computed by considering various parameters, such as the mean values of the uniaxial compressive strength of intact rock, Hoek-Brown strength properties, coefficient of variance, and correlation lengths. In addition to the RAFELA, this study introduces a novel soft-computing approach for potential future applications of bearing capacity prediction by employing a machine learning model called the eXtreme Gradient Boosting (XGBoost) approach. The proposed XGBoost model underwent thorough verification and validation, demonstrating excellent agreement with the numerical results, as evidenced by an impressive R2 value of 99.99%. Furthermore, Shapley's analysis revealed that the specified factor of safety (FoS) has the most significant influence on the probability of failure (PoF), whereas the geological strength index (GSI) has the most significant effect on the random bearing capacity (mu Nran). These findings could be used to enhance engineering computations for strip footings resting on Hoek-Brown rock masses.