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.

Antislide piles are currently applied widely in slope reinforcement engineering, but investigation of the stability of slopes stabilized with this measure under the action of mainshock-aftershock (Ms-As) sequences is very limited. In this study, the probability density evolution method (PDEM) and the Newmark method is adopted to evaluate the reliability of slope reinforced by antislide piles subjected to Ms-As sequences considering the spatial variability of material parameters. Firstly, stochastic Ms-As sequences are generated by combining a physical function model, the Copula function, and the narrowband harmonic group superposition method. In addition, the spectral representation method is taken to generate the random field and the parameters are assigned to the numerical model. Then, the Newmark method is applied to batch-calculate the permanent displacement (Disp) of the slope caused by the Ms-As sequences. The effects of pile position, pile length, and coefficient of variation of cohesion and friction angle (COVC and COVF) on the average value of Disp are discussed. Finally, based on the PDEM, the seismic reliability of the slope strengthened by antislide piles subjected to the Ms-As sequences are obtained. The research results indicate that with the COV increases, the average value of Disp of the slope shows a gradual tendency to increase, and the average value is more sensitive to COVC. Compared with the unreinforced slope, the Disp of the slope strengthened by antislide piles is reduced. The cumulative damage caused by the aftershock and the risk of failure can be significantly reduced by setting a reasonable antislide pile.

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.

Determining the burial depth for offshore pipelines to resist impact load is challenging owing to the spatial variability of soil strengths, which proves to significantly affect failure behaviours of soils and pipelines. To facilitate the design, accurate and fast evaluation on pipeline damage is required. Here, an integrated surrogate model was developed to forecast impact damage of pipelines buried in spatially varied soils. Through coupling the random field and numerical simulation, a stochastic finite element analysis framework was derived and verified to yield the datasets; Based on the scheme of feature extraction - integration from convolution neural network, the surrogate model was established, which mapped the three-dimensional soil spatial field to the structural response. Prediction mechanism of the developed model was explored, where correlations among soil spatial distribution patterns, failure mechanisms and feature recognitions were discussed. The models enabled to capture the key features representing the failure mechanisms under random soil conditions, including the local failure mode of soil and pipe-soil interactions, which theoretically explained its feasibility in damage estimation. Further, model performance was comprehensively evaluated with regard to prediction accuracy, uncertainty quantification, and transfer learning, and the corresponding causes were investigated. Satisfactory performance and high computation efficiency were demonstrated.

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 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 mechanical properties of soil, resulting from the weathering of rocks through physical and chemical processes, exhibit spatial variability. This variability introduces uncertainties in the design and characteristics of excavation projects. To address these uncertainties caused by soil spatial variability, safety factors are commonly used in excavation design. However, using the same safety factor for different indicators of soil spatial variability is illogical. Therefore, specialized research on the characteristics of deep excavations in the context of soil spatial variability is necessary, as it provides the theoretical basis for rational excavation design. In this study, we assumed that soil parameters follow a lognormal distribution, while spatial correlation adheres to a Gaussian function. We developed a random finite element algorithm for deep excavations, which incorporated Python programming and the ABAQUS computational platform. This algorithm was created within the framework of random field theory and Monte Carlo simulation. The results of our study indicate that, influenced by soil spatial variability, the lateral wall movements and ground surface settlements exhibit discrete distributions near the deterministic results. The maximum deformation of the excavation follows a normal distribution, while the pattern of ground surface settlements demonstrates diversity and chaotic characteristics. The extent to which soil spatial variability affects deep excavations is correlated with indicators of this variability. As the coefficient of soil spatial variability increases, the diversity and chaotic characteristics of ground surface settlements become more prominent. The locations of maximum ground surface settlement and maximum deformation becomes more scattered. Consequently, the probability of excavation failure increases, and the reliability index of the excavation decreases. In summary, soil spatial variability significantly impacts deformation prediction and safety control during the design and construction stages of deep excavations. Therefore, it is crucial to consider the influence of soil spatial variability when designing deep excavations, based on the variability indicators.

To investigate the asymmetric deformation and stress characteristics of tunnels and support structures in high geostress layered fractured rock, this paper establishes two refined modeling methods: a numerical model for anchor bolt failure and a model for fractured layered surrounding rock, while considering the spatial variability of soil. The study analyzes tunnel deformation and bolt tensile-shear fracture mechanics under varying bedding angles. The results indicate that: (1) the most unfavorable stress position for tunnel structures in layered fractured rock typically occurs normal to the bedding planes; (2) the tunnel's asymmetric deformation is due to normal compressive and tangential sliding effects of geostress on the bedding planes. When the bedding angle is gently inclined, significant extrusion deformation occurs at the tunnel crown and invert; when steep, substantial tangential sliding forces cause maximum deformation at points where the bedding direction is tangent to the tunnel profile. (3) Fracture development in the surrounding rock primarily occurs normal to the foliation planes, similar to maximum displacement deformation patterns, while other areas propagate outward due to joint shear slip. (4) In layered fractured rock, failed bolts predominantly show tensile-shear fractures, influenced by bedding angle, particularly near the left shoulder to the crown and right invert. Finally, based on the deformation characteristics of layered fractured surrounding rock and the mechanical properties of anchor rod fracture, reasonable differential support optimization measures were proposed, and the simulation results were applied to the Yangjiaping Tunnel of the Chenglan Railway in China.