Bedrock-soil layer slopes (BSLSs) are widely distributed in nature. The existence of the interface between bedrock and soil layer (IBSL) affects the failure modes of the BSLSs, and the seismic action makes the failure modes more complex. In order to accurately evaluate the safety and its corresponding main failure modes of BSLSs under seismic action, a system reliability method combined with the upper bound limit analysis method and Monte Carlo simulation (MCS) is proposed. Four types of failure modes and their corresponding factors of safety (Fs) were calculated by MATLAB program coding and validated with case in existing literature. The results show that overburden layer soil's strength, the IBSL's strength and geometric characteristic, and seismic action have significant effects on BSLSs' system reliability, failure modes and failure ranges. In addition, as the cohesion of the inclination angle of the IBSL and the horizontal seismic action increase, the failure range of the BSLS gradually approaches the IBSL, which means that the damage range becomes larger. However, with the increase of overburden layer soil's friction angle, IBSL's depth and strength, and vertical seismic actions, the failure range gradually approaches the surface of the BSLS, which means that the failure range becomes smaller.

The horizontal displacement of monopile under cyclic loading is subject to uncertainty due to variations in metocean conditions and soil parameters at offshore wind farms. However, the current design for cyclically loaded monopiles relies on the p-y method recommended by API and DNV, which does not accurately capture the horizontal displacement of the monopiles. In this study, finite element simulations are performed using ABAQUS, where the soil is modeled with the Einav-Randolph model to account for soil softening effects. The impact of parameter uncertainties, such as soil stiffness, undrained shear strength, and the pile-soil friction coefficient, on the reliability index of the monopile's horizontal displacement for different length diameter (L/D) ratios is investigated. A case study is provided to assess the horizontal displacement reliability of a monopile under cyclic loading. The results show that the horizontal displacement reliability index decreases as the coefficient of variation (COV) of the random variables, the correlation coefficient, and the monopile's L/D ratio increase. Conversely, the reliability index increases with an increase in the allowable horizontal displacement. The horizontal displacement reliability index is most sensitive to soil stiffness, followed by undrained shear strength and pile-soil friction coefficient. The findings of this study offer valuable insights into how parameter uncertainties influence the horizontal displacement of monopiles under cyclic loading.

The influence of soil variability on the probabilistic bearing capacity of strip footings near slopes has been extensively studied, particularly under short-term undrained conditions. However, these investigations, predominantly based on the plane-strain assumption, fall short in accurately estimating the bearing capacity of square and rectangular footings and in capturing the spatial variability of soils. This study focuses on short-term undrained conditions and employs the random finite element method (RFEM) and Monte Carlo simulation (MCS) techniques to explore the effect of rotational anisotropy on the bearing capacity response and failure probability of a square and rectangular footing-cohesive slope system under a three-dimensional (3D) framework. The findings reveal that the rotation angles of soil strata significantly impact both the mean and coefficient of variation of the bearing capacity, with distinct variation patterns emerging for different footing orientations and aspect ratios. Typical failure patterns are identified, illustrating the correlation between the bearing capacity response, the footing orientations and aspect ratios, and the extension direction of plasticity. The probabilistic results are presented as probability density functions (PDF) and cumulative distribution functions (CDF) for various rotation angles around the x-axis and y-axis and for different L/B ratios of the footings. Additionally, detailed design tables, including failure probability results and corresponding safety factors for specific target failure probabilities, are provided to guide engineering applications.

Steel and reinforced concrete buildings are popular structural systems. The design of these buildings is regulated by deterministic building codes. In this context, it is established that if building codes are followed, the structure will resist demands without collapsing. However, no regulation is required to control the damage of structures in terms of performance criteria. In this paper, the seismic performance and structural reliability of both steel and reinforced concrete buildings, respectively, are analyzed as a benchmark case of study. Both buildings are designed in an earthquake-prone area for two soil types, respectively. Subsequently, nonlinear dynamic analyzes are conducted and the seismic responses of the models are determined in terms of inter-story drift. To obtain seismic responses, eleven characteristic ground motions of the region are selected corresponding to three performance levels: (1) immediate occupancy, (2) life safety, and (3) collapse prevention, respectively. It was documented that the resulting maximum inter-story drift was much lower than the one obtained from modal analysis. In addition, the risk was computed in terms of reliability index integrating a novel probabilistic approach with performance-based design criteria. According to the results, a small variation in the structural risk among the buildings under consideration is observed. However, buildings designed for rigid soil proved to be more reliable. Additionally, it is observed that the buildings designed with current regulations are too conservative based on the performance criteria limits. Hence, structures located on earthquake-prone areas may be overdesigned when implementing deterministic building codes.

For offshore platforms installed in seismically active regions, maintaining the safety of operations is an important concern. Therefore, the reliability of these structures, under earthquake ground motions, should be evaluated accurately. In this study, reliability methods are applied to determine the probability of failure of jacket platforms against extreme level earthquake (ELE), considering uncertainties in ground motions and the properties of the structure and soil. They are verified by two variance reduction Monte Carlo sampling methods to find the most efficient method in terms of both accuracy and calculation time. During the ELE event, also called strength level earthquake, structural members and foundation components are permitted to sustain localised and limited nonlinear behaviour, so a force-based criterion is utilized for the limit-state function. The results indicate that all reliability methods, except for FOSM, provide a good approximation of the probability of failure. Also, Point-fitting SORM is the most efficient method.

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 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.

Buried steel gas pipelines are increasingly facing safety challenges due to the escalating traffic loads and varying burial depths, which could potentially lead to hazards such as leakage, fire, and explosion. This paper investigates stress mechanisms in buried steel gas pipelines subjected to vehicular loading through integrated analytical approaches. Theoretical modeling incorporates three key components: dynamic vehicle load characteristics, soil-pipeline interaction pressures, and stress distribution angles across pipeline cross-sections. Stress variations are systematically quantified under varying soil conditions and load configurations. A finite-element model was developed to simulate pipeline responses, with computational results cross-validated against theoretical predictions to establish stress profiles under multiple operational scenarios. Additionally, this paper employ fatigue accumulation damage and reliability theories, utilizing Fe-Safe software to evaluate pipeline reliability, determining fatigue life and strength coefficients for various loads and burial depths. Based on these analyses, this paper develop risk control measures and protective methods for buried steel gas pipelines, validated through finite-element and fatigue analyses. Overall, this paper offers insights for preventing and controlling risks to buried steel gas pipelines under vehicle loads.

In order to investigate the impact of plant root systems on the stability of loess shallow slope, this study conducted plant morphology investigations and direct soil shear tests to analyse the morphological characteristics of alfalfa and the shear characteristics of alfalfa root-loess composites under different soil bulk densities and soil moisture saturation levels. Additionally, the reinforcing effect of the alfalfa root system on the reliability of loess slopes was assessed using the Monte Carlo method. Slope reliability analysis refers to the estimation of the probability of slope failure under specific conditions. The results showed that plant weight and root weight both decreased following an exponential function with increasing soil bulk density. Root weight had a positively linear correlation with plant weight. The cohesion and internal friction angle of both loess samples without roots and with roots increased with increasing soil bulk density. The cohesion and internal friction angle of the two kinds of samples could decreased at less and more than 30% soil moisture saturation. The cohesion and internal friction angle of the root-soil composites were significantly higher than those of the rootless soil. The decrease of soil bulk density and the increase of soil moisture could increase the difference of the two mechanical parameters between the two kinds of samples. Assuming the thickness of the landslide body was 0.3 m, the failure probability of loess slopes covered with alfalfa significantly decreased from 34.97 to 14.51% compared to slopes without vegetation cover. Alfalfa roots significantly increased the reliability of the loess slopes in stability.

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.