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.

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.

This paper presents a reliability analysis of circular footings on unsaturated soils. Two methods were used to capture the unsaturated soil behavior: implementing two elastoplastic constitutive models, including the Barcelona Basic Model (BBM) and the Sun Model (SM), which are explicitly proposed for unsaturated soils, and incorporating the apparent cohesion in the Mohr-Coulomb Model (MCM). The effect of soil suction on the bearing capacity of circular footings was investigated. It was shown that for low values of suction, the bearing capacities obtained from MCM were higher than those obtained from BBM and SM. However, as suction increased, MCM tended to predict lower bearing capacities. In practice, geotechnical engineers are still concerned with the measurement and determination of suction as a key stress state variable of unsaturated soils. In this context, the Monte Carlo simulation technique has been incorporated into numerical modeling for the investigation of the effect of suction uncertainties on the bearing capacity. Uncertainties associated with the suction value were modeled as normally and log-normally distributed random variables. It was shown that assuming a normal distribution for suction resulted in slightly lower probabilistic bearing capacity values (i.e., more conservative design) compared to the log-normal distributions. The results emphasized the important role of the coefficient of variation (COV) of suction in determining the probabilistic bearing capacity. A negative linear correlation was observed between the COV of suction and the probabilistic bearing capacity. Finally, a simple relationship was proposed to estimate the probabilistic bearing capacity of the circular footing in an unsaturated soil when its deterministic value and the COV of suction are known.

This study puts forward a reliability analysis for the bearing performance of piles subjected to the coupled action of chloride corrosion and scouring. A chloride diffusion model was constructed based on the stiffness degradation factor and Fick's law. The Monte Carlo simulation method, along with the consideration of the scouring effect of water flow on the pile foundation, was employed to assess the impact of key factors on the failure probability, considering both the bending moment and lateral displacement damage criteria. The results show that for the same exposure period, the failure probability increases as the bending moment, lateral and vertical loads, and seawater velocity increase; furthermore for the same conditions, the failure probability increases with longer exposure times. According to a particular case study, the mean bending moment, mean lateral and vertical loads, and seawater velocity all have an impact on the lateral displacement failure criterion, making it more sensitive than the bending moment failure criterion.

Unsupported excavations are frequently performed in several geological and geotechnical projects, particularly for constructing roads and railways, and they are often carried out in different materials. The design of such cuts in soils needs the determination of representative values of its mechanical properties, particularly of the strength parameters, and the application of adequate safety factors. The procedure should ensure a sustainable design of those cuts, allowing for economical solutions that guarantee a low probability of geological-geotechnical failure. This paper assesses the reliability of unsupported cuts in soils, under drained conditions, assuming a Mohr-Coulomb strength criterion. Statistical meshes are generated considering the spatial variability of the friction angle and of the true effective cohesion, which are assumed to be uncorrelated. In this process, typical values of the coefficients of variation and of the horizontal and vertical scales of fluctuation are applied. Soil characterisation is simulated in each statistical mesh, and the characteristic values of the strength parameters are determined using statistical methods. Unsupported cuts of different heights and inclinations are designed using typical safety factors. Slope stability analyses are carried out using Random Finite Element Limit Analysis. The uncertainty in the actions is considered, and the probability of failure is determined by direct reliability analysis. The results show the relevance of the ratio between the scale of fluctuation and the excavation depth, the slope inclination, and the characteristic value of the soil strength parameters on the probability of failure. Values of adequate safety factors are proposed towards obtaining an appropriate probability of failure, compatible with the sustainable design of the cuts.

The Lesser Himalayan regions face significant geotechnical challenges due to unstable and erosive soil. This study investigates stabilizing these soils with Nano-silica (NS), a reliant additive that has been demonstrated to enhance soil mechanical properties. A comprehensive set of investigations, including multiple laboratory analyses, was conducted to evaluate the mechanical and physical characteristics of problematic soil stabilized with NS. The study also includes reliability analysis to assess the long-term performance and durability of the treated soil. The results of the experiment showed that adding NS greatly increased the soil's compressibility. More precisely, the right amount of NS increased the strength of the problematic soil and resulted in a notable rise in compressibility. According to the durability test results, stabilizing problematic soil with NS and allowing it to cure preserves its improved properties for an extended length of time. Reliability research utilizing probabilistic methodologies showed that applying NS considerably decreased the likelihood of problematic soil failure. The findings show that NS has the potential to be a stable, troublesome soil stabilizer that can lower the probability of soil failure in the Lesser Himalayan regions over the long run. This work provides a foundational understanding for future applications and paves the way for the construction of more robust infrastructure in mountainous terrain.

This paper compares the probabilistic analysis results of earth slopes using Random Variable (RV) and Random Field (RF) approaches, with a focus on potential differences in the mobilized sliding mass. The Finite Element Method (FEM) with Shear Strength Reduction (SSR) is utilized to determine Pore Water Pressure (PWP) and the Factor of Safety (FoS). In the RF approach, random FEM is conducted using crude Monte Carlo Simulation (MCS) and the Karhunen-Lo & egrave;ve expansion, while the RV approach employs the First-Order Reliability method (FORM) and Importance Sampling Monte Carlo Simulation (IMCS). Sensitivity analysis was performed to reveal the most important parameters. The RV results may either underestimate or overestimate the probability of failure (Pf) compared to those obtained by the RF approach. Smaller Pf values are observed in RF with smaller correlation lengths (L) of soil properties. The mean value of the factor of safety (mu FoS) closely matches the deterministic FoS when L is largest, while the coefficient of variation of FoS (COVFoS) increases. Finally, in the RF analysis, it was found that intermediate sliding volumes carry higher risks, with smaller volumes having higher occurrence probabilities and larger volumes having much lower probabilities.

As the threat of natural disasters to structures intensifies, risk assessment of infrastructure has gained much importance. Fragility curves are essential tools in predicting disaster-related losses and making disaster mitigation decisions. In this paper, we propose a new method to efficiently derive accurate fragility curves for structures with high levels of nonlinearity or complexity, addressing the computational challenges of conventional finite element reliability analysis (FERA). To reduce the computational cost for calculating probability of failure in FERA, the proposed method utilizes the first-order reliability method (FORM). However, even with this approach, the computational cost of deriving the fragility curve may remain high; therefore, a surrogate model is used to further reduce costs. By training the surrogate model using the initial structural damage probabilities for a few hazard intensities, an optimal starting point can be calculated for the subsequent FORM analysis. During the fragility analysis, the surrogate model can be updated sequentially to increase the efficiency of FORM analysis continuously. In particular, the training process of the surrogate model requires no separate or additional finite element analysis because it is constructed using previous FERA results. The accuracy and efficiency of the proposed method are tested using conventional FERA and Monte Carlo simulations through a hypothetical short-column example. In addition, fragility curves are derived through a bridge flood fragility assessment considering the scour and seismic vulnerability assessment of a buried gas pipeline considering soil-structure interactions. The derived fragility curves closely match those derived using the conventional FERA, and the computational costs are reduced by 36.54 % and 52.38 %, respectively, compared with the conventional FERA, confirming its cost-effectiveness.

Quantitative assessment of landfill slope failure risk provides valuable information about slope design and risk reduction. This study presents a reliability-based analysis in which an accurate method is applied to assess slope failure risk using the stochastic finite difference method. This method incorporates the spatial variability of municipal solid waste properties due to anisotropic autocorrelation structures and evaluates the consequence associated with each failure separately. This method was evaluated using the data of the Saravan landfill (Rasht, Iran) and presenting a parametric analysis. Several Monte Carlo simulations were conducted to indicate the heterogeneity of the municipal solid waste, taking into account the shear strength and the unit weight of the municipal solid waste randomly. Finally, the safety factor, probability of failure, and risk were assessed using different analysis cases. Deterministic analysis was also performed for all modes using mean values for various municipal solid waste properties. The results show that spatial variability of municipal solid waste parameters and autocorrelation structures significantly affect the safety factor, probability of failure, and risk. Also, comparing the obtained results revealed that for the given slope, the safety factor values in deterministic analyses are overestimated compared to those of the probabilistic analyses. However, risk shows the opposite behavior.