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.

This research investigates a methodology for probabilistic life prediction of buried steel pipelines subjected to external corrosion. A unified methodology is developed considering multiple stages of degradation related to external corrosion (due to soil) and fatigue. These stages include corrosion pit nucleation, pit growth, transition from pit to short crack, short crack growth, transition from short to long crack, stable long crack growth, and unstable fracture. The methodology is useful in obtaining stage-specific forecasts for the fatigue life of buried steel pipelines subjected to external pitting corrosion fatigue. State-of-the-art computational models are used to predict damage initiation and evolution at each stage. The variability in environmental, material, and loading parameters is propagated through these models to obtain a probabilistic estimate of the remaining service life (RSL) of the pipe. Insights from probabilistic RSL prediction highlight the influence of soil type and pipe coating material on corrosion fatigue life. Global sensitivity analysis is then employed to quantify the relative importance of environmental factors (pH, pipe/soil potential, and chloride concentration), material properties (threshold stress intensity factor), and the range of cyclic stress experienced by the pipe.

The seismic performance of underground structures is strongly influenced by the characteristics of both the surrounding soil and the earthquake. In contrast to traditional deterministic analysis methods, this study uses a stochastic analysis approach to investigate the effect of uncertainties in nonlinear soil characteristics, shear wave velocity, density, and earthquake randomness on the response of underground stations. The equivalent linearization method is employed to approximate the nonlinear behavior of the soil. The soil was modeled using a linear elastic constitutive model combined with Rayleigh damping in the finite element model. Inter-story displacements are used to determine structural damage. Probabilistic analysis methods are used to obtain their statistical characteristics, and the probability of failure is calculated. The results show that, according to single parameter analysis, random ground motion results in the greatest probability of exceeding the threshold (PET), while ground shear wave velocity significantly affects the coefficient of variation (COV), and the effect of density is the smallest. The study also found that when soil nonlinearity, shear wave velocity, and random ground motion are considered simultaneously, the range, mean, standard deviation, and COV of interstory displacement all increase significantly, but the PET slightly decreases. In summary, the analysis results indicate that random ground motion has the greatest impact on interstory displacement, followed by shear wave velocity, with nonlinear soil characteristics having a smaller effect, and density the least. Therefore, the impact of various uncertainties should be fully considered in the analysis of underground structures, especially random ground motion and shear wave velocity.

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.

The metropolitan region of Belo Horizonte city is home to several high-risk areas with a significant number of mass movement occurrences. Additionally, there are cases of movements in areas that are not considered high-risk, where constructions exhibit a medium to high construction standard. This emphasizes that, in addition to disordered occupations, the terrains have a natural susceptibility to the process. Intervention in slopes through cuts and fills is an unquestionable necessity in geotechnical projects to reinforce unstable or damaged areas. This article explores the field of soil nailing and presents the necessary design practices for its utilization, including safety checks based on deterministic, probabilistic, and finite element analysis. The case study is based in Belo Horizonte, more specifically in the 'Buritis' neighborhood, Brazil. The reinforced slope has a height of 18.5 meters and covers a total area of 1425 square meters. Based on different methodologies, the solution was validated as the most technically feasible, executable, and financially viable.

The interaction of closely-spaced footings on soils is of concern for recent decades. The inherent variability of soil makes the topic more challenging. This study investigates the behaviour of twin strip foundations on both unreinforced and geogrid-reinforced spatially random sands. The Random Finite Difference is performed by coupling Matlab and FLAC2D in each Monte Carlo simulation. Two types of sands, dense and loose, are assumed as the spatially correlated log-normal random fields and the friction angle is considered a random parameter. This study discusses how much the bearing capacity of twin footings is impressed by the heterogeneity of random sands. The unreinforced soil results show that when the uncertainty of phi is high, the homogeneous soil assumption could overestimate the interference effect by about 18% and 9% in the dense and loose sands, respectively. While soil reinforcement reduces the difference between results obtained from probabilistic analysis with those calculated with deterministic analysis. Moreover, the isotropic random fields with rapid fluctuation of phi yield the greatest interference influence in the unreinforced and reinforced dense sands. The combined impact of interference and reinforcement is greater in loose sand than in dense sand, regardless of whether the soil is heterogeneous or homogeneous.HIGHLIGHTRandom heterogeneous variability of phi on the interaction of the twin foundations on both unreinforced and geogrid-reinforced sand was investigated.For twin footings on unreinforced dense sand, Scr/B changes from 1.25 to somewhere between 1.25 and 1.5 by increasing COV phi, while on the unreinforced loose sand, Scr/B = 1 remains constant, irrespective of COV phi values.For high variability of phi, the assumption of soil without variability results in overestimation of twin footings interference effect by about 18% and 9%, which means the risk acceptance yields irrevocable damages.Increasing the number of geogrid layers, N, declines the risk of estimating the analysis with homogeneous soil, especially for high variability of phi. By all means, the footing interference and geogrid effects become lower when N is added.The interference effect is usually higher for twin footings on unreinforced sand than on the same reinforced sand. Overall, the integrated influence of interference and reinforcement in loose sand is more than that in dense sandThe combined influence of interference and the first geogrid layer is the most in the isotropic random field (theta x = theta y = 1 m) for both sand since the rapid variation of phi in both directions increases the influence and reinforcement effects.The deterministic analysis underestimates the interaction of twin foundations on the reinforced loose sand compared to the anisotropic random fields.

The critical aspect of the seismic bearing capacity of footings holds significant importance in the field of geotechnical engineering. Past research has primarily focused on deterministic analyses, mainly neglecting or ignoring the spatial variability of the soil. This study aims to address this gap by employing a probabilistic approach to assess the seismic bearing capacity of foundations while considering the seismic force effect by adopting the pseudo-static approach. To achieve this goal, this study utilizes the random adaptive finite element limit analysis technique and Monte Carlo simulations to cover a wide range of potential outcomes, taking into account the uncertainties in the parameters. This research investigated the influence of soil strength variability on three key factors: the horizontal seismic coefficient, coefficient of variation, and dimensionless correlation length. The study revealed that an increase in the coefficient of variation of the undrained shear strength (COVsu) and the dimensionless correlation length (Theta su) leads to a reduction in the mean of the random seismic bearing capacity factor (mu Nran). Conversely, the horizontal seismic coefficient (kh) negatively impacts the seismic bearing capacity, thereby diminishing the overall soil stability. Additionally, the factor of safety must be selected with caution to ensure that the probability of failure is less than a specified value, particularly when the coefficient of variation of the undrained shear strength (COVsu) is high. To establish surrogate models capable of predicting the random seismic bearing capacity, multivariate adaptive regression spline (MARS) models have been developed. Utilizing the proposed MARS surrogate models offers a more convenient and computationally efficient means of evaluating the impact of variability in soil strength properties on geotechnical stability calculations.

The fundamental issue of bearing capacity of footings on anisotropic clays holds significant importance in geotechnical engineering. Previous investigations predominantly focused on deterministic analyses, disregarding the spatial variability of soil. A probabilistic analysis of the bearing capacity of footings is conducted in this paper, incorporating the spatial variability of anisotropic clays. To achieve this, Random Adaptive Finite Element Limit Analysis (RAFELA) and Monte Carlo simulations are utilised to capture the full spectrum of potential outcomes under parametric uncertainty. The impact of anisotropic soil strength variability is explored across three input parameters such as the anisotropic strength ratios, coefficients of variation, and dimensionless correlation lengths. In order to establish surrogate models capable of predicting random bearing capacity of anisotropic clays, Artificial Neural Network (ANN) models are developed. The use of the proposed ANN surrogate models presents a more convenient and computationally efficient approach for predicting the ultimate vertical load of footings on spatially random anisotropic clays.

The susceptibility mapping of rainfall-induced landslides is an effective tool for predicting and locating disaster-prone zones at the regional scale. One of the most important parts of landslide susceptibility models is the hydrological model. In this context, the present study considers three pore water pressure (PWP) profiles with surface runoff to estimate the spatiotemporal variation of wetting front depth (WFD) during rainfall episodes. To reasonably simulate the inherent uncertainty and variability involved in the hydrogeomechanical properties of the surficial soil layers at the regional scale, probabilistic analysis based on the recursive first-order reliability method (FORM) is employed to calculate the probability of slope failure. The regional time-dependent landslide susceptibility mapping is realised using a newly developed model called Physically-based probabilistic modelling of Rainfall Landslides using Simplified Transient Infiltration Model (PRL-STIM). The proposed model is applied in a representative area that suffered extensive rainfall-induced landslides in July 2013 (Niangniangba Town, Gansu Province, China). The results indicate that the PRL-STIM model achieved a satisfactory prediction accuracy of 75% AUC compared to existing models like transient rainfall infiltration and grid-based regional slope-stability model (72%) and the probabilistic analysis results based on the first-order second moment method (74%). It also performed well in predicting the spatial distribution of shallow landslides, with a success rate of 81.6%. Regarding the model efficiency, the completion of a raster file for calculating the landslide probabilities of the study area (including 711,051 cells) requires only 17.1 s. It is thus hoped that the proposed calculation framework of PRL-STIM that considers various uncertainties (e.g., nonlinearity of the physical model, non-normal probability distributions, random variable cross correlations, etc.) in geotechnical parameters is better suited for landslide susceptibility mapping at the regional scale, where only limited historical event data is available.

Engineers are tasked with the challenging task of evaluating the performance and analyzing the risk of systems in the context of performance-based seismic design. All sources of random uncertainty must be taken into account during the design phase in order to complete this assignment. The performance limit states for a structure must be defined using appropriate procedures that take into consideration the system characteristics describing the structure, the soil, and the loads applied to the structural reactions. The main objective of this study is to conduct an in-depth analysis, both linear and non-linear (Pushover), of seismic vulnerability for a reinforced concrete (RC) structure. This aims to probabilistically evaluate the effectiveness of composite materials, particularly those reinforced with glass and carbon fibers, in reducing seismic risk when used to reinforce structural columns. The outcomes of this study will provide valuable insights into the efficacy of FRP reinforcements in enhancing seismic resistance, regardless of the analytical approach adopted (linear or non-linear). They reveal a seismic risk reduction of 48 % for structures equipped with glass fiber-reinforced columns and 67 % for those with carbon fiber-reinforced columns.