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A novel approach based on the upper bound theory is proposed to assess the stability of excavated slopes with spatially variable clay in undrained conditions. The proposed random limit analysis is a combination of the deterministic slope stability limit analysis together with random field theory and Monte Carlo simulation. A series of analyses is conducted to verify the potential application of the proposed method and to investigate the effects of the soil undrained shear strength gradient and the spatial correlation length on slope stability. Three groups of potential sliding surfaces are identified and the occurrence probability of each sort of failure mechanism is quantified for various slope ratios. The proposed method is found to be feasible for evaluating slope reliability. The obtained results are helpful in understanding the slope failure mechanism from a quantitative point of view. The paper could provide guidance for slope targeted local reinforcement. [ABSTRACT FROM AUTHOR]

A novel deep learning method based on the two-dimensional convolutional neural network (2D-CNN) was proposed to predict the horizontal and vertical convergences of high-speed railway tunnels considering the spatial variability of soil Young's modulus. The input and output of the neural network were the soil Young's modulus random field and tunnel convergence, respectively. The coefficient of determination (R2) and the relative error of the predicted results were determined to evaluate the prediction performance and extrapolating ability of the proposed CNN model. The prediction accuracy increased with increasing scale of fluctuation (SOF) from 10 to 60 m as the R2 increased. Two prediction data sets with 10,000 samples (per set) were generated to illustrate the model, where the R2 values were greater than 0.99. Also, the relative errors of the limit values of 90% and 99% exceeding the probability between the CNN-predicted and random finite difference method (RFDM)-calculated convergences were within 0.64%. The computational efficiency was significantly improved by 2,371 times with satisfactory accuracy. The trained CNN model showed excellent extrapolation ability in solving cases with an anisotropic random field and variation of COV. Results indicated that the proposed CNN model is a promising surrogate of RFDM with Monte Carlo simulations to analyze tunnel convergence considering soil Young's modulus in an isotropic random field. The spatial variability of soil parameters is commonly believed to have a significant influence in assessing tunnel reliability. Traditional probabilistic analysis of tunnel deformation was generally conducted by time-inefficient random finite-element/difference methods with Monte Carlo simulations. Recently, machine learning methods are vastly applied in geotechnical engineering with the rapid development of computational techniques, aiming to improve calculation efficiency. This study develops a two-dimensional convolutional neural network-based model to predict tunnel convergence with consideration of soil spatial variability. The input and output of the surrogate model are the soil Young's modulus random field and tunnel convergence, respectively. The coefficient of determination, mean square error, and relative error are used to evaluate the prediction performance. The surrogate model is trained by isotropic random field data sets and performs excellent extrapolation ability on the data sets of the anisotropic random field. It suggests that the proposed model can conduct a probabilistic analysis of tunnel convergence in spatially variable soil with high accuracy. [ABSTRACT FROM AUTHOR]

Most slope collapses have three-dimensional (3D) characteristics due to the uniform soil. The traditional plane-strain analyses neglect the 3D effects and could yield an overestimation or underestimation of the slope stability. The present study analyzes the stability of 3D slopes characterized by spatially variable undrained shear strength. A 3D slope reliability analysis approach that can fully consider the spatial variability of soil properties is proposed based on the plastic limit analysis upper-bound theorem. Within the framework of Monte Carlo simulation, the effects of strength gradient, the coefficient of variation, and the scale of fluctuation of soil undrained shear strength on the slope reliability index are examined. The length of the 3D failure surface is highlighted as an essential characteristic in 3D slope analysis. The slope failure mechanisms are classified, and the occurrence probability of each type is quantified. The obtained results indicate that the degree of nonstationarity and the coefficient of variation of undrained shear strength have significant impacts on the slope failure width, and the variation of failure mechanism highly depends on the combined effect of slope inclination and soil strength. The findings could guide slope reinforcement and facilitate a more efficient and accurate risk evaluation of slopes. [ABSTRACT FROM AUTHOR]

The paper presented probabilistic analyses of the bearing capacity of strip footings in spatially variable undrained soil with a linearly increasing mean shear strength profile. The probabilistic response of strip footings was approached by the random finite element method (RFEM) in conjunction with the Monte Carlo simulation. Probabilistic failure envelopes were constructed to analyze the effect of spatial variability on strip footings subjected to different combinations of horizontal (H) and moment (M) loading. The probability of failure was independent on the strength gradient in the HM plane, but tended to increase with a wide fluctuation. Tabulated values of factor of safety for the probability of failure at 1% in different undrained shear strength random fields were also provided, which could be applied toward a foundation safety assessment. [ABSTRACT FROM AUTHOR]

The objective of this study was to investigate the liquefaction response of soil using the spatial variability of the shear modulus by considering different values of the coefficient of variation (COV) and the horizontal scale of fluctuation (SOF). For this purpose, a Monte Carlo simulation, combining the digital generation of a non-Gaussian random field with finite difference analyses, was utilized. Parametric studies were performed from the perspectives of the liquefaction area, excess pore water pressure (EPWP), and displacement at the ground surface. We found that a larger COV of the soil shear modulus was correlated with a slower reduction of liquefaction area and a lower EPWP ratio. To explain the influence from the perspective of the spatial distribution characteristics of the shear modulus, a deterministic model test was carried out. Additionally, it was found that the displacement history and the differential settlement at the end of shaking were regularly affected by the COV and the horizontal SOF, especially for large COV and horizontal SOF. [ABSTRACT FROM AUTHOR]

A probabilistic study on the bearing capacity of two parallel strip footings on a spatially variable soil where the mean of undrained shear strength increased linearly with depth was performed. For the comparative purpose, the single footing case was also investigated. Stationary and nonstationary random fields obeying log-normal distribution of undrained shear strength were generated and further mapped into nonlinear finite-element analysis. Monte Carlo simulations were then performed to evaluate the bearing capacity for the selected ranges of the degree of nonstationarity and the spatial correlation length in undrained shear strength. The normalized bearing capacities derived from two different random field models for the cases of single and two footings were compared, and the effect of footing interference was also discussed. [ABSTRACT FROM AUTHOR]

• An efficient method to simulate stationary strongly non-Gaussian process is proposed. • The proposed method performs well in some cases in terms of the convergence speed and accuracy. • The importance of upgrading both amplitude and phase contents is demonstrated. Random excitations, such as wind velocity, always exhibit non-Gaussian features. Sample realisations of stochastic processes satisfying given features should be generated, in order to perform the dynamical analysis of structures under stochastic loads based on the Monte Carlo simulation. In this paper, an efficient method is proposed to generate stationary non-Gaussian stochastic processes. It involves an iterative scheme that produces a class of sample processes satisfying the following conditions. (1) The marginal cumulative distribution function of each sample process is perfectly identical to the prescribed one. (2) The ensemble-averaged power spectral density function of these non-Gaussian sample processes is as close to the prescribed target as possible. In this iterative scheme, the underlying processes are generated by means of the spectral representation method that recombines the upgraded power spectral density function with the phase contents of the new non-Gaussian processes in the latest iteration. Numerical examples are provided to demonstrate the capabilities of the proposed approach for four typical non-Gaussian distributions, some of which deviate significantly from the Gaussian distribution. It is found that the estimated power spectral density functions of non-Gaussian processes are close to the target ones, even for the extremely non-Gaussian case. Furthermore, the capability of the proposed method is compared to two other methods. The results show that the proposed method performs well with convergence speed, accuracy, and random errors of power spectral density functions. [ABSTRACT FROM AUTHOR]

The objective of this paper is to investigate the effect of soil variability on bearing capacity of an embedded foundation in the presence of nonstationary undrained shear strength. The nonstationary undrained shear strength is simulated by a nonstationary random field generator based on the spectral representation method. An embedded foundation buried into the soil to two times of width is presented to investigate the influence of spatially variable undrained shear strength on bearing capacity. Firstly, Monte Carlo simulations are carried out to discuss the effect of distribution type, nonstationary gradient parameter, and horizontal autocorrelation length on the bearing capacity from the standpoint of mean value and standard deviation. Then, the influence of the distribution type on the failure probability of nonstationary random soil is also investigated, with the failure probability for the Beta distribution being demonstrated to be always larger than that for the Lognormal and Gamma distribution. [ABSTRACT FROM AUTHOR]

Abstract The objective of this paper is to investigate the bearing capacity of spatially varying soil in the presence of non-stationary feature of undrained shear strength. Firstly, undrained shear strength is modeled by a non-stationary random field. In this model, the mean of undrained shear strength is non-zero at the ground surface and linearly increases with depth, while the coefficient of variation (COV) of undrained shear strength keeps constant. Based on this non-stationarity, an algorithm is proposed to produce the corresponding random field. Then, Monte Carlo Simulations are carried out to evaluate the statistical characteristics of the resulted bearing capacity, followed by a detailed discussion on the effects of COV, strength gradient parameter, distribution type, and vertical autocorrelation length. At last, two computation schemes that enable the prediction of statistical characteristics (e.g., mean, standard deviation, and cumulative probability function) of bearing capacity in non-stationary random fields utilizing results from a stationary one are proposed, and demonstrated through numerical examples. [ABSTRACT FROM AUTHOR]

Accurate prediction of tunnel convergence is important to ensure the stability of tunnel structures. Reliability analysis of tunnel convergence on spatially variable soils was performed based on Monte Carlo simulations. The Young's modulus of soils was shown to be spatially varied. The influence of the coefficient of variation, the vertical scale of fluctuation and the distribution type (i.e. beta distribution, gamma distribution and lognormal distribution) of soils on the tunnel convergence were systematically discussed. From measuring the mean and standard deviation of tunnel convergence, and the probability of exceeding some thresholds, it was found that the distribution type significantly influenced the results. The results were accompanied by a detailed analysis of the mechanisms of tunnel convergence in spatially random soils. [ABSTRACT FROM AUTHOR]

The objective of this paper is to investigate how the non-stationary features of soil properties affect the stochastic result of bearing capacity of embedded shallow foundations. Undrained shear strength was modelled as a non-stationary random field with mean value increasing with depth. A nonlinear finite element analysis combined with random fields generated by the Spectral Representation Method was employed to obtain the bearing capacity in random soils. Monte Carlo simulations were applied to obtain statistical characteristics of the resulting bearing capacity. The effect of non-stationary features of random soil properties on foundations with different embedment depths is discussed from three aspects, i.e. the failure mechanisms, the statistical characteristics of the bearing capacity factors, and the probability of failure of the foundation. Interestingly, it was found that the effects of non-stationary random soil properties on some of the three aspects change with the embedment depths of the foundations. Furthermore, some suggestions for foundation design are given, based on the obtained results. [ABSTRACT FROM AUTHOR]

Spudcan foundations for mobile jack-up units are large diameter conical foundations that can penetrate into the seabed to a maximum depth of three times the diameter of the spudcan. As a deeply penetrated foundation, the bearing capacity of a spudcan is highly dependent on the failure mechanism and the strength distribution of the seabed soil, which exhibits strong spatial variability. While many recent studies have explored the failure mechanism and bearing capacity of spudcan foundations, these studies have commonly deterministically described the soil in which the spudcan is embedded. Therefore, this paper aimed to investigate the probabilistic bearing capacity of spudcan foundations embedded in the seabed at various depths, under the condition of spatially variable undrained shear strength that increased linearly with depth. The random finite element method was used to study this problem, where nonlinear finite element analysis was combined with random field theory within a Monte Carlo framework. The variability in undrained shear strength was modelled as a random field and characterised by a log-normal distribution with anisotropic autocorrelation distances. The influence of autocorrelation distance on the mean bearing capacity and the failure mechanism was discussed for each embedment depth. A correlation between the probability of failure and the factor of safety was established based on the obtained results. These findings can provide guidance for reliability-based design of spudcan foundations embedded in spatially variable soil. [ABSTRACT FROM AUTHOR]

Spudcan foundations have been widely used in offshore oil and gas engineering for jack-up rigs. During penetration into seabed soil, spudcan foundations may encounter large uncertainties in soil properties, which have a strong impact on its bearing capacity. A large number of studies have been conducted to demonstrate the failure mechanisms and the bearing capacity of spudcan foundations in soils with deterministic properties, but the influence of spatially variable soil properties on spudcan foundations remains unclear and should be accounted for. In this study, we aimed to investigate the failure mechanisms and the bearing capacity of a spudcan foundation embedded in soils where the mean undrained shear strength increased linearly with depth. The spectral representation method (SRM) was used to generate a non-stationary non-Gaussian random field. The random finite element method (RFEM) in conjunction with Monte Carlo simulations was carried out to evaluate the statistical characteristics of the bearing capacity for spudcan foundations, followed by a series of comparisons and discussion. The results indicated that the mean bearing capacity for the spatial variability of undrained shear strength was smaller than that obtained from the corresponding deterministic case. The probability of failure decreased slightly with an increase in the degree of non-stationarity under the constant coefficient of variation (COV) condition. Upon comparing the results obtained from different random field models, we found that the probability of failure under the non-constant condition was smaller than that under the stationary and constant COV conditions. • A modified spectral representation method is proposed to generate two different kinds of non-stationary random fields. • Establish the connection between dimensionless bearing capacities and failure mechanism modes. • Typical factors of safety under different degrees of non-stationarity are calculated and compared. [ABSTRACT FROM AUTHOR]