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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]

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]

In reality, many high-speed railway tunnels are built by sequential excavation method in spatially variable soil. This study introduces an efficient deep learning-based solution for the probabilistic analysis of tunnel crown settlements considering the spatial variability of surrounding soil. The two-dimensional convolutional neural network (2D-CNN) is employed to uncover the implicit correlation between the soil elastic modulus random field and tunnel crown settlements. The correlation coefficient (R) of the surrogate model is greater than 0.9664. Meanwhile, the mean relative error of the predictions remains within 2.38%, under various scales of fluctuation (SOFs). An additional 10,000 samples were produced to assess the practical performance of the trained model in probabilistic analysis. The relative errors of predictions generally fall within 5%, with a minimum confidence interval of 98.15%. These results demonstrate that the developed 2D-CNN model can effectively substitute the traditional method in predicting tunnel crown settlements considering soil spatial variability. • A machine learning based method is developed to predict the tunnel crown settlement in each construction step. • The prediction performance of the developed model under various anisotropic soil random fields is investigated. • The surrogate model can effectively substitute the time-consuming RFDM in probabilistic analysis. [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]

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]

Spudcan foundations are widely used in the offshore gas and oil industry to support mobile jack-up drilling rigs. During the service period, the spudcan foundations need to resist large vertical-horizontal-moment (VHM) loads that are transmitted from the superstructure. The bearing capacity of foundations in complicated stress conditions is usually based on VHM failure envelopes. These are commonly constructed by using numerical methods where the soil properties are assumed to be deterministic, ignoring the inherent spatial variability. This paper investigates the influence of spatially variable undrained shear strength and embedment depth on the capacity of spudcan foundations under VHM combined loads. The linearly increasing undrained shear strength with depth obeying log-normal distribution was taken into account. Probabilistic failure envelops were constructed to analyse the effect of spatial variability on the bearing capacity of spudcan foundations at various embedment depths when subjected to different combinations of VHM loads. The influence of horizontal scale of fluctuation for a specific embedment depth was also investigated. The results indicated that under combined loading the embedment depth significantly influenced the shape and size of failure envelopes. The probability of failure at each embedment depth based on the obtained probabilistic failure envelopes was intuitionally represented by means of a factor of safety, which can provide specific guidance for foundation reliable designs. • A non-stationary random field model was established. • Uniaxial ultimate bearing capacities were analyzed and VHM failure envelopes were constructed for various embedment depths. • Factors of safety were provided. [ABSTRACT FROM AUTHOR]

Random fields, such as the wind velocity field and the seismic ground motion field, are usually simulated by the spectral representation method (SRM). The SRM mainly relies on two methods: the random amplitudes method and the random phases method. However, the temporal statistics estimated from one SRM-simulated sample process differs from the target characteristics. Such differences can usually be assessed by the statistical errors, i. e., bias errors and stochastic errors. The closed-form solutions of statistical errors produced by random phases method have been given. This paper gives the closed-form solutions of statistical errors produced by the random phases methods and compares the statistical errors produced by both methods. The comparison of the stochastic errors of power spectral density functions produced by different methods demonstrates that (1) the random amplitudes method exhibits higher but more uniformly distributed stochastic errors than the random phases method; and (2) the stochastic errors produced by the random phases method are dependent on the decomposition method, whereas those produced by the random amplitudes method are not. [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]

• A new method of simulating soil spatial variability based on the UHPM is proposed. • Ignoring soil spatial variability leads to small monitoring result. • The influence of horizontal and vertical SOF on the crown settlement is studied. High-speed railways (HSRs) are extensively constructed in China, with the help of tunnels to cross through complex geological conditions. The sequential excavation method (SEM) is vastly adopted in the construction of loess tunnel. This study performs a probabilistic analysis of crown settlement, taking into account the spatial variability of the surrounding soil through Monte Carlo (MC) simulations. To illustrate the influence of horizontal and vertical scale fluctuations (SOFs) on crown settlement, an anisotropic random field of loess elastic modulus is simulated using the spectral representation method (SRM) and unified Hermite polynomial model (UHPM) for the random finite difference method (RFDM). The mean crown settlements obtained through stochastic analysis are consistently larger than the deterministic results in the 1st, 6th, and 9th construction steps. The maximum probabilities of stochastic crown settlement exceeding the deterministic results are 77.3% and 78.2% with varying horizontal and vertical SOFs, respectively. Amplification factors of 1.417 and 1.306 are necessary to ensure that the stochastic crown settlement of the HSR tunnel, constructed in spatially variable loess, satisfies a 5% and 10% exceeding probability. This study provides valuable guidance for the construction of HSR tunnels. [ABSTRACT FROM AUTHOR]

The objective of this paper was to investigate the dynamic response of a tunnel-soil system in the soil with spatial variability of shear modulus with various coefficients of variation and scales of fluctuation. The soil shear modulus was highlighted and modeled as an isotropic random field using the spectral representation method, then mapped into the finite difference model. The dynamic stochastic responses of the excess pore water pressure ratio, the liquefied zone, the ground displacement, and the uplift displacement of the tunnel were discussed. It was observed that the effect of coefficient of variation was pronounced in which an increase of the coefficient of variation brought out a reduction in the corresponding dynamic stochastic responses. However, the scale of fluctuation was found to be insignificant in the tunnel soil system. • A dynamic reliability method for soil-tunnel behaviors was proposed. • Soil shear modulus was modeled as isotropic random fields using spectral representation method. • Dynamic stochastic responses of the tunnel were investigated. [ABSTRACT FROM AUTHOR]

The behaviour of skirted foundations subjected to combined vertical (V), horizontal (H) and moment (M) loading is of particular interest to the geotechnical engineers. The bearing capacity of skirted foundations under combinations of VHM loading is represented by failure envelopes, which is commonly used in its stability assessment. In current studies, failure envelopes for skirted foundations were established deterministically, ignoring the spatial variability of natural soils. The paper aimed to investigate the probabilistic failure envelope of skirted foundations in the presence of soil undrained shear strength linearly increasing with depth. Random finite element method (RFEM) combining with random field theory, finite element method and Monte Carlo simulation was conducted to evaluate the uniaxial bearing capacities and define the HM failure envelopes. The influence of spatial variability on the stochastic response of bearing capacity in the HM space was discussed. • The effect of the degree of non-stationarity on the stochastic bearing capacities was investigated. • Probabilistic HM failure envelopes were established and compared. • The probability of failure was studied. [ABSTRACT FROM AUTHOR]