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The copula dependence structure underlying the correlated shear strength parameters of soils can significantly affect the results of slope reliability analysis and risk assessment of slope failure. Currently, how do copula dependence structures affect the failure modes of slopes in spatially variable soils still remains an open question. This study systematically investigates the effect of copula dependence structures on the failure modes of a cohesive-frictional slope in spatially variable soils via an adapted random finite difference method (RFDM) that incorporates the copula-based random fields. The proposed RFDM proceeds with the simulation of cross-correlated random fields considering the copula dependence between the shear strength parameters of the slope. The strength reduction analyses are then performed within the framework of Monte Carlo simulation to obtain the stability analysis results, including the critical slip surface (CSS) and associated factor of safety (FS) and sliding volume. Finally, various statistical analyses on the number and distribution of CSS, FS and sliding volume as well as the failure modes versus different statistics of soil properties are analyzed considering different dependence structures. The results show that the overall distribution range of CSS obtained by the commonly used Gaussian copula is more concentrated, whereas the result by the No. 16 copula is the widest. The differences in the overall distribution range of CSS among different copulas decrease with the increase of the scale of fluctuation, coefficient of variation, and cross-correlation coefficient of the strength parameters. The proportions of different failure modes are comparable for the Gaussian, Plackett and Fran copulas, whereas the No.16 copula has the smallest proportion for the shallow failure and largest proportions for the deep and multi-slip failures. The influence of copula dependence structure on the slope failure mode is more significant than the statistical parameters of soil properties. The results provide useful references for copula selection when the underlying dependence structure is difficult to be determined. [ABSTRACT FROM AUTHOR]

Natural slopes often exhibit tilted stratification with rotated transverse anisotropy in multiple soil properties, including the mechanical (e.g., friction angle φ and cohesion c) and hydraulic properties (e.g., saturated hydraulic conductivity k s). This phenomenon indicates that to achieve an accurate assessment of slope reliability under rainfall infiltration, the anisotropic spatial variation of the shear strength parameters and k s should be incorporated in a combined manner. Thus, this paper discusses the combined influence of rotated transverse anisotropy in the shear strength parameters and k s on the reliability and failure mechanism of an unsaturated slope under rainfalls. It is found that for a slope with tilted stratification, the failure mechanism and reliability estimator are dominantly influenced by the rotated transverse anisotropy in the shear strength parameters, while the influence induced by that in k s is slight. In particular, only incorporating the rotated transverse anisotropy in k s may lead to an incorrect reliability estimator of a slope with tilted stratification. Herein, the reliability index β would be estimated to be dramatically higher, and β of a slope with horizontal bedding would be higher than that of an anti-dip slope, which is inconsistent with the engineering experiences. Nonetheless, the rotated transverse anisotropy in k s should not be ignored in slope reliability assessment, because ignoring the rotated transverse anisotropy in k s would lead to overestimation of the reliability index β , which is adverse to the safety design of a slope. [ABSTRACT FROM AUTHOR]

Soils often exhibit spatial variability with nonstationarity, which has not yet been studied in the context of postfailure analysis of slopes. In this study, the random material point method is adopted to investigate the influence of nonstationarity on the large deformation characteristics of a slope with spatially variable undrained shear strength (S u). The nonstationarity has significant influences on the mean and standard deviation of the large deformation characteristics, where ignoring the nonstationarity can lead to higher mean and standard deviation values. In addition, when the nonstationarity is insignificant with a small increase in the rate of the soil strength, the model boundary can significantly affect the standard deviation of influence and run-out distances, but the influence is slight on those of the volume of the sliding mass. In addition, the mean and standard deviation of the large deformation characteristics increase with a higher coefficient of variation of S u. This study reveals that the nonstationarity of soil spatial variability can influence the failure mechanism in the failure initiation stage and thus the volume of the sliding mass, which controls the kinetic energy of the sliding mass in the postfailure stage and affects the influence and run-out distances. [ABSTRACT FROM AUTHOR]

Due to complex geological deposition, post-deposition processes and limited site investigation data in engineering practice, soil properties are often spatially variable and the stratigraphic boundary in layered soils is generally characterized by uncertainty. The spatial variability of soil properties has been well investigated in past years, whereas the question of how the stratigraphic boundary uncertainty affects the slope stability remains unanswered. This paper attempts to investigate the effects of the stratigraphic boundary uncertainty on the system reliability and risk of a layered slope in spatially variable soils. In this paper, the spatial variability of soil properties is simulated by non-stationary random fields that are generated by an extended Cholesky decomposition technique, while the stochastic nature of the stratigraphic boundary location is simulated by a discrete random variable. Monte Carlo simulation (MCS) is suggested for evaluating the system failure probability and risk. Various comparisons between probabilistic analysis results obtained from considering and neglecting the stratigraphic boundary uncertainty have been made for different statistics of soil properties. Results show that the stratigraphic boundary uncertainty plays an important role in identifying the slope failure mechanism. Moreover, neglecting the stratigraphic boundary uncertainty would generally overestimate the slope failure risk for different statistics, except at small coefficients of variation of the friction angle, where the results are underestimated. [ABSTRACT FROM AUTHOR]

Theoretical autocorrelation functions (ACFs) are generally used to characterize the spatial variation of permeability due to the limited number of site investigation data. However, many theoretical ACFs are available in the literature, and there are difficulties in selecting a suitable ACF for general cases. This paper proposes using the random finite element method to investigate the effects of ACF on the seepage through an embankment. Five commonly used ACFs—the squared exponential (SQX), single exponential (SNX), second-order Markov (SMK), cosine exponential (CSX) and binary noise (BIN) ACFs in the literature—are compared systematically by a series of parametric studies to investigate their influences on the seepage flow problem. Both stationary and non-stationary random fields are considered in this study. The results show that the commonly used SQX and SNX ACFs may overestimate and underestimate the seepage flow rate, respectively. It is also known that the maximum exit gradient associated with the SNX ACF is larger than those obtained using the other four ACFs. Additionally, it is proved that the deterministic approach-based design is on the conservative side and tends to be too conservative when dealing with soils with greater variation in the properties. It is also found that the SQX ACF has a higher probability of providing a more conservative design in practice. Overall, the differences between different ACFs are not significant and are within acceptable ranges. [ABSTRACT FROM AUTHOR]

Discarding known data from cored samples in the reliability analysis of a slope in spatially variable soils is a waste of site investigation effort. The traditional unconditional random field simulation, which neglects these known data, may overestimate the simulation variance of the underlying random fields of the soil properties. This paper attempts to evaluate the reliability of a slope in spatially variable soils while considering the known data at particular locations. Conditional random fields are simulated based on the Kriging method and the Cholesky decomposition technique to match the known data at measured locations. Subset simulation (SS) is then performed to calculate the probability of slope failure. A hypothetical homogeneous cohesion-frictional slope is taken as an example to investigate its reliability conditioned on several virtual samples. Various parametric studies are performed to explore the effect of different layouts of the virtual samples on the factor of safety (FS), the spatial variation of the critical slip surface and the probability of slope failure. The results suggest that whether the conditional random fields can be accurately simulated depends highly on the ratio of the sample distance and the autocorrelation distance. Better simulation results are obtained with smaller ratios. Additionally, compared with unconditional random field simulations, conditional random field simulations can significantly reduce the simulation variance, which leads to a narrower variation range of the FS and its location and a much lower probability of failure. The results also highlight the great significance of the conditional random field simulation at relatively large autocorrelation distances. [ABSTRACT FROM AUTHOR]

System effects should be considered in the probabilistic analysis of a layered soil slope due to the potential existence of multiple failure modes. This paper presents a system reliability analysis approach for layered soil slopes based on multivariate adaptive regression splines (MARS) and Monte Carlo simulation (MCS). The proposed approach is achieved in a two-phase process. First, MARS is constructed based on a group of training samples that are generated by Latin hypercube sampling (LHS). MARS is validated by a specific number of testing samples which are randomly generated per the underlying distributions. Second, the established MARS is integrated with MCS to estimate the system failure probability of slopes. Two types of multi-layered soil slopes (cohesive slope and c – φ slope) are examined to assess the capability and validity of the proposed approach. Each type of slope includes two examples with different statistics and system failure probability levels. The proposed approach can provide an accurate estimation of the system failure probability of a soil slope. In addition, the proposed approach is more accurate than the quadratic response surface method (QRSM) and the second-order stochastic response surface method (SRSM) for slopes with highly nonlinear limit state functions (LSFs). The results show that the proposed MARS-based MCS is a favorable and useful tool for the system reliability analysis of soil slopes. [ABSTRACT FROM AUTHOR]

Slope stability analysis based on different stratigraphic boundary conditions may have significant differences in terms of factor of safety (FS) and the location of the critical slip surface. Therefore, traditional reliability analysis of layered slopes that assumes the stratigraphic boundary between two soil layers being a deterministic line or surface can be misleading. This study aims to investigate the influence of the stratigraphic boundary uncertainty (SBU) arising from limited site investigation data on slope stability analysis with the consideration of soil spatial variability. A modified one-dimensional conditional Markov chain model is proposed to model the SBU. Cholesky decomposition technique is subsequently utilized to simulate the inherent spatial variability of soil properties based on the simulated stratigraphic boundary within the framework of Monte Carlo simulation. A sample example on a two-layered soil slope with limited number of boreholes shows that the proposed method can well simulate the stratigraphic boundary based on limited borehole information. The statistics of FS and probability of failure are found not to increase or decrease monotonically with the number of boreholes, but can converge to the correct results if the number of boreholes increases. Moreover, the conventional reliability analysis with an implicit assumption of deterministic stratigraphic boundary condition can significantly overestimate the reliability of the slope, but this overestimation decreases with the increase in the scale of fluctuation. [ABSTRACT FROM AUTHOR]

Stabilizing piles have been widely used to remediate landslides and reinforce potentially unstable slopes. Previous investigations on the stability analyses of pile-reinforced slopes, however, were mainly based on deterministic analysis methods, where the spatial variability of soil properties was rarely incorporated. Meanwhile, the assumption of isotropy and horizontal transverse anisotropy in previous studies may bring bias to the slope reliability assessment, and thus the optimization design of piles. This study hence aims at systematically investigating the influence of soil spatially variable anisotropy on statistical characteristics of the factor of safety, failure mechanisms, and probability of failure (P f) of pile-reinforced slopes. An integrated probabilistic analysis framework is used to obtain an optimal reinforcement scheme of stabilizing piles considering different rotational angles of soil strata. Subset simulation is used to enhance the computational efficiency for reliability analysis. A hypothetical slope and a practical slope are studied as illustrative examples with various parametric studies. Results show that the rotated anisotropy has a significant influence on the performance of pile-reinforced slopes and can largely affect the P f depending on the strata inclination. For slopes with different rotational angles of strata, the number of critical slip surfaces and the slip band range are different and thereby result in different optimal pile designs. [ABSTRACT FROM AUTHOR]

Kriging metamodel is an effective method for slope reliability analysis because of its flexibility and accuracy in data interpolation. However, the accuracy of traditional Kriging metamodel needs to be improved when facing complex limit state functions in slope stability problems. In addition, traditional Kriging metamodel cannot provide the key component—slope failure consequence—for risk assessment of slope failure, which greatly hinders the application of the Kriging method. This paper develops a multiple Kriging (MK) metamodels method to address the above problems within the framework of limit equilibrium method. The proposed MK metamodels are developed by simultaneously establishing a Kriging metamodel for each potential slip surface of a slope, with a global optimization search for the correlation parameters by the genetic algorithm. Slope stability analysis is then efficiently performed on the MK metamodels to obtain the associated factor of safety (FS) and locate the critical slip surface (CSS). Since the FS and the associated CSS are available, slope reliability analysis and risk assessment can be conducted with ease, thereby circumvent the abovementioned issues. For illustration and validation, the proposed model is applied to two examples, including a two-layered cohesive soil slope and a practical case of the Congress Street cut slope in Chicago. Both the influence of regression models and correlation models on the accuracy of the MK metamodels are discussed. The results show that the proposed model is more accurate than the conventional model in estimating the slope failure probability. More importantly, it is shown that the proposed model can effectively assess the risk of slope failure, which greatly extends the application scope of the Kriging based method. [ABSTRACT FROM AUTHOR]