Dian-Qing Li

Efficient System Reliability Analysis of Slope Stability in Spatially Variable Soils Using Monte Carlo Simulation

Abstract Monte Carlo simulation (MCS) provides a conceptually simple and robust method to evaluate the system reliability of slope stability, particularly in spatially variable soils. However, it suffers from a lack of efficiency at small probability levels, which are of great interest in geotechnical design practice. To address this problem, this paper develops a MCS-based approach for efficient evaluation of the system failure probability P f , s of slope stability in spatially variable soils. The proposed approach allows explicit modeling of the inherent spatial variability of soil properties in a system reliability analysis of slope stability. It facilitates the slope system reliability analysis using representative slip surfaces (i.e., dominating slope failure modes) and multiple stochastic response surfaces. Based on the stochastic response surfaces, the values of P f , s are efficiently calculated using MCS with negligible computational effort. For illustration, the proposed MCS-based system reliab...

Enhancement of random finite element method in reliability analysis and risk assessment of soil slopes using Subset Simulation

Random finite element method (RFEM) provides a rigorous tool to incorporate spatial variability of soil properties into reliability analysis and risk assessment of slope stability. However, it suffers from a common criticism of requiring extensive computational efforts and a lack of efficiency, particularly at small probability levels (e.g., slope failure probability Pf < 0.001). To address this problem, this study integrates RFEM with an advanced Monte Carlo Simulation (MCS) method called “Subset Simulation (SS)” to develop an efficient RFEM (i.e., SS-based RFEM) for reliability analysis and risk assessment of soil slopes. The proposed SS-based RFEM expresses the overall risk of slope failure as a weighed aggregation of slope failure risk at different probability levels and quantifies the relative contributions of slope failure risk at different probability levels to the overall risk of slope failure. Equations are derived for integrating SS with RFEM to evaluate the probability (Pf) and risk (R) of slope failure. These equations are illustrated using a soil slope example. It is shown that the Pf and R are evaluated properly using the proposed approach. Compared with the original RFEM with direct MCS, the SS-based RFEM improves, significantly, the computational efficiency of evaluating Pf and R. This enhances the applications of RFEM in the reliability analysis and risk assessment of slope stability. With the aid of improved computational efficiency, a sensitivity study is also performed to explore effects of vertical spatial variability of soil properties on R. It is found that the vertical spatial variability affects the slope failure risk significantly.

Bivariate distribution models using copulas for reliability analysis

The modeling of joint probability distributions of correlated variables and the evaluation of reliability under incomplete probability information remain a challenge that has not been studied extensively. This article aims to investigate the effect of copulas for modeling dependence structures between variables on reliability under incomplete probability information. First, a copula-based method is proposed to model the joint probability distributions of multiple correlated variables with given marginal distributions and correlation coefficients. Second, a reliability problem is formulated and a direct integration method for calculating probability of failure is presented. Finally, the reliability is investigated to demonstrate the effect of copulas on reliability. The joint probability distribution of multiple variables, with given marginal distributions and correlation coefficients, can be constructed using copulas in a general and flexible way. The probabilities of failure produced by different copulas can differ considerably. Such a difference increases with decreasing probability of failure. The reliability index defined by the mean and standard deviation of a performance function cannot capture the difference in the probabilities of failure produced by different copulas. In addition, the Gaussian copula, often adopted out of expedience without proper validation, produces only one of the various possible solutions of the probability of failure and such a probability of failure may be biased towards the non-conservative side. The tail dependence of copulas has a significant influence on reliability.

Bootstrap method for characterizing the effect of uncertainty in shear strength parameters on slope reliability

This paper aims to propose a bootstrap method for characterizing the effect of uncertainty in shear strength parameters on slope reliability. The procedure for a traditional slope reliability analysis with fixed distributions of shear strength parameters is presented first. Then, the variations of the mean and standard deviation of shear strength parameters and the Akaike Information Criterion values associated with various distributions are studied to characterize the uncertainties in distribution parameters and types of shear strength parameters. The reliability of an infinite slope is presented to demonstrate the validity of the proposed method. The results indicate that the bootstrap method can effectively model the uncertain probability distributions of shear strength parameters. The uncertain distributions of shear strength parameters have a significant influence on slope reliability. With the bootstrap method, the slope reliability index is represented by a confidence interval instead of a single fixed index. The confidence interval increases with increasing factor of slope safety. Considering both the uncertainties in distribution parameters and distribution types of shear strength parameters leads to a higher variation and a wider confidence interval of reliability index.

A new classification of seepage control mechanisms in geotechnical engineering

Abstract Seepage flow through soils, rocks and geotechnical structures has a great influence on their stabilities and performances, and seepage control is a critical technological issue in engineering practices. The physical mechanisms associated with various engineering measures for seepage control are investigated from a new perspective within the framework of continuum mechanics; and an equation-based classification of seepage control mechanisms is proposed according to their roles in the mathematical models for seepage flow, including control mechanisms by coupled processes, initial states, boundary conditions and hydraulic properties. The effects of each mechanism on seepage control are illustrated with examples in hydroelectric engineering and radioactive waste disposal, and hence the reasonability of classification is demonstrated. Advice on performance assessment and optimization design of the seepage control systems in geotechnical engineering is provided, and the suggested procedure would serve as a useful guidance for cost-effective control of seepage flow in various engineering practices.

Model Uncertainty for Predicting the Bearing Capacity of Sand Overlying Clay

In this paper, 62 centrifuge tests are collected from the literature and used to perform a statistical evaluation of the model factor for conventional methods to calculate the bearing capacity of dense sand overlying clay. The model factor is defined as a ratio of measured capacity to calculated capacity. The variations of the model factor with input parameters are established as regression equations based on the results of finite-element limit analysis (FELA). Conventional methods that multiply by regression equations are shown to be more accurate on average for all data sets. Further verification exercise from 27 additional centrifuge tests indicates the modified method could also be applicable for medium dense sand overlying clay. The mean and coefficient of variation of the model factor for the modified methods are finally characterized as a lognormal random variable with a mean of 1.06 and coefficient of variation of 0.17. DOI: 10.1061/(ASCE)GM.1943-5622.0000898.© 2017 American Society of Civil Engineers.

Impact of translation approach for modelling correlated non-normal variables on parallel system reliability

The adequacy of two approximate methods based on incomplete information, namely method P and method S, for constructing multivariate distributions with given marginal distributions and covariance has not been studied systematically. This article aims to study the errors of the method P and method S. First, the method P and method S as well as the exact method are presented. Second, the performance of the two approximate methods is evaluated based on their abilities to match exact solutions for system probabilities of failure. Finally, an illustrative example of a parallel system is investigated to demonstrate the errors associated with the two methods. The results indicate that the errors in system probabilities of failure for the two methods highly depend on the level of system probability of failure, the performance function underlying the system, and the degree of correlation. Such errors increase greatly with decreasing system probabilities of failure. When the target system probability of failure is larger than 1.0E−03, the system probabilities of failure obtained from the two methods and the exact method are of the same order of magnitude. The maximum error in the system probability of failure may not be associated with a large correlation. It can happen at an intermediate correlation.

Reliability analysis of serviceability performance for an underground cavern using a non-intrusive stochastic method

This paper proposes a non-intrusive stochastic analysis procedure for reliability analysis of the serviceability performance of an underground cavern with an implicit limit state function. This procedure is formulated on the basis of the stochastic response surface method (SRSM) and the deterministic finite element method. First, the SRSM is briefly introduced and implemented through a MATLAB code. Then, the software SIGMA/W is used to perform a deterministic finite element analysis. Next, a link between the MATLAB code and SIGMA/W is developed to automatically pass exchange data between the two platforms. Finally, two examples are presented to illustrate the capacity and validity of the proposed procedure. In the first example, a closed-form limit state function is adopted to validate the SRSM by comparing it with the results obtained from a direct Monte Carlo simulation. In the second example, the serviceability performance of an underground cavern is analyzed to illustrate the capacity of the proposed procedure to handle a reliability problem with an implicit limit state function. The proposed procedure does not require the user to modify the existing deterministic finite element code. The deterministic finite element analysis and the probabilistic analysis are decoupled. This is a major practical advantage because realistic probabilistic analyses are made possible. The SRSM can produce sufficiently accurate reliability results. Furthermore, the method is much more efficient than the direct Monte Carlo simulation. Sensitivity analyses show the effect of the variability of input random variables and the correlation between them on: (1) the probability density functions, (2) the first four order statistical moments, and (3) the probability of failure, which is investigated and discussed.

A softening block approach to simulate excavation in jointed rocks

The instability of rock masses as a result of excavation is one of the most important rock mechanics problems. This paper proposes a new “softening block” approach for the simulation of stage-wise sequential excavations in jointed rock masses. The concept of a softening block is presented and the corresponding algorithm developed and implemented into the original Discontinuous Deformation Analysis program proposed by Shi. The proposed softening block approach obviates the need to remove the excavated blocks from the calculation model, which further simplifies the work of pre-processing for sequential excavation simulations. Finally, two numerical examples are presented to demonstrate the validity and capability of the proposed approach. The results indicate that it can be used to simulate the excavation in jointed rock mass efficiently and accurately.RésuméL’instabilité de masses rocheuses résultant de travaux d’excavation constitue l’un des plus importants problèmes de mécanique des roches. L’article propose une nouvelle approche de “bloc affaibli” pour la simulation de processus d’excavation progressive dans des masses rocheuses fissurées. Le concept du bloc affaibli est présenté, les algorithmes correspondants sont développés et implémentés dans le programme original d’analyse des déformations en milieu discontinu proposé par Shi. L’approche proposée évite d’avoir à enlever les blocs excavés du modèle de calcul, ce qui ensuite simplifie le travail de pré-traitement pour les simulations d’excavations successives. Finalement, deux exemples numériques sont présentés pour démontrer la validité et la capacité de l’approche proposée. Les résultats indiquent qu’elle peut être utilisée pour simuler l’excavation de masses rocheuses fissurées de manière efficace et précise.

Full probabilistic design of slopes in spatially variable soils using simplified reliability analysis method

ABSTRACT A simplified reliability analysis method is proposed for efficient full probabilistic design of soil slopes in spatially variable soils. The soil slope is viewed as a series system comprised of numerous potential slip surfaces and the spatial variability of soil properties is modelled by the spatial averaging technique along potential slip surfaces. The proposed approach not only provides sufficiently accurate reliability estimates of slope stability, but also significantly improves the computational efficiency of soil slope design in comparison with simulation-based full probabilistic design. It is found that the spatial variability has considerable effects on the optimal slope design.