Probabilistic slope stability analysis by a copula-based sampling method

Wu, Xing Zheng

doi:10.1007/s10596-013-9353-3

Cited by 53 publications

(27 citation statements)

References 50 publications

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“…As claimed by Lumb (1970), Matsuo and Kuroda (1974), Phoon and Kulhawy (1999), and Duncan (2000), the input parameters of shear strengths of soils or rocks are associated with a considerable amount of uncertainty. The randomness and uncertainty have been implemented in the studies of a probabilistic slope stability analysis by Nguyen (1984), Tang et al (1999), Liang et al (1999), and Wu (2013a). Similarly, they should also be incorporated into the interpretation of fragility functions.…”

Section: Analytical Approachmentioning

confidence: 99%

“…For the CBSM, considering n sim synthetic observations generated by the method of copulas (Wu 2013a) associated with the basic variable Z, P f is estimated as the ratio of the number of failures to the total number of simulation runs n sim . The CBSM is one of the Monte Carlo sampler approaches and provides a flexible tool for representing arbitrarily marginal distribution types and dependence structures of Z.…”

Section: Analytical Approachmentioning

confidence: 99%

“…The CBSM is one of the Monte Carlo sampler approaches and provides a flexible tool for representing arbitrarily marginal distribution types and dependence structures of Z. A more detailed coverage of these probabilistic approaches is provided in the extant literature (Low and Tang 2007;Wu 2013a).…”

Section: Analytical Approachmentioning

confidence: 99%

“…This limit equilibrium method based on the effective stress analysis received the wide acceptance (Tobutt 1982;Husein Malkawi et al 2000;Wu 2013a). In this approach, the soil mass is divided into a number of vertical slices of equal width.…”

Section: Calculation Examplesmentioning

confidence: 99%

“…earthquake and rainfall events. Beneficial to the recent development of probabilistic analysis approaches, including the copula-based sampling method (CBSM, Wu 2013a, b) andFORM (Hasofer andLind 1974;Zahn 1990;Ang and Tang 2007;Low and Tang 2007;Wu 2013a), these techniques are integrated to recognise and evaluate the failure probability of slope stability considering the uncertainties of shear strength parameters. Subsequently, two approaches to constructing fragility functions are outlined and compared.…”

Section: Introductionmentioning

confidence: 99%

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Development of fragility functions for slope instability analysis

2014

Landslides

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This paper presents a methodology for constructing fragility functions to characterise slope stability under a range of catastrophic earthquakes and rainfalls. The procedures for creating fragility functions, including the first-order reliability method (FORM) and the copula-based sampling method (CBSM), are demonstrated using a selection of typical slopes. The most common failure modes are included, such as the shallow sliding of an infinite slope, circular slip surface of a homogeneous slope, and tetrahedral wedge failure in a rock slope. Owing to the proposed approach, the fragility function can be applied to quantify the failure probabilities over a range of loading conditions with ease, as these are attributed to a function, rather than a design point. The advantage of these definitions is that the uncertainties of correlated soil shear strengths can be incorporated into the reliability models. The established procedure can provide a basis for describing vulnerable behaviour of a slope under various loading conditions and geometries.

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Section: Analytical Approachmentioning

confidence: 99%

Section: Analytical Approachmentioning

confidence: 99%

Section: Analytical Approachmentioning

confidence: 99%

Section: Calculation Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Development of fragility functions for slope instability analysis

2014

Landslides

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Copula‐based joint probability function for PGA and CAV: a case study from Taiwan

Tang

Wang

et al. 2016

Earthq Engng Struct Dyn

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Summary This study aims to develop a joint probability function of peak ground acceleration (PGA) and cumulative absolute velocity (CAV) for the strong ground motion data from Taiwan. First, a total of 40,385 earthquake time histories are collected from the Taiwan Strong Motion Instrumentation Program. Then, the copula approach is introduced and applied to model the joint probability distribution of PGA and CAV. Finally, the correlation results using the PGA‐CAV empirical data and the normalized residuals are compared. The results indicate that there exists a strong positive correlation between PGA and CAV. For both the PGA and CAV empirical data and the normalized residuals, the multivariate lognormal distribution composed of two lognormal marginal distributions and the Gaussian copula provides adequate characterization of the PGA‐CAV joint distribution observed in Taiwan. This finding demonstrates the validity of the conventional two‐step approach for developing empirical ground motion prediction equations (GMPEs) of multiple ground motion parameters from the copula viewpoint. Copyright © 2016 John Wiley & Sons, Ltd.

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Parametric and nonparametric inference for the reliability of copula‐based stress‐strength models

Andrade

Nascimento²,

Rathie

2020

Quality & Reliability Eng

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This paper provides a general treatment of statistical inference for the reliability in copula-based stress-strength models. Most of the current literature is either focused on specific models that yield clean formulas or restricted to estimation and engineering aspects without addressing statistical inference. We present two general frameworks, one parametric, one nonparametric, for the estimation of the reliability. The parametric methodology is presented under the general framework of estimating equations, mostly as a combination of existing methodologies from the fields of multivariate analysis, reliability, and econometrics, with some new results. The nonparametric methodology is a novel application based on an existing bivariate kernel method combined with Monte Carlo estimation of the reliability without specification of the copula or the margins. We present results from a small simulation study designed to assess the robustness of the methods discussed in terms of model misspecification. We used geotechnical data and data from the Brazilian Household Survey to illustrate the proposed methodologies in the estimation of factors of safety and financial fragility.

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Probabilistic slope stability analysis by a copula-based sampling method

Cited by 53 publications

References 50 publications

Development of fragility functions for slope instability analysis

Development of fragility functions for slope instability analysis

Copula‐based joint probability function for PGA and CAV: a case study from Taiwan

Parametric and nonparametric inference for the reliability of copula‐based stress‐strength models

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