Extension of quasi-Newton approximation-based SORM for series system reliability analysis of geotechnical problems

Zeng, Peng; Li, Tianbin; Jimenez, Rafael E.; Feng, Xianjin; Chen, Yu

doi:10.1007/s00366-017-0536-8

Cited by 19 publications

(8 citation statements)

References 38 publications

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“…The applications of the second-order reliability method (SORM), in engineering problems (e.g., see [1,[3][4][5][6][7][8][9][10][11]), in recent years, suggest a relevant interest in the SORM, and thus, there is much room for new research in this area, the main challenge being to calculate the main curvatures of the limit state surface, which involves a lot of mathematical complexity and computational effort.…”

Section: Introductionmentioning

confidence: 99%

Obtaining the Main Curvatures of Orientable Hypersurfaces, Based on Differential Geometry

Ferreira¹

2023

Topology - Recent Advances and Applications [Working Title]

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Most of the literature on differential geometry presents the coefficients of the 1st and 2nd fundamental form to simplify the calculation of the curvatures on a surface and also to obtain other important information, such as the area of a surface. In this text, as the interest lies on the generalization of the idea of surface (hypersurface), such simplification by the use of these coefficients was not possible, in view of the complexity of the mathematical operations involved in the calculation of curvatures (if n = number of variables in the implicit function of the surface> 3), opting to use the linear operator –DNp. To facilitate the calculation of the normal vector the surface was described as the graph of a differentiable function f: Rn-1→R. The example of the sphere thoroughly illustrates the procedure of calculating the main curvatures of a surface in the space R3, and such procedure is extensive to the space Rn. Some examples from the engineering area in which the variables of the implicit functions of the hypersurfaces are random were solved, and the results of the main curvatures, calculated by the proposed procedure, were exact and coincident with those provided in the literature.

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Section: Introductionmentioning

confidence: 99%

Obtaining the Main Curvatures of Orientable Hypersurfaces, Based on Differential Geometry

Ferreira¹

2023

Topology - Recent Advances and Applications [Working Title]

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“…In the FORM, high nonlinearity in the failure surface induces inaccurate and unreasonable POF. The SORM, using the second-order Taylor series (or other polynomials), was proposed to address this problem [11,17,18]. Although the POF estimated by the second-order approximation is more accurate than the POF estimated by the first-order approximation, it requires a much more complex computation [11].…”

Section: Introductionmentioning

confidence: 99%

“…Although the POF estimated by the second-order approximation is more accurate than the POF estimated by the first-order approximation, it requires a much more complex computation [11]. Since there is no closed-form expression in a quadratic polynomial function to define the POF, most SORMs adopted a parabolic approximation of the fitted quadratic polynomial surface in order to estimate the POF of the limit state [16][17][18][19][20]. In these methods precise probability distributions of the random variables are inevitably required, which are based on a significant number of experimental samples that are often limited in many applications [1,7,14,21].…”

Section: Introductionmentioning

confidence: 99%

A New SORM Method for Structural Reliability with Hybrid Uncertain Variables

et al. 2020

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(1) Background: in practical applications, probabilistic and non-probabilistic information often simultaneously exit. For a complex system with a nonlinear limit-state function, the analysis and evaluation of the reliability are imperative yet challenging tasks. (2) Methods: an improved second-order method is proposed for reliability analysis in the presence of both random and interval variables, where a novel polar transformation is employed. This method enables a unified reliability analysis taking both random variables and bounded intervals into account, simplifying the calculation by transforming a high-dimension limit-state function into a bivariate state function. The obtained nonlinear probability density functions of two variables in the function inherit the statistic characteristics of interval and random variables. The proposed method does not require any strong assumptions and so it can be used in various practical engineering applications. (3) Results: the proposed method is validated via two numerical examples. A comparative study towards a contemporary algorithm in state-of-the-art literature is carried out to demonstrate the benefits of our method. (4) Conclusions: the proposed method outperforms existing methods both in efficiency and accuracy, especially for cases with strong nonlinearity.

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“…These methodologies have been applied to geotechnical analyses by means of the First-Order Second-Moment method (FOSM) [6], [7], First-Order Reliability Method (FORM) [8], Second-Order Reliability Method (SORM) [9], and Monte Carlo simulation (MCS) [10]- [12].…”

Section: Introductionmentioning

confidence: 99%

Reliability Analysis of Bored-pile Wall Stability Considering Parameter Uncertainties

Mattos

Marin

2020

TecnoL.

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In geotechnical engineering, bored-pile wall stability is evaluated using deterministic design methods based on safety factors to establish a margin against failure. In recent years, reliability-based design methods have been adopted to include uncertainty in the assessment of bored-pile wall stability as well as in the calculation of the feasible embedment depth of the walls. In this study, an expanded reliability-based design approach, along with finite element analysis, was applied to conduct parametric analyses of bored-pile wall stability. In serviceability limit state design framework, the results indicate that cohesion and groundwater level are factors that significantly affect bored-pile wall stability. Moreover, high variability in the cohesion range causes great uncertainty to determine the embedment depth of bored-pile wall. The feasible embedment depth can reach 4 times the free height considering the maximum coefficient of variation (50 %) of the cohesion. In turn, when the groundwater level is located at the retained ground surface, the horizontal displacement of the upper end of the wall reaches 15.2 mm, i.e., 0.0038 times the free height of the wall, for which the soil mobilizes active earth pressures. It was also found that the resolution of probabilistic results is highly influenced by the number of iterations in Monte Carlo simulations.

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Extension of quasi-Newton approximation-based SORM for series system reliability analysis of geotechnical problems

Cited by 19 publications

References 38 publications

Obtaining the Main Curvatures of Orientable Hypersurfaces, Based on Differential Geometry

Obtaining the Main Curvatures of Orientable Hypersurfaces, Based on Differential Geometry

A New SORM Method for Structural Reliability with Hybrid Uncertain Variables

Reliability Analysis of Bored-pile Wall Stability Considering Parameter Uncertainties

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