The simulation and discretisation of random fields for probabilistic finite element analysis of soils using meshes of arbitrary triangular elements

Green, David K. E.; Douglas, Kurt; Mostyn, Garry

doi:10.1016/j.compgeo.2015.04.004

Cited by 21 publications

(7 citation statements)

References 24 publications

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“…Moreover, it is worth highlighting again that we focus on providing a finite representation of the response function u (x, θ ) rather than of the input quantities. On the contrary, many literature works are devoted to model input quantities [1,14,32].…”

Section: Efficient Monte Carlo Sampling Based On Functional Pcamentioning

confidence: 99%

Efficient uncertainty quantification in stochastic finite element analysis based on functional principal components

et al. 2015

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The great influence of uncertainties on the behavior of physical systems has always drawn attention to the importance of a stochastic approach to engineering problems. Accordingly, in this paper, we address the problem of solving a Finite Element analysis in the presence of uncertain parameters. We consider an approach in which several solutions of the problem are obtained in correspondence of parameters samples, and propose a novel non-intrusive method, which exploits the functional principal component analysis, to get acceptable computational efforts. Indeed, the proposed approach allows constructing an optimal basis of the solutions space and projecting the full Finite Element problem into a smaller space spanned by this basis. Even if solving the problem in this reduced space is computationally convenient, very good approximations are obtained by upper bounding the error between the full Finite Element solution and the reduced one. Finally, we assess the applicability of the proposed approach through different test cases, obtaining satisfactory results

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Section: Efficient Monte Carlo Sampling Based On Functional Pcamentioning

confidence: 99%

Efficient uncertainty quantification in stochastic finite element analysis based on functional principal components

et al. 2015

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“…Several of these methods have found their way into the field of geotechnics for generating random fields describing the spatial variability of a range of soil parameters (e.g. Huang et al (2013); Green et al (2015); Suchomel and Mašín (2011)). Of particular interest with respect to subset simulation are the methods of covariance matrix decomposition, because of their ability to describe the correlated random field (after discretization) as a linear function of a set of uncorrelated standard normal variables.…”

Section: Random Field Discretization In Finite Element Analysismentioning

confidence: 99%

“…From (6) and (7) it follows that: From this relation it follows that A is a decomposition of covariance matrix C. As covariance matrices are generally positive definite, Cholesky decomposition C = LL is a possible method of decomposition. However, in the case of strongly correlated cells, Cholesky decomposition is prone to numerical instabilities and additional measures are needed for decomposing the covariance matrix (Green et al, 2015). Other methods are based on eigen-decomposition of the covariance matrix, as is the case in Karhunen-Loève decomposition (Huang et al, 2001).…”

Section: Random Field Discretization In Finite Element Analysismentioning

confidence: 99%

Efficient subset simulation for evaluating the modes of improbable slope failure

Eijnden

Hicks

2017

Computers and Geotechnics

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For analysing low probability slope failures, a modified version of subset simulation, based on performance-based subset selection rather than the usual probability-based subset selection, is combined with the random finite element method. The application to an idealized slope is used to study the efficiency and consistency of the proposed method compared to classical Monte Carlo simulations and the shear strength reduction (SSR) method. Results demonstrate that failure events taking place without strength reduction have different modes of failure than stable slopes brought to failure by SSR. The correlation between sliding volume and factor of safety is also demonstrated.

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“…Although the failure consequences are in general site-specific (e.g., loss of life and property), the volume of sliding mass (i.e., failure mechanism) can be a preliminary measure of failure consequence [4][5][6]. e failure probability and failure mechanism can be calculated in a probabilistic manner combing the finite element method (FEM) [3,5,[7][8][9][10][11][12][13][14][15], finite difference method (FDM) [16] with the strength reduction technique (SRT), and limit equilibrium method (LEM) [17][18][19][20][21][22][23][24][25][26][27]. On the one hand, FEM and FDM are preferably adopted for deterministic slope stability evaluation owing to their abilities of automatically searching the critical failure mechanism, modeling complicated constitutive law, and considering sophisticated external loads.…”

Section: Introductionmentioning

confidence: 99%

Failure Mechanism and Factor of Safety for Spatially Variable Undrained Soil Slope

Chu

2019

Advances in Civil Engineering

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This paper aims to investigate the differences in factor of safety (FS) and failure mechanism (FM) for spatially variable undrained soil slope between using finite element method (FEM) , finite difference method (FDM), and limit equilibrium method (LEM). The undrained shear strength of cohesive soil slope is modeled by a one-dimensional random field in the vertical direction. The FS and FM for a specific realization of random field are determined by SRT embedded in FEM- and FDM-based software (e.g., Phase2 6.0 and FLAC) and LEM, respectively. The comparative study has demonstrated that the bishop method (with circular failure surface) exhibits performance as fairly good as that of SRT both in FS and FM for the undrained slope cases where no preferable controlling surfaces such as hydraulic tension crack and inclined weak seams dominate the failure mechanism. It is, however, worthwhile to point out that unconservative FM is provided by the Bishop method from the aspect of failure consequence (i.e., the failure consequence indicated by the FM from the Bishop method is smaller than that from SRT). The rigorous LEM (e.g., M-P and Spencer method with noncircular failure surface) is not recommended in the stability analysis of spatially variable soil slopes before the local minima and failure to converge issues are fully addressed. The SRT in combination with FEM and/or FDM provides a rigorous and powerful tool and is highly preferable for slope reliability of spatially variable undrained slope.

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The simulation and discretisation of random fields for probabilistic finite element analysis of soils using meshes of arbitrary triangular elements

Cited by 21 publications

References 24 publications

Efficient uncertainty quantification in stochastic finite element analysis based on functional principal components

Efficient uncertainty quantification in stochastic finite element analysis based on functional principal components

Efficient subset simulation for evaluating the modes of improbable slope failure

Failure Mechanism and Factor of Safety for Spatially Variable Undrained Soil Slope

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