Influence of copula approaches on reliability analysis of slope stability using random adaptive finite element limit analysis

Abstract

Recently, random field copulas have been deployed to characterise the dependent structures of spatially variable soil parameters. This study expands on this concept by implementing finite element limit analysis (FELA) with adaptive meshing alongside the copula approach to perform reliability assessment of a geotechnical problem. A hypothetical slope with drained and undrained soil conditions was used as an example. First, adaptive FELA was carried out on the hypothetical slope. Second, single and multiple dependency soil parameter structures were represented by several selected copulas (Gaussian, Frank and Clayton). Finally, random adaptive FELA was implemented to explore the effects of copula selection on slope stability and reliability analyses. Results show that considerably different slope failure probabilities are produced by different copula approaches, and that failure probabilities reduce for simulating multiple dependency structures. In addition, failure probability exhibits different tendencies between drained and undrained soil conditions as soil parameter crosscorrelations become stronger. Failure probabilities are also different when performing lower and upper bound (UB) random adaptive FELA with each of the selected copulas.

Geotechnical reliability‐based design optimization updating under changing design scenarios

“…As for how to model the joint PDF $$f({{\bf x}})$$, the copula theory 41,42 has been found to be a useful tool. Copula theory effectively accommodates both the dependence structure and nonlinear correlation coefficients 43 .…”

Stability of unsaturated soil slope considering stratigraphic uncertainty and rotated anisotropy of soil properties

“…Most studies focus on the dry or saturated soil slope stability analysis. [15][16][17][18][19][20][21] In the studies on the stability analysis of unsaturated soil slopes, some researchers only considered the spatial variability of saturated hydraulic conductivity k. [22][23][24][25][26] For example, Dou et al 27,28 proposed stationary and non-stationary random variable models to characterize the variability of saturated hydraulic conductivity and established a probabilistic framework of unsaturated soil slopes based on Monte Carlo Simulation method. Le et al 29,30 took into account the spatial variability of saturated hydraulic conductivity k, and studied its influence on the stability and sliding mass size of unsaturated soil slope under constant rainfall.…”

“…In terms of the stability analysis of slopes, researchers have considered the spatial variability of soil properties nowadays. Most studies focus on the dry or saturated soil slope stability analysis 15–21 . In the studies on the stability analysis of unsaturated soil slopes, some researchers only considered the spatial variability of saturated hydraulic conductivity k 22–26 .…”

Effect of soil anisotropy and variability on the stability of undrained soil slope

“…RFEM has been applied in many different areas of geotechnical engineering, such as bearing capacity under foundation, slope stability, pile foundation, etc. (Smith and Griffiths, 1998;Griffiths and Lane, 1999;Fenton and Griffiths, 2008;Jiang et al, 2022a;Jiang et al, 2022b;Nguyen et al, 2022;Shu et al, 2023). It allows the soil properties to be changed spatially but still correlated with the neighbouring soils (Fenton and Vanmarcke, 1990;Fenton and Griffiths, 2007).…”