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 cross-correlations become stronger. Failure probabilities are also different when performing lower and upper bound (UB) random adaptive FELA with each of the selected copulas.

中文翻译：

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copula方法对随机自适应有限元极限分析边坡稳定性可靠性分析的影响

最近，随机场 copulas 已被用于表征空间可变土壤参数的相关结构。本研究通过实施有限元极限分析 (FELA) 与 copula 方法一起使用自适应网格对岩土工程问题进行可靠性评估，从而扩展了这一概念。以具有排水和不排水土壤条件的假设斜坡为例。首先，在假设斜坡上进行自适应 FELA。其次，单个和多个依赖土壤参数结构由几个选定的 copulas（高斯、弗兰克和克莱顿）表示。最后，实施随机自适应 FELA 来探索 copula 选择对边坡稳定性和可靠性分析的影响。结果表明，不同的 copula 方法产生了相当不同的斜坡失效概率，并且在模拟多个依赖结构时失效概率降低。此外，随着土壤参数互相关性的增强，排水和不排水土壤条件之间的失效概率表现出不同的趋势。对每个选定的 copula 执行下限和上限 (UB) 随机自适应 FELA 时，失败概率也不同。