Some characteristic values of the stability analysis of MAL dams

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This paper proposes a Bayesian Copula identification method for shear strength parameters of soils and rocks. First, the characterization of dependence structure between shear strength parameters using Copulas is presented. Two commonly-used methods, namely least square method of Euclidean distance and akaike information criterion(AIC), for identifying the best-fit Copula, are given. Then, Monte Carlo simulations are conducted to validate the Bayesian Copula identification method. Moreover, the identification accuracy in the three methods is compared, and the main factors affecting the accuracy in the Bayesian Copula identification are identified. Finally, a total of twenty-three sets of shear strength data are compiled to demonstrate the application of Bayesian theory Copula model identification. The results indicate that with limited project-specific data and prior information, the Bayesian Copula identification method can successfully identify the best-fit Copula from a set of alternative Copulas for shear strength parameters. In comparison with the least square method of Euclidean distance and AIC, the Bayesian Copula identification method produces more accurate results for identifying the best-fit Copula. The sample size, correlation, the type of the true Copula and prior information of shear strength parameters has a significant impact on the accuracy of the Bayesian Copula selection method. Furthermore, the commonly adopted Gaussian copula for characterizing the dependence structure between shear strength parameters does not always provide the best fit to the shear strength data.
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Accurate estimates of the dependence of soil shear strength parameters (including cohesion and friction angle) play a crucial role in decision making by civil engineers about geotechnical engineering safety. Increased site-specific information comes the need for joint soil strength models to account for correlation characteristics between shear strength properties. In this study, firstly, using 16 sets of soil shear strength observations (consists of 391 samples) as examples, the suitability of the dependence structure for these experimental observations is identified by a goodness-of-fit test based on the Bayesian Information Criterion (BIC) with the normal, Student's t, Clayton, Frank, Gumbel, and Plackett copulas. The dependence structure between shear strength components is found to be asymmetric in most cases. Secondly, a set of paired samples of shear strengths simulated from the different bivariate copulas, which contributed to various dependencies, is implemented as an input to two typical geotechnical probabilistic analyses, e.g., an infinite slope stability against a single sliding plane and a bearing capacity of shallow foundation. The impact of different choices of these dependence structures on the resulting reliability index is discussed. In both illustrative examples, the normal copula leads to an overestimation of the reliability index, whereas the Gumbel copula achieves the lowest reliability index. The conservative reliability indices are obtained when the joint behaviour of soil shear strengths follows a bivariate normal distribution.
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