基于多维Gaussian Copula的岩土体设计参数概率转换模型构建方法
Establishing probabilistic transformation models for geotechnical design parameters using multivariate Gaussian Copula
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摘要: 岩土工程中经常需要基于直接测量参数去预测设计参数,概率转换模型是确定设计参数真实分布范围的有效工具。常用的基于多维正态分布的概率转换模型构建方法容易引起误差且受边缘分布类型限制。为此,提出了基于多维Gaussian Copula的岩土体设计参数概率转换模型构建方法。以全球黏土数据库CLAY/6/535为例验证了所提方法的有效性,分别推导了不排水抗剪强度和超固结比与孔压静力触探试验指标之间的概率转换模型。结果表明:基于多维Gaussian Copula的概率转换模型构建方法可以将相关结构与边缘分布分开构建,该方法不受岩土体参数的边缘分布类型限制,有效地避免了误差由边缘分布向相关结构的传播。在构建的概率转换模型中,岩土体设计参数的不确定性、相关性与直接测量参数的数目以及直接测量参数与设计参数之间的相关性成反比。Abstract: In geotechnical practice, it is common to transform the measured parameters to the design ones. It is also known that the probabilistic transformation models provide an effective tool for predicting the actual range of the design parameters. The commonly-used methods for establishing probabilistic transformation models based on multivariate normal distribution may induce large errors and have a limitation of incorporating various types of marginal distribution for soil parameters. In this study, a new method for establishing the probabilistic transformation models for geotechnical design parameters based on the multivariate Gaussian Copula is proposed. The global clay database CLAY/6/535 compiled in the literature is employed to verify the effectiveness of the proposed method. The probabilistic transformation models from CPTU indices to undrained shear strength and OCR are then derived. The results indicate that by modeling the marginal distribution and dependence structure individually, the proposed method removes the limitation of incorporating various types of marginal distribution and avoids error propagation from marginal distribution to dependence structure. For the proposed probabilistic transformation models, the uncertainty and correlation of design parameters are inversely proportional to the number of the measured parameters and the correlation between the measured and design parameters.