Construction of a joint probability distribution for correlated geotechnical properties is often needed in geotechnical reliability-based analysis and design. Geotechnical properties vary across sites and follow site-specific and non-Gaussian probability distribution, because of different geological processes that soils and rocks in different sites have undergone. In addition, site-specific measurements on geotechnical properties are usually sparse and correlated in geotechnical practice, leading to the difficulty in estimation of meaningful joint probability distribution when using conventional parametric statistical methods. To address this issue, this paper develops a non-parametric and data-driven approach for characterizing the site-specific non-Gaussian multivariate joint probability distribution without pre-selection of the marginal probability distribution type. Two key components for constructing a multivariate joint probability distribution (i.e., marginal probability distribution for each variable and correlation matrix for all variables) are estimated separately using Bayesian Gaussian mixture and Bayesian compressive sampling (BCS) and Karhunen-Loève (KL) expansion. The proposed method is illustrated using both simulated and real data in geotechnical site investigation. The results show that the proposed method performs well for both examples. The proposed method does not model spatial variability explicitly but is based on the assumption of independent measurement data along depth, and thus measurement records are required to be sufficiently spaced apart in depth (e.g., more than 1 scale of fluctuation) to satisfy this assumption.

在基于岩土工程可靠性的分析和设计中，经常需要为岩土工程属性建立联合概率分布。由于不同地点的土壤和岩石经历了不同的地质过程，因此各个地点的岩土属性会有所不同，并遵循特定地点和非高斯的概率分布。此外，在岩土实践中，针对岩土属性的特定于位置的测量通常是稀疏的并且相关联，从而导致在使用常规参数统计方法时难以估计有意义的联合概率分布。为了解决这个问题，本文开发了一种非参数和数据驱动的方法来表征特定于地点的非高斯多元联合概率分布，而无需预先选择边际概率分布类型。使用贝叶斯高斯混合和贝叶斯压缩采样（BCS）和Karhunen-Loève（KL）展开分别估计构造多元联合概率分布的两个关键成分（即，每个变量的边际概率分布和所有变量的相关矩阵）。在岩土现场调查中使用模拟和真实数据说明了该方法。结果表明，所提出的方法对于两个示例均表现良好。