Statistical modeling of multivariate loess properties in Taiyuan using regular vine copula with optimized tree structure

Loess properties play a crucial role in design and analysis of geotechnical and geological engineering projects, particularly in linear projects, such as subways that are constructed on the Loess Plateau. Linear engineering projects often traverse different types of loess areas and strata, necessitating collection and testing of a large number of loess samples in the laboratory and/or in situ, which may be costly and time-consuming, especially when numerous tests are required. As loess properties are typically interrelated, the properties of interest (e.g., collapsibility coefficient of loess) can be indirectly obtained from other readily obtainable properties of loess (e.g., its physical properties), through empirical correlations or multivariate models. Therefore, a database complied from a linear project, such as the Taiyuan Metro Line, is first analyzed to explore correlations among loess properties. Results show that loess parameters are correlated in either linear or non-linear manners, and exhibit non-Gaussian distributions. To model this complex dependence among non-Gaussian distributions, a flexible and optimizable Regular vine copula is proposed. Real-life loess properties collected from the Taiyuan Metro Line project are used to demonstrate superiority of the proposed method over the Canonical and Drawable vine copulas in terms of accuracy and robustness. The proposed method offers a viable method for utilizing a significant amount of loess test data to obtain loess parameters of interest (e.g., the collapsibility coefficient) in a statistical and cost-efficient manner. Furthermore, it provides a basis for implementing probability-based design or analysis of geo-structures, even when abundant data of loess properties are not available.