Three-Dimensional Cross-Correlated Random Field Modelling Based on Hierarchical Archimedean Copulas

The spatial variability of geotechnical parameters is usually characterized by random field theory. However, there are few studies on three-dimensional (3D) random field modelling, especially considering the cross-correlation characteristics of geotechnical parameters. In this study, a 3D random field modelling method considering cross-correlation between different soil parameters using asymmetric hierarchical Archimedean Copulas (HACs) is presented. The proposed method considered the different cross-correlated structure of cohesion (c), friction angle (ø), and compressive modulus (E_s) of soils. The marginal distribution function of c, ø and E_s and the optimal HAC among these parameters are established firstly. The generated functions are then combined by Sklar's theorem to set up the joint distribution function. The joint distribution function between three different parameters is next sampled by inverse Laplace-Stieltjes transform. The autocorrelation of single parameter is finally generated using matrix decomposition method. A dataset of laboratory test results of soil strength and stiffness parameters is employed to verify the proposed approach. The proposed approach can not only describe the different asymmetric dependence structure by HACs among c, ø and E_s, but also be applied to the modelling of three-dimensional (3D) random field.

Keywords: Spatial variability, 3-D Random field, Hierarchical Archimedean Copulas, Cross-correlation structure, modified matrix decomposition method (M-MD).