Random field theory is widely used to model spatial variability of soil properties. However, random field modeling focuses mainly on the estimate of spatial correlation structure. The dependence structure that is necessary to construct the joint probability distribution over a random field is usually not characterized. The aim of this research is twofold. First, this paper focuses on characterizing the dependence structure underlying a random field based on cone penetration test (CPT) data. The copula approach is adopted to represent dependencies and the best-fit dependence (copulas) are identified from the CPT data. It is found that the nonGaussian dependencies can be a real phenomenon in spatial fluctuation of the soil shear strength parameter. Second, this paper provides formulations for generating random fields with Gaussian or nonGaussian dependencies, and investigates whether the improper use of the dependence structure could lead to significant bias in failure probability. The generated one-dimensional (1-D) and two-dimensional (2-D) random fields of a cohesive slope under different dependencies are compared. Large deviation in probabilistic results implies that the effect of dependencies on failure probability can be nontrivial. Therefore, the complete random field characterization should involve the estimate of both correlation structure and dependence structure.
On the dependence structure of wavelet coefficients for spherical random fields