The role of copulas in random fields: Characterization and application

The spatial fluctuation of material properties is commonly modeled using random fields. However, descriptions of random fields in terms of marginal distributions and correlation structure are actually incomplete. The copulas that specify the dependence structure underlying the joint probability distribution over random fields are not provided and a Gaussian dependence structure is assumed without proper validation in practice. This study, therefore, tests the fitness of several non-Gaussian dependence structures in addition to the common use of the Gaussian dependence structure. A soil profile of cone penetration test (CPT) data is collected, and a pair-wise likelihood estimate approach is adopted to identify the best fit dependence structure. The results reveal that both qc and fs of the CPT profile exhibit the same non-Gaussian dependence characteristics, which challenges the Gaussian assumption. Generation of random fields with a non-Gaussian dependence structure is then proposed. Two slope examples where the spatial fluctuation of shear strength is respectively modeled using stationary and non-stationary random fields are used to investigate the deviation in failure probability due to different dependence structures. The effect of the dependence structure is non-trivial except when the random field is highly ragged or highly smooth. The results highlight the importance of copulas for dependence characterization in random fields.