On the need for dependence characterization in random fields: Findings from cone penetration test (CPT) data

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. Key words: random field, spatial variability, dependence structure, copulas, geotechnical reliability. La theorie des champs aleatoires est largement utilisee pour modeliser la variabilite spatiale des proprietes du sol. Cependant, la modelisation de champs aleatoires se concentre principalement sur l'estimation de la structure de correlation spatiale. La structure de dependance necessaire pour construire la distribution de probabilite conjointe sur un champ aleatoire n'est generalement pas caracterisee. Le but de cette recherche est double. Tout d'abord, cet article se concentre sur la caracterisation de la structure de dependance sous-jacente a un champ aleatoire base sur des donnees de tests de penetration au cone (CPT). L'approche de la copule est adoptee pour representer les dependances et la meilleure dependance d'ajustement (copules) est identifiee a partir des donnees du CPT. On trouve que les dependances non-gaussiennes peuvent etre un phenomene reel dans la fluctuation spatiale du parametre de resistance au cisaillement du sol. Deuxiemement, cet article fournit des formulations pour generer des champs aleatoires avec des dependances gaussiennes ou non-gaussiennes, et etudie si l'utilisation inappropriee de la structure de dependance pourrait conduire a un biais significatif dans la probabilite de defaillance. Les champs aleatoires unidimensionnelles (1D) et bidimensionnelles (2D) generes d'une pente cohesive sous differentes dependances sont compares. Un grand ecart dans les resultats probabilistes impliquait que l'effet des dependances sur la probabilite de defaillance pouvait etre non trivial. Par consequent, la caracterisation complete du champ aleatoire devrait impliquer l'estimation de la structure de correlation et de la structure de dependance. Mots-cles : champ aleatoire, variabilite spatiale, structure de dependance, copules, fiabilite geotechnique.
Introduction Spatial variability is widely observed in soil properties (Low 2014). As a major source of uncertainty, the spatial fluctuation of soil properties is found to have significant influence on [...]