Evaluation of spatial variability characteristics based on anisotropic modes of random fields

This paper introduces a framework for modeling random fields, with a particular emphasis on analyzing anisotropic spatial variability. It establishes a clear connection between the correlation function and the Kriging variogram across various anisotropic modes, providing mathematical models to enhance our understanding of random fields. A new anisotropy index, called LS AI , is introduced to quantify anisotropy based on the autocorrelation length and the orientation of the principal axes within the variogram. An LS AI value closer to one indicates a lower degree of anisotropy. The present study examines how the degree of anisotropy varies with different autocorrelation lengths and angles between the principal axes, providing valuable insights into these relationships. To improve the accuracy of parameter probability distribution estimations, this study integrates limited field test data using a Bayesian inference approach. Additionally, the Markov chain Monte Carlo simulation method is employed to develop a conditional random field (CRF) for the deformation modulus. By incorporating data from field bearing plate tests, the posterior variance data for the deformation modulus are derived. This process facilitates the construction of a detailed and reliable CRF for the deformation modulus.