Bayesian Stochastic Soil Modeling Framework Using Gaussian Markov Random Fields

Stochastic soil modeling aims to provide reasonable mean, variance, and spatial correlation of soil properties with quantified uncertainty. Because of difficulties in integrating limited and imperfect prior knowledge (i.e., epistemic uncertainty) with observed site-specific information from tests (i.e., aleatoric uncertainty), a reasonably accurate estimate of the spatial correlation is significantly challenging. Possible reasons include (1) only sparse data being available (i.e., one-dimensional observations are collected at selected locations); and (2) from a physical point of view, the formation process of soil layers is considerably complex. This paper develops a Gaussian Markov random field (GMRF)-based modeling framework to describe the spatial correlation of soil properties conditional on observed electric cone penetration test (CPT) soundings at multiple locations. The model parameters are estimated using a novel stochastic partial differential equation (SPDE) approach and a fast Bayesian algorithm using the integrated nested Laplace approximation (INLA). An existing software library is used to implement the SPDE approach and Bayesian estimation. A real-world example using 185 CPT soundings from Alameda County, California is provided to demonstrate the developed method and examine its performance. The analyzed results from the proposed model framework are compared with the widely accepted covariance-based kriging method. The results indicate that the new approach generally outperforms the kriging method in predicting the long-range variability. In addition, a better understanding of the fine-scale variability along the depth is achieved by investigating one-dimensional residual processes at multiple locations.