Three-Dimensional Random Field Modeling of Soil Properties Considering Cross-Correlation

It is widely recognized that there is spatial variability in soil properties in the geotechnical engineering. Spatially variable soils demonstrate auto-correlation of parameters, and also show significant cross-correlation between different parameters. At present, random field theory is often used to model the spatial variability of soil. However, in most studies, only two-dimensional (2D) random field is established, and there is a limitation of research on establishing three-dimensional (3D) random field. This paper aims to develop a 3D random field modeling method based on modified matrix decomposition method (M-MD) characterize the soil heterogeneity in 3D. Compared with the traditional matrix decomposition method (MD), the modified matrix decomposition considers the influence of relative distance on the cross-correlation matrix, which can more accurately reflect the cross-correlation between different soil parameters. The proposed method is applied to generate a multi-parameter 3D random field model considering cross-correlation between cohesion and friction angle. This study paves a way for future safety and risk assessment considering cross-correlation in geotechnical engineering.

Keywords: Spatial variability, 3D Random field, Modified matrix decomposition method, Cross-correlation structure.