An Efficient Method for the Discretization of 3-D Random Fields of Soil Properties in the Stochastic Finite Element Analysis of Geotechnical Problems

The spatial variability of soil properties is a significant aspect that should be considered in the analysis related to geotechnical safety and risk. Random field theory has been used for the discretization of soil properties in space and integrated with the stochastic finite element method for the probabilistic analysis of geotechnical structures. However, efficient discretization of three-dimensional random fields with large geometric size and high definition remains a challenging issue because of the heavy computational costs during the process stemming from the large physical memory demand for the storage of the autocorrelation matrix and the long computing time for the large matrix decomposition. A decomposed Karhunen-Loève expansion scheme was proposed in the present study. The proposed method is applicable when a separable autocorrelation function is employed. In this scheme, the generation of a three-dimensional random field will be decomposed into that of three separate one-dimensional random fields, and the eigenpairs needed for the random field discretization could be solved using the autocorrelation matrix in each direction respectively. A stepwise procedure was then employed to further reduce the memory usage when multiplying these one-dimensional solutions to get the final results. The precision and efficiency of the decomposed K-L expansion method for the discretization of random fields are verified. Compared with the traditional method, the proposed method significantly reduces the computing time and storage space, making the discretization of three-dimensional random fields more efficient.

Keywords: random field, spatial variability, soil properties, Karhunen-Loève expansion, stochastic finite element method.