A Critical Examination of the Karhunen–Loève Expansion for Random Field Generation in Geotechnical Analysis

ABSTRACT Random field modelling is widely used in geotechnical reliability analysis, as the relevant properties of soil and rock often exhibit significant spatial variability. The Karhunen–Loève expansion (K–L) has gained popularity as a method for generating random fields involving the decomposition of covariance structures into an infinite series of orthogonal eigenfunctions. In practice, this series needs to be truncated after a finite number of terms due to computational constraints. K–L truncation is directly controlled by the domain size, correlation length and spatial grid size on which the random field is to be generated. Truncation results in discretisation errors in the random field generation, which must be carefully managed. This paper reviews the principles of K–L, its implementation for random field generation, and its use in a geotechnical context. The presence of streakiness and checkerboard effects as observed by some investigators using K–L is critically examined. An example of a finite element geotechnical stability problem using K–L generated random fields is presented, highlighting the possibility of distinctly different failure mechanisms depending on the level of truncation employed in the K–L random field generation.