A direct simulation method and lower-bound estimation for a class of gamma random fields with applications in modelling material properties

Abstract

Existing approaches for generating non-Gaussian random fields typically utilize translation process theory that applies a memoryless nonlinear transformation to an underlying Gaussian random field. In the current study, a direct non-translation approach is proposed to generate random fields with a marginal gamma distribution. The proposed approach is based on the additive reproductive property of the gamma distribution; it results in a conceptually simple algorithm that is straightforward to implement in Monte-Carlo simulations. It is demonstrated that an arbitrary marginal gamma distribution is achievable. The resulting auto-correlation functions are non-negative and decreasing functions with a prescribed scale of fluctuation. These characteristics make the proposed non-translation approach suitable for modelling the spatial variability in material properties. The engineering implications of the proposed approach are illustrated through an application example wherein the proposed approach is utilized to generate a spatially varying undrained shear strength field for a two-dimensional plane strain slope, and the stability of the slope is analyzed by the finite element method with Monte-Carlo simulations. Since many material properties have a non-zero lower bound, the three-parameter gamma distribution is also discussed, and an asymptotically unbiased and consistent estimate of the lower bound is proposed.