A novel method for simulating large-scale 3D non-Gaussian random fields in geotechnical engineering

The spatial variability of the soil properties usually represented by random fields, is crucial for structural failure modes determination and reliability assessments. In this paper, a novel and efficient method was proposed for simulating non-Gaussian three-dimensional (3D) random fields. This method fully leverages the characteristics of circulant embedding matrix and uses an L-moment-based quartic Hermite polynomial for non-Gaussian transformation. It has three main advantages. Firstly, this method significantly reduces computational memory consumption and saves computation time, enabling efficient simulation of large-scale 3D random fields. Compared to the traditional Cholesky decomposition method (CDM), it improves the resolution of discretized random fields by more than 50 times and reduces computational time by up to five orders of magnitude. Moreover, it offers notable advantages over widely used approaches such as the Karhunen–Loève expansion method (KLM). Secondly, this method shows notable advantages in adapting to various stationary auto-correlation functions (ACFs) and scale of fluctuations (SOFs) through theoretical analysis and statistical validation. It also effectively captures the statistical characteristics of the marginal distribution with strong variability. Thirdly, this method is adaptable to various model geometries without requiring any modifications to the core algorithm. Two numerical cases, slope stability and foundation bearing capacity analyses validate its performance. In short, principal research achievements addresses key challenges in large-scale, high-dimensional, and non-Gaussian processing to some extent. The method proposed in this paper facilitates spatial variability modeling for general 3D geotechnical reliability analysis.