Characterizing soil properties heterogeneity in complex tectonic regions using anisotropic random fields with nonlinear variation directions

The spatial variability of soil and rock properties is generally characterized by two or three principal linear directions in conventional anisotropic random field models. However, a single set of linear directions cannot effectively characterize the spatially variable soil properties at complex tectonic regions where the soil may also be squeezed, flipped, rotated or inclined. Typical cases are the sites with a folded soil stratum or a basin zone where the soil property may exhibit strong autocorrelation along a nonlinear line or surface. Characterizing spatially variable soil properties with such nonlinear variation directions remains a challenging problem. To address this problem, this study proposes a novel approach to characterize the spatial variability of soil properties at complex tectonic regions, using a curve or curved surface instead of linear directions to represent the spatial variation directions. Simulation methods are proposed to generate the anisotropic 2D and 3D random fields with nonlinear spatial variation. Virtual sites with different anisotropic conditions are employed to verify the accuracy of the proposed methods by comparing with the analytical solution. The proposed methods are also compared with the simulation methods for conventional linear anisotropic random fields. It is shown that the proposed methods can effectively simulate both linear and nonlinear anisotropic random fields with comparable computational efficiency to conventional approaches. The proposed methods are applied to a retaining wall example. The results show that the rotation of nonlinear anisotropic random fields significantly impacts the failure probability of the retaining wall. The effect of the rotation angle differs considerably between the linear and nonlinear anisotropic random fields.