Simulating Spatial Averages of Stationary Random Field Using the Fourier Series Method

A Fourier series method (FSM) of simulating spatial averages of stationary Gaussian random fields is presented. The FSM is able to simulate spatial averages over nonequally spaced rectangular cells, and by adopting Gauss quadrature, it can be further applied to nonrectangular cells. It is also capable of simulating line averages over any prescribed line segment in two dimensions. The former (spatial averaging over cells) is essential for finite-element analysis, while the latter (line averaging over line segments) is essential for slope-stability analysis using limit equilibrium. To resolve the issue of unrealistic periodical correlation pertaining to the FSM, a rule of thumb is provided to extend the simulation space. For cases with nonrectangular cells, the required number of Gauss points to achieve a prescribed accuracy is calibrated for both one-dimensional (1D) and two-dimensional (2D) cases and for both the single-exponential (SExp) and squared-exponential (QExp) autocorrelation models. The consistency of the FSM is verified through 1D and 2D examples for both SExp and QExp models. DOI: 10.1061/(ASCE)EM.1943-7889.0000517. (C) 2013 American Society of Civil Engineers.