Evaluation of the scale of fluctuation based on variance reduction method

Many uncertainties exist in geotechnical engineering. Spatial variability is a type of uncertainty that has received more and more attention in recent years. Scale of fluctuation (SOF) is a parameter for measuring the spatial variability of soil properties. To investigate the proper method for computing the SOF of soil properties, two types of methods (auto-correlation function method (ACM), and variance reduction method (VRM)) are compared theoretically and numerically, and the influence factors, such as number of data points involved in curve fitting for the auto-correlation function (ACF) or variance reduction function (VRF) and sampling interval, on the SOFs are analyzed. To improve the accuracy of curve fitting for the ACF or VRF, a weighted least squares (WLS) method is proposed, in which the weight of each data point of sample function decreases with the increasing of lag distance between two points in a random field. Three types of soil parameters, including the CPT, the physical, and the hydraulic parameters, are tested by in-situ and laboratory tests, and the SOFs of these parameters are computed. Computation of the SOFs proves that the VRM combined with the suggested WLS is a good method for computing the SOFs of soil properties. Comparison of the SOFs shows that there are negligible differences among the three types of soil parameters of clay layers in Hefei, which is further proved by the Wilcoxon test from a statistical point of view. By using the VRM combine with WLS, the SOFs of clay are computed based on 509 sets of CPT data from 34 sites in Hefei. The statistics of SOFs can give a reference for the selection of SOF for reliability analysis or reliability-based design of geo-structures with spatial variability.