Abstract
•It is shown that sample path smoothness and scale of fluctuation (SOF) are two different characteristics.•Classical auto-correlation models are not suitable to characterize sample path smoothness.•The maximum likelihood (ML) method can produce misleading SOF estimates due to the smoothness-SOF false tradeoff.•The Whittle-Matérn model together with the ML method can capture SOF and smoothness simultaneously.
Recent studies have shown that the sample path smoothness in soil spatial variability can have a significant effect on the failure probability of geotechnical problems. The purpose of the current study is to propose a procedure that can identify the sample path smoothness based on site investigation data. It is shown that two factors determine whether or not the sample path smoothness can be identified: the type of auto-correlation function (ACF) model and the parameter estimation method. In order to identify the sample path smoothness, a non-classical two-parameter ACF model, such as the powered exponential (PE) model and Whittle-Matérn (WM) model, must be adopted together with the maximum likelihood (ML) method. The method of moments (MM) is incapable of identifying the sample path smoothness regardless of the ACF model type, classical or otherwise, although it is effective in identifying the scale of fluctuation (SOF). Between the two non-classical ACF models, the WM model is more flexible because it covers a wider range of sample path smoothness than the PE model. Neither the PE model nor the WM model is able to model the “hole effect” (non-monotonic auto-correlation). The development of a sufficiently flexible non-classical model that can simultaneously identify SOF, sample path smoothness, and hole effect remains an open research question.