On the Hole Effect in Soil Spatial Variability

Abstract

A hole-effect autocorrelation function is one that is non-monotonic or pseudo-periodic as defined in the geostatistics literature. This paper shows that such an autocorrelation function (ACF) can influence the probability of failure of some geotechnical structures. As such, it is relevant to ask whether this hole effect does exist and is identifiable from the cone penetration test data. For this purpose, a novel hole-effect ACF model, called the cosine Whittle-Matérn (CosWM) model, is proposed to simultaneously identify the scale of fluctuation (SOF), sample path smoothness, and hole effect. Based on simulation examples and two real case histories, it is found that the hole effect is identifiable only if the hole effect is significant and the data record is of sufficient length. One real case history exhibits a significant hole effect, and this hole effect is successfully identified by the CosWM model. It is also found that if a monotonic ACF is adopted in place of the CosWM model for this case history, not only can the hole effect not be identified (as is to be expected) but also the SOF will be overestimated significantly.