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<p>The scale of fluctuation (SOF) is a key parameter for characterizing spatial variability in soil properties. While established methods for SOF estimation exist, they predominantly rely on large, high-resolution datasets such as cone penetration test (CPT) profiles, leaving their performance in data-scarce contexts—typical of laboratory-measured unsaturated soil properties—largely unexamined. This study addresses this gap by systematically evaluating two prominent SOF estimation methods, the conventional autocorrelation function method (ACM) and an improved variance reduction function method (iVRM), under small-sample conditions. The evaluation is conducted and validated using a representative case of soil–water characteristic curve (SWCC) parameter datasets, which are notoriously limited in size. Controlled numerical experiments demonstrate that the iVRM exhibits superior stability and accuracy when sample sizes are limited and is less sensitive to initial fitting values compared to ACM. To demonstrate its practical utility, the validated iVRM is then applied to field data from unsaturated clay deposits in Hefei City, yielding horizontal SOF values between 1.62 and 3.74&#xa0;m and vertical SOF values between 0.27 and 0.40&#xa0;m for the SWCC fitting parameters. The primary contribution of this work is twofold: it provides (1) a robust methodological framework for quantifying spatial correlation in data-scarce scenarios common in geotechnical practice, as demonstrated for unsaturated soil hydraulic properties, and (2) a set of&#xa0;quantified SOF estimates for the SWCC parameters of Hefei clays, providing essential spatial variability parameters for reliability-based analyses in unsaturated soil mechanics.</p>

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A Comparative Evaluation of Scale-of-Fluctuation Estimation Methods for Small-Sample SWCC Data in Unsaturated Soils

  • 期刊论文

  • 发表日期：

    2026年1月19日

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  • Suozhu Fei,
  • Zhichun Fang,
  • Xinyu Xu,
  • Dandan Fang

摘要

The scale of fluctuation (SOF) is a key parameter for characterizing spatial variability in soil properties. While established methods for SOF estimation exist, they predominantly rely on large, high-resolution datasets such as cone penetration test (CPT) profiles, leaving their performance in data-scarce contexts—typical of laboratory-measured unsaturated soil properties—largely unexamined. This study addresses this gap by systematically evaluating two prominent SOF estimation methods, the conventional autocorrelation function method (ACM) and an improved variance reduction function method (iVRM), under small-sample conditions. The evaluation is conducted and validated using a representative case of soil–water characteristic curve (SWCC) parameter datasets, which are notoriously limited in size. Controlled numerical experiments demonstrate that the iVRM exhibits superior stability and accuracy when sample sizes are limited and is less sensitive to initial fitting values compared to ACM. To demonstrate its practical utility, the validated iVRM is then applied to field data from unsaturated clay deposits in Hefei City, yielding horizontal SOF values between 1.62 and 3.74 m and vertical SOF values between 0.27 and 0.40 m for the SWCC fitting parameters. The primary contribution of this work is twofold: it provides (1) a robust methodological framework for quantifying spatial correlation in data-scarce scenarios common in geotechnical practice, as demonstrated for unsaturated soil hydraulic properties, and (2) a set of quantified SOF estimates for the SWCC parameters of Hefei clays, providing essential spatial variability parameters for reliability-based analyses in unsaturated soil mechanics.