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<p>A borehole is used to sample a natural soil layer of more than 1000 m<sup>3</sup> with unknown stratification and heterogeneity. Each split-spoon sample gives 0.001 m<sup>3</sup> of remolded soil. Sample remolding masks in situ stratification, which biases the evaluation of in situ permeability, which is central for groundwater studies, mainly contaminant migration. The grain size distribution (GSD) of a field sample results from long-term actions of unknown intensity and duration, on a few sources of solids. As a result, the GSD is polymodal. There is no expected result or preconceived ideas to compare GSD data. This precludes the use of a Gaussian mixture model, GMM, or the end-member method (EMM), which require expected values. A debate remains open: are the GSD data better described by the sum of lognormal (LN) functions or Weibull (WEI) functions? Previous comparisons were questionable. A statistically sound comparison is made using the free and recently developed modal decomposition method (MDM). The sums are compared for goodness of fit, <i>GOF</i>, and respect of assumptions for least squares estimates. They perform similarly for a unimodal GSD. It appears, though, that the LN sum outperforms the WEI sum for a polymodal GSD. Unlike the WEI sum, the LN sum is parsimonious, yields Gaussian residuals, and clearly reveals the structure of the dataset. Contrarily to other methods, the recent and free MDM includes tools to illustrate the transition from underfitting to overfitting, which give the correct number of modes, a problem that has been poorly solved in previous studies.</p>

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Grain size distributions of natural soils: are they sums of lognormal or Weibull functions?

  • 期刊论文

  • 发表日期：

    2026年7月15日

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  • Robert P. Chapuis

摘要

A borehole is used to sample a natural soil layer of more than 1000 m3 with unknown stratification and heterogeneity. Each split-spoon sample gives 0.001 m3 of remolded soil. Sample remolding masks in situ stratification, which biases the evaluation of in situ permeability, which is central for groundwater studies, mainly contaminant migration. The grain size distribution (GSD) of a field sample results from long-term actions of unknown intensity and duration, on a few sources of solids. As a result, the GSD is polymodal. There is no expected result or preconceived ideas to compare GSD data. This precludes the use of a Gaussian mixture model, GMM, or the end-member method (EMM), which require expected values. A debate remains open: are the GSD data better described by the sum of lognormal (LN) functions or Weibull (WEI) functions? Previous comparisons were questionable. A statistically sound comparison is made using the free and recently developed modal decomposition method (MDM). The sums are compared for goodness of fit, GOF, and respect of assumptions for least squares estimates. They perform similarly for a unimodal GSD. It appears, though, that the LN sum outperforms the WEI sum for a polymodal GSD. Unlike the WEI sum, the LN sum is parsimonious, yields Gaussian residuals, and clearly reveals the structure of the dataset. Contrarily to other methods, the recent and free MDM includes tools to illustrate the transition from underfitting to overfitting, which give the correct number of modes, a problem that has been poorly solved in previous studies.