Premium
Brittle Fracture of Soil Aggregates
Author(s) -
Munkholm L.,
Perfect E.
Publication year - 2005
Publication title -
soil science society of america journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.836
H-Index - 168
eISSN - 1435-0661
pISSN - 0361-5995
DOI - 10.2136/sssaj2004.0290
Subject(s) - weibull distribution , nonlinear regression , statistics , goodness of fit , loam , mathematics , weibull modulus , linear regression , shape parameter , power function , nonlinear system , estimation theory , regression analysis , soil science , geology , soil water , mathematical analysis , physics , quantum mechanics
Brittle fracture of soil aggregates is usually analyzed with the Weibull “weakest‐link” model. Failure is expressed in terms of a probability distribution function (pdf) of aggregate strengths. Traditionally a two‐parameter Weibull model is fitted to double log‐transformed data with the Weibull parameters (α and β) estimated using linear regression. The main objective of this study was to compare the goodness‐of‐fit for a three‐parameter versus a two‐parameter Weibull model. In addition, we compared three common methods of parameter estimation: linear regression, nonlinear regression, and maximum likelihood. The different models and methods of estimation were evaluated using previously published and unpublished aggregate rupture energy data from three contrasting soil types (Bygholm sandy loam, Maury silt loam, and Karnak silty clay). Overall, the goodness‐of‐fit was not markedly improved by using a three‐parameter as compared with a two‐parameter Weibull model. The choice of model had a significant effect on the parameter estimates. The three‐parameter model produced lower estimates of β than the two‐parameter model. The data were always best fitted using nonlinear regression. Nonlinear regression also resulted in a greater power of distinction between management treatments and aggregate sizes for α on the Maury soil. We recommend fitting aggregate rupture data to a two‐parameter Weibull model and estimating the model parameters using nonlinear regression.