Brittle fracture of soil aggregates: Weibull models and methods of parameter estimation

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 (alpha and beta) 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 The different models and methods of estimation were evaluated using previously published and unpublished aggregate rupture energy data from three contrasting soil types (Bygholm sandy loam, Maury silt loam, and Karnak silty clay).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 beta 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 alpha on the Maury soil. We recommend fitting aggregate rupture data to a two-parameter Weibull model and estimating the model parameters using nonlinear regression.