Performance analysis of methods to estimate Weibull parameters for the compressive strength of concrete

Abstract

The compressive strength of normal-weight concrete can be well-described by the Weibull distribution, but there is a lack of research on the efficiency of the estimation methods employed for determining the Weibull distribution parameters. This study investigates the three common methods of estimating the parameters of the Weibull distribution, namely, linear regression, maximum likelihood, and moment methods. These methods are implemented on three datasets comprising a total of 490 compressive strength values of different concretes prepared using various mix proportions as well as varying sizes, shapes, and types of specimens. The effectiveness of the three estimation methods is evaluated based on the Anderson-Darling and Kolmogorov-Smirnov tests as well as the AIC and BIC approaches. The present performance analysis reveals that: (i) the maximum likelihood method shows the most accuracy, while the moments method exhibits the least relevance in estimating the Weibull distribution parameters; (ii) as an impact of the sample-size dependency of concrete compressive strength, the efficiency of the Weibull distribution and its parameters are influenced by the specimen size; (iii) the less dispersion in the dataset, the better the compatibility of the Weibull distribution of concrete compressive strength; and (iv) the Weibull modulus of concrete is linearly proportional to the inverse of the coefficient of variation of the measured strength data, with a proportionality coefficient of 1.09, regardless of the types and sizes of the concrete sample as well as mix proportions.