A comparative study on the probability distribution model for the compressive strength of concrete with consideration of the size effect

In the present paper, a comparative investigation on the size dependence of the probability distribution of the compressive strength of concrete by using three common probability models, including normal, log-normal, and Weibull distributions, was carried out on a set of 360 measured strength values. These strength datasets were derived from a comprehensive set of compression tests conducted on 240 molded cylinders of four distinct cylindrical sizes ($d\times l$= 50 ×100 mm, 75 ×150 mm, 100 ×200 mm, and 150 ×300 mm) and 120 concrete cores of two different sizes ($d\times l$= 50 ×100 mm and 75 ×150 mm), which were prepared using two different concrete mix proportions. From this analysis, it is indicated that: (i) regardless of the mix proportion, size, and type of the concrete specimen, the normal distribution provides the most relevant model for interpreting not only the probability distribution of the compressive strength of concrete but also its size dependence, as confirmed by both the maximum log-likelihood and minimum distance criteria; (ii) the size dependency of concrete compressive strength results in its probability distribution also being affected by the specimen size; (iii) the size dependence of the probability distribution of concrete compressive strength can be interpreted through the normal and log-normal distributions, but not through the Weibull distribution; and (iv) using large-sized molded specimens (i.e., concrete samples with a characteristic dimension exceeding 100 mm) instead of small specimens or cores should be recommended in investigating the probability distribution of the compressive strength of concrete.