Estimation of Population Standard Deviation for Post-Crack Performance of Fiber-Reinforced Concrete

Abstract

The post-crack performance of fiber-reinforced concrete (FRC) is widely reported to exhibit a high degree of variability. Several reasons exist to explain this problem, most notably the small area of crack surface involved in most beam tests. Of less widely recognized significance to variability is the relationship between the sample standard deviation and the population standard deviation for this material. Standard statistical theory can be used to estimate the relationship between the variance in a sample of observations and the variance in the population from which the observations are drawn, but this critically depends on the observations being drawn from a population displaying a normal distribution. Moreover, the observations must also exhibit covariant stationary characteristics. In this investigation, it is shown that neither of these assumptions are necessarily true for FRC specimens produced using standard mixing procedures. Instead, the distribution of post-crack performance parameters obtained from standard beam and panel-based tests exhibit inconsistent characteristics that possibly require an empirical approach to effective estimation of the population standard deviation.

Design of Steel Fibre Reinforced Concrete Structures According to the Annex L of the Eurocode-2 2023

“…fR,1k and fR,3k shall be computed considering that: fR follows a log-normal probability density distribution according to EN 1990 [13] (5% quantile, 75% of confidence level); and that the standard deviation of fR is unknown unless explicitly agreed. Criteria to determine the statistic properties of fR and to assess the population standard deviation could be found in [38,39]. The value of fR,1k establish the strength class: SC (1,0; 1,5; 2,0; 2,5; 3,0; 3.5; 4,0; 4.5; 5,0; 6,0; 7,0; 8,0) and the ductility class is denominated by a letter "a", "b", "c", "d" or "e" when the ratio fR,3k…”