Title:
Comparison of Normal and Lognormal Frequency
Distribution for Representing Variations of Concrete
Compressive Strength
Author(s):
P. Balaguru
Publication:
Materials Journal
Volume:
92
Issue:
2
Appears on pages(s):
191-199
Keywords:
compressive strength; concretes; field tests; quality control;
standard deviation.
DOI:
10.14359/9770
Date:
3/1/1995
Abstract:
Variation of concrete compressive strength is usually assumed to follow normal distribution. This assumption facilitates computation of the required average compressive strength fcr’ to comply with the specified compressive strength of concrete. The magnitude of overdesign, or difference between fcr’ and f, depends on the standard deviation of the data used for the computation of fc,.‘. ACI 318-89 specifications are aimed at achieving no more than I in 100 samples falling below a certain compressive strength. ACI Committee 214, Evaluation of Results of Tests Used to Determine the Strength of Concrete, recommends a set of t-values that can be used for any specified low tests. Both the code procedure and Committee 214 recommendations are based on the assumption that variation of concrete strengths follow normal distribution. In this paper, the validity of this assumption is evaluated using 100 different sets of data collected in the filed. The aim of the study was to evaluate whether the number of low tests can be predicted accurately using normal or lognormal distribution rather than checking whether the distributions provide an overall good fit. The chi-square test can be used to check whether a given data set follows normal distribution. The effectiveness of this test in improving the accuracy of low test prediction is also studied. Since most concrete data have a skew to the left side of the curve, lognormal distribution was also evaluated to compare its performance with normal distribution. Results show that the chi-square test cannot be used to improve accuracy of the prediction of low tests. Lognormal distribution provides an overall better representation for prediction of low tests in the range of 1 in 4 to 1 in 200. However, at the 1 in 100 low-test range, normal distribution is more conservative than lognormal distribution.