Experimental verification for a probabilistic model of fibers distribution along a reinforced concrete bar

A probabilistic model developed by the authors, of the fibers distribution in a reinforced concrete element has been verified in a series of tests described in this paper. The tests comprised twelve square cross-section bars made of fiber reinforced concrete with standard deformed rebars of different diameters, located at their center, as well as three specimens without conventional reinforcement. Each specimen was sawed into equal slices, where the width of each slice was equal to the length of a single fiber, and the fibers were counted. The statistical analysis included calculation of the average value and standard deviation of a non-dimensional variable, defined as the ratio between the actual and average volumes of steel, that of the rebars and of the steel fibers, in a typical segment of the bar. It was shown that there is a good agreement between the linear prediction of the standard deviation assumed by the model and the values obtained from the statistical analysis of the fibers count. Such assumption is not trivial and the empirical results prove its validity, which was not obvious prior to the tests. A good agreement was also obtained between the cumulative distribution functions predicted by the model and obtained from the count.