Error estimate in the probabilistic characterisation of concrete fatigue

Experimental results of fatigue tests in concrete present a wide scatter, with a difference of even several orders of magnitude between the highest and lowest obtained fatigue lives. The behaviour of fatigue results can be described by a probability model like the Weibull distribution. However, it is not clear how many tests are necessary to properly estimate the distribution parameters for a given concrete and loading conditions. In this work, a method has been developed so that the number of tests can be selected on the basis of the admissible error for the characterisation of the probabilistic behaviour of fatigue. As support for the performed study, a fibre-reinforced concrete was produced and 105 cubic specimens were tested. Afterwards, the sampling method known as ‘bootstrap’ was applied, which consists in generating multiple random samples of a given number of fatigue life results taken from the experimental set. The difference between the distribution fitted to each sample and the reference distribution of the complete set of values is the error made by the sample to characterise the material. The distribution followed by the error itself after all the sample simulations allows to determine the expected maximum error for a given safety level in relation to the number of tests. Different sample sizes from 3 to 90 tests have been analysed. The results provided by the method also allow to define a fatigue design distribution for the studied concrete and loading conditions.