EstimationofFracture Energy fromBasicCharacteristicsofConcrete

Approximate formulae for predicting the concrete fracture energy and effective process zone size from basic design parameters of concrete are presented. The formulae are based on statistical analysis of 238 test series extracted from the literature. The coefficient of variation of the errors of fracture energy prediction is about 183. 1. THE PREDICTION PROBLEM The differences of the test results from their mean This paper deals with the difficult problem of pre- value reflect the differences between various con- dicting the fracture energy of concrete and its other cretes and cannot be regarded as the statistical fracture parameters, such as the effective length of scatter of random errors. To get a picture of the the fracture process zone, critical crack tip open- scatter of random errors in the huge data sets, in- ing displacement and the fracture toughness, from cluding the test results from the literature obtained simple characteristics of concrete. on many different concretes, one must first elimi- Although it has already become clear that an ac- nate from the data their systematic (i.e., determin- curate prediction cannot dispense with the testing istic, mean) trends. In other words, one must first the given concrete, approx- find the formulae optimally describing the mean of notched specimens of imate (and admittedly crude) formulae predicting trends of the data, and the statistical errors are these parameters on the basis of standard com- then the deviations from these formulae. pression strength, maximum aggregate size, water- A study by Bafant and Becq-Giraudon (2000) cement ratio and aggregate type (river or crushed) deals with this problem in detail. It shows that it is can nevertheless be developed using several hun- possible to use the standard compression strength, dred test data that have by now been accumulated maximum aggregate size, ·water-cement ratio and in the literature.