Approximate linear analysis of concrete fracture by R-curves

Using linear elastic fracture analysis, the energy consumed per unit length of fracture (fracture energy) varies with the crack length, as described by the resistance curve (R-curve). This concept, originally proposed for metals, is developed here into a practical, applicable form for concrete. The energy release rate is determined by an approximate linear elastic fracture analysis based on a certain equivalent crack length, which differs from the actual crack length, and is solved as part of structural analysis. It is shown that such an analysis, coupled with the R-curve concept, allows achieving satisfactory fits of the presently existing fracture data obtained with three-point and four-point bent specimens. Without the R-curve, the use of an equivalent crack length in linear analysis is not sufficient to achieve a satisfactory agreement with these data. The existing data can be described equally well with various formulas for the R-curve, and the material parameters in the formula can vary over a relatively broad range without impairing the representation of test data. Only the overall slope of the R-curve, the initial value, and the final value are important. A parabola seems to be the most convenient shape of R-curve because the failure load may then be solved from a quadratic equation. For the general case, a simple algorithm to calculate the failure load is given. Deviations from test data are analyzed statistically, and an approximate relationship of the length parameter of the R-curve to the maximum aggregate size is found.