A three-parameter R-curve of concrete-like quasi-brittle materials

•We propose a new R-curve of concrete where the initial cracking resistance is included.•The proposed R-curve is independent of specimen size.•We suggest a possible explanation for the new R-curve.

A three-parameter R-curve is derived where R-curve is defined as the envelope of critical energy release rate of specimens with different size. The idea underpinning the proposed R-curve is that energy required for progressing a pre-crack is composed of two parts: initial fracture energy and driving energy for crack extension. The three crucial parameters introduced in the proposed R-curve are material properties, and they can be determined experimentally on concrete specimens of regular size. The predicted fracture responses of mortar under single-edge notch tension (SENT), concrete and rock beams under three-point bending (TPB) from the proposed R-curve agree well with the test results. The proposed R-curve is independent of specimen size, and the local fracture energy from the material’s softening function may provide a possible explanation for the nature of the R-curve.