Theory of critical distances and static/dynamic fracture behaviour of un-reinforced concrete: length scale parameters vs. material meso-structural features

The Theory of Critical Distances (TCD) groups together a number of approaches that make use of specific length scale parameters to model and estimate the strength of cracked/notched engineering materials. In the TCD framework, the critical distance is assumed to be an intrinsic property and this length is somehow related to the material micro-/meso-/macro-structural features. In recent years, a number of comprehensive theoretical/experimental investigations proved that the TCD is successful also in assessing the static/dynamic Mode I/Mixed-Mode I-II strength of unreinforced concrete containing geometrical features of all kinds. However, the scientific community has not yet agreed on a commonly accepted answer to the most obvious fundamental research question, i.e. “what is the physical meaning of the TCD critical distance?” In order to answer this question, a number of experimental results were generated by testing specimens of unreinforced concrete under static and dynamic Mode I bending. According to what is recommended by RILEM for the determination of fracture parameters of plain concrete, this comprehensive experimental work involved not only plain samples, but also specimens containing crack-like saw-cut notches. The specimens being tested were manufactured by using different bespoke mixes so that the meso-structural features of the concrete materials being tested could be controlled and then modelled in a very accurate way. The results from this systematic experimental/theoretical study led to the conclusion that, as far as the specific unreinforced concrete mixes used in the present investigation are concerned, the TCD critical length approaches the average distance between the crack-like saw-cut notch tip line and the first aggregates, with these aggregates acting as barriers slowing down/affecting the crack propagation process.