The Theory of Critical Distances to assess failure strength of notched plain concrete under static and dynamic loading

The Theory of Critical Distances (TCD) is a design method that is widely used in situation of practical interest to estimate the strength of notched/cracked components subjected to either static, dynamic, or fatigue loading. The TCD makes use of a characteristic length to post-process the linear-elastic stress fields damaging the material in the vicinity of the stress concentrators being designed. The employed length scale parameter depends on the specific microstructural features of the material under investigation. By making the most of the TCD's unique features, the present paper summarises an attempt of reformulating this powerful theory to make it suitable for assessing static and dynamic strength of notched plain concrete. The accuracy and reliability of the proposed reformulation of the TCD is checked against a number of experimental results that were generated by testing, under different displacement rates, square section beams of plain concrete containing notches of different sharpness. This validation exercise allowed us to demonstrate that the proposed reformulation of the TCD, which is based on the use of simple power laws, is capable of accurately assessing the static and dynamic strength of the notched un-reinforced concrete being tested, with the estimates falling within an error interval of ± 20%. The obtained level of accuracy is certainly satisfactory, especially owing to the fact that static and dynamic strength is predicted without explicitly modelling those non-linearities characterising the stress vs. strain dynamic behaviour of concrete