A multi-scale model from microscopic cracks to macroscopic damage of concrete at elevated temperatures

A multi-scale model is established to describe the relationship between the macroscopic damage evolution and microscopic cracks behaviors of concrete at elevated temperatures. The evolution equation of the ideal microscopic crack system of concrete at elevated temperatures is deduced for construct the model, which can predict the microscopic crack density and macroscopic damage of concrete at elevated temperatures. The multi-scale model fuses some advantages of the traditional microscopic and macroscopic damage models. Finally, multi-scale damage of a concrete block under high temperature is predicted and compared with the corresponding experimental results, which is utilized to support the ability of the developed model. The results show that the developed multi-scale model can be used to evaluate fire damage of concrete structures in macro-scale as well as explain its physical mechanisms in micro-scale.