# Numerical investigation of statistical variation of concrete damage properties between scales

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## Abstract

Concrete is typically treated as a homogeneous material at the continuum scale. However, the randomness in micro-structures has profound influence on its mechanical behavior. In this work, the relationship of the statistical variation of macro-scale concrete properties and micro-scale statistical variations is investigated. Micro-structures from CT scans are used to quantify the stochastic properties of a high strength concrete at the micro-scale. Crack propagation is then simulated in representative micro-structures subjected to tensile and shear tractions, and damage evolution functions in the homogenized continuum are extracted using a Helmholtz free energy correlation. A generalized density evolution equation is employed to represent the statistical variations in the concrete micro-structures as well as in the associated damage evolution functions of the continuum. This study quantifies how the statistical variations in void size and distribution in the concrete microstructure affect the statistical variation of material parameters representing tensile and shear damage evolutions at the continuum scale. The simulation results show (1) the random variation decreases from micro-scale to macro-scale, and (2) the coefficient of variation in shear damage is larger than that in the tensile damage.

## Keywords

Statistical variations Multi-scale Damage evolution Concrete Micro-structure## Notes

### Acknowledgements

The support of this work by US Army Engineer Research and Development Center under contract W912HZ-07-C-0019 to the second, fourth, fifth, sixth and seventh authors, and National Science Foundation of China under Grant No. U1134209 and Grant No. 91315301 to Tongji University for the third author is gratefully acknowledged.

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