Indentation tests based multi-scale random media modeling of concrete

In the present paper, a multi-scale random media model is proposed based on the indentation tests for each constituent of concrete including hydrated cement paste (HCP), aggregate and interfacial transition zone (ITZ). Firstly, systematic indentation tests are performed for each constituent of concrete at the nano- and micro-scales. Following the random field theory, each constituent of concrete materials is modeled as a random field. The scale of fluctuation is investigated based on the results of indentation tests. At the nano-scale, the scales of fluctuation of HCP and ITZ both turn to be roughly 20 µm, but that of aggregate is much larger. At the micro-scale, the scales of fluctuation of HCP and aggregate stay from 167 to 569 µm. Then the pointwise parameter estimation and model verification are performed for each constituent of concrete, and the one-dimensional (1-D) probabilistic density function (PDF) of the random field is obtained based on the proposed maximum possibility criterion. The probability distributions of the indentation modulus and hardness for each constituent of concrete are identified based on the statistical analysis. By introducing the reconstruction technique, concrete materials could be reconstructed as the random medium at the nano- and micro-scales. With the local averaging theory, the reduce factor for mechanical properties between the nano- and micro-scales is studied and it is shown that the experimental reduce factor agrees well with the theoretical one.