RESEARCH ON THE HETEROGENEOUS STATISTICAL PROPERTIES OF ELASTIC MODULUS OF A CONCRETE MESO-SCALE UNIT

Concrete was assumed to compose of aggregate particles and a mortar matrix, and the concrete unit was processed equivalently based on the Voigt parallel model in the paper. The distribution of equivalent elastic modulus of a meso-unit was studied, based on the Weibull distribution, and a graphical method and the stepwise regression were applied to optimizing the estimated parameters. Furthermore, the validity of the assumed distribution was examined by the Kolmogorov test. The statistical parameter of element Young’s modulus with different element-scale, and the spatial distribution randomness of aggregate were studied in the paper. The problem on material characteristic element scale of concrete of different grade-level was analyzed at the end of the paper. The analytical results indicate that: 1) the form and the parameters of random distribution of elastic modulus of a concrete meso-scale unit have size effects, and not fully obey the Weibull distribution. 2) the variability of elastic modulus of a concrete meso-element associates with scales; and the variability increases firstly and tends to be stable gradually with the decrease of element size, which reflects the facts that there exists a reasonable representation of non-uniform degree of concrete at meso level. The reasonable scale, i.e. the variation coefficients tending to the inflection point of a smooth transition to the corresponding scale, is defined as a characteristic element scale. 3) The characteristic element scale of concrete material on two-grade, three-grade and four-grade are 10mm, 15mm and 18mm, respectively. 4) The spatial distribution randomness of aggregate has little effects on random distribution properties of elastic modulus of a concrete meso-unit.