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假定混凝土是由骨料颗粒及砂浆基质组成的复合材料,基于Voigt并联模型对混凝土细观单元进行等效化,对单元的等效弹性模量进行统计分析。以Weibull分布为假设分布,采用图解法结合逐步回归优选法进行参数估计,探讨了混凝土细观单元弹性模量的分布形式,并根据Kolmogorov非参数检验,对假设分布进行了检验;对不同尺度下的细观单元弹性模量进行统计分析,并对骨料空间分布随机性的影响作了初步分析;最后对不同级配下混凝土材料的特征单元尺度问题进行了研究。结果表明:1)混凝土细观单元弹性模量的随机分布形式及参数具有尺度效应,且并不完全服从Weibull模型;2)混凝土细观单元弹性模量的变异性与尺度相关,随单元尺度的减小,变异性先随之增大后逐渐趋于稳定,它反映了混凝土材料细观不均匀程度存在一个合理的细观尺度表述的事实,对应于变异系数向平稳段过渡的拐点所对应的单元尺度称为特征尺度;3)二级、三级、四级配下混凝土材料的特征单元尺度分别为10mm、15mm和18mm;4)骨料空间分布的随机性对细观单元弹性模量随机分布特征影响可以忽略。
It is assumed that concrete is a composite material composed of aggregate particles and mortar matrix. Based on the Voigt parallel model, the concrete mesoscopic units are equivalentized, and the equivalent elastic modulus of the units is statistically analyzed. The Weibull distribution is assumed to be a distribution. The parameter estimation is carried out by the graphic method combined with the stepwise regression optimization method. The distribution of the elastic modulus of the concrete is discussed and the distribution of the assumed distribution is tested according to the Kolmogorov nonparametric test. The analysis of the elastic modulus of meso-unit was carried out, and the influence of the randomness of the aggregate distribution was analyzed preliminarily. Finally, the characteristic element scale of concrete materials with different grades was studied. The results show that: 1) The random distribution and the parameters of the elastic modulus of concrete have the effect of scale, and they are not completely obeyed by Weibull model; 2) The variability of the elastic modulus of concrete is related with the scale, Decreases, and the variability increases first and then becomes stable gradually. It reflects the fact that there is a reasonable mesoscale expression of the mesoscopic heterogeneity of concrete material, corresponding to the fact that the inflexion point of the transition from the coefficient of variation to the plateau The unit scale is called the feature scale; 3) The characteristic unit scale of the second, third and fourth grade concrete materials is 10mm, 15mm and 18mm respectively; 4) The random distribution of the aggregate spatial distribution has random distribution of the elastic modulus of the meso- Features can be ignored.