The minimum void ratio is a fundamental physical index for evaluating particle properties in soil mechanics, ceramic processing, and concrete mixes. Previous research found that both particle size distribution and particle shape characteristics would affect minimum void ratio, while the current research generally uses a linear model to estimate the minimum void ratio of a binary mixture, ignoring quantitative effect of particle shape on the minimum void ratio. Based on a study of binary mixtures of natural sand from three different origins and iron particles of two different shapes, this paper analyzes the influence factors of the minimum void ratio, and a quadratic nonlinear model is proposed for estimating the minimum void ratio of binary mixture. The model contains only one undetermined coefficient, , the value of which is correlated to the particle sphericity, particle size, and particle size ratio. A theoretical calculation formula for the coefficient is proposed to quantitatively analyze the effects of these three factors on the size of the parameters. In the end, the model is used to estimate the minimum void ratios of sand and substitute particles from different producing areas; the average difference between the estimated values and the fitted values is about 2.03%, suggesting that the estimated values of the model fit well with the measured data.

中文翻译：

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不同尺寸/形状的沙质二元混合物最小空隙率的预测模型

最小空隙率是评估土壤力学，陶瓷加工和混凝土混合物中颗粒性质的基本物理指标。先前的研究发现，粒径分布和颗粒形状特征都会影响最小空隙率，而当前的研究通常使用线性模型来估算二元混合物的最小空隙率，而忽略了颗粒形状对最小空隙率的定量影响。在研究了三种不同来源的天然砂和两种不同形状的铁颗粒的二元混合物的基础上，分析了最小空隙率的影响因素，并提出了一个二次非线性模型来估算二元混合物的最小空隙率。 。该模型仅包含一个不确定的系数，其值与颗粒的球形度，粒径和粒径比相关。提出了一个系数的理论计算公式，以定量分析这三个因素对参数大小的影响。最后，该模型用于估算不同产地的沙子和替代颗粒的最小空隙率。估计值与拟合值之间的平均差约为2.03％，这表明模型的估计值与实测数据非常吻合。