Abstract
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, a, the value of which is correlated to the particle sphericity, particle size, and particle size ratio. A theoretical calculation formula for the coefficient a 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.
Highlights
Granular soil, such as sand and gravel, is a packing of soil particles of different sizes
Due to dispersion of granular materials, the basic properties of particles, such as particle size, particle shape, and friction between particles, all have important impacts on the mechanical properties, resulting in a very complicated macromechanical behavior of granular materials [1,2,3,4,5,6]. e minimum void ratio represents the densest condition of the soil; it is an important parameter affecting the mechanical behavior of granular soil [7, 8]
Comparing the curves of ΔVv with solid volume of the added sand, we find that even if the binary mixtures are from the same origin and at the same particle size ratio, the curves of ΔVv-Vs2 are not completely consistent, as shown in Figure 11. e test result shows that the larger the fine particle size is, the larger the ΔVv of the binary mixture is, which can be attributed to particle size difference and deviation of particle shapes between large and small particles [39]. ese two factors may contribute to the difference in total area of interparticle contact, resulting in a difference in ΔVv
Summary
Granular soil, such as sand and gravel, is a packing of soil particles of different sizes. E minimum void ratio represents the densest condition of the soil; it is an important parameter affecting the mechanical behavior of granular soil [7, 8]. Many researchers have obtained the mathematical expressions of the minimum void ratio of sand according to the particle morphology, especially the particle size [9,10,11,12] and shape [13,14,15,16,17,18,19,20]. Bahari et al [25] proposed a nonlinear model to estimate the minimum void ratio in sand-silt mixtures with various fines contents
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