A novel nonlinear model for estimating ideal packing density of mixtures

Qiang Liu; Liang Guo; Jiali Miao; Detao Jia

doi:10.1038/s41598-025-87856-1

A novel nonlinear model for estimating ideal packing density of mixtures

Sci Rep. 2025 Feb 18;15(1):5950. doi: 10.1038/s41598-025-87856-1.

Authors

Qiang Liu¹, Liang Guo¹, Jiali Miao², Detao Jia¹

Affiliations

¹ College of Earth Science and Engineering, Shandong University of Science and Technology, Qingdao, China.
² College of Earth Science and Engineering, Shandong University of Science and Technology, Qingdao, China. miaojiali@sdust.edu.cn.

Abstract

Packing density models could predict the bulk density and void ratio of particulate materials. The original linear packing density model (LPDM) is linearly related to each grain size fraction. However, when using the LPDM model, the predicted packing density and void ratio have large deviation compared with the experimentally measured values. The authors believe this is due to the wedging effect. Therefore, the LPDM model is modified based on wedging effect and converted into a nonlinear model. In this paper, the novel nonlinear model is extended to ternary mixtures. Then, the wedging effect parameter is fitted through the experimental data of binary mixing of quartz sand particles. The obtained wedging effect parameter is correlated to the characteristic diameter ratio between particles. The novel nonlinear model is verified via measured values and cited data from binary and ternary mixes. The results show the calculated values of the novel nonlinear model are closer to the experimental results than that of LPDM.

Keywords: Packing density; The novel nonlinear model; Void ratio; Wedging effect.

Abstract

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