李振杰¹， 胡力群¹， 褚嘉玮¹， 成高立²

1.长安大学 公路学院， 特殊地区公路工程教育部重点实验室， 陕西 西安 710064；

2.陕西高速机械化工程有限公司， 陕西 西安 710038

引用格式：

李振杰， 胡力群， 褚嘉玮， 等. 垂直振动条件下混合料均匀性定量评价方法［J］. 中国粉体技术， 2026， 32（2）： 1-14.

LI Zhenjie， HU Liqun， CHU Jiawei， et al. Quantitative evaluation methods for mixture uniformity under vertical vibration conditions［J］. China Powder Science and Technology， 2026， 32（2）： 1-14.

DOI：10.13732/j.issn.1008-5548.2026.02.003

收稿日期： 2025-11-05， 修回日期： 2025-12-24，上线日期： 2026-01-23。

基金项目： 国家自然科学基金重点项目， 编号： 52038001； 陕西省交通运输厅2023年度交通科研项目， 编号： 23-80X。

第一作者简介： 李振杰（2001—），男，硕士生，研究方向为道路与机场工程研究。E-mail：2023121157@chd.edu.cn。

通信作者简介： 胡力群（1971—），男，教授，博士，交通部交通科技英才，博士研究生导师。研究方向为路面结构与材料。E-mail：hlq123@126.com。

摘要： 【目的】 为了实现垂直振动条件下混合料各组分混合均匀性的定量分析与判定，提出混合料均匀性综合评价指标。【方法】 基于颗粒三维空间坐标，引入搜索半径与簇数的函数关系，结合聚类思想构建表征单一粒径颗粒分布连续性的自离析系数（I_S）；利用三角构网算法构建单一粒径集料及混合料整体的外轮廓模型，通过体积比提出反映颗粒分散程度的表面轮廓体积分率（I_V）；依据质量加权原则结合I_S与I_V，形成综合指标均匀度指数（I_U）_，并结合垂直振动重筛分试验与离散元仿真数据进行分析。【结果】 在混合料垂直振动条件下，分形维数分析表明，不同级配混合料在振动30～40 s即可出现分形维数接近设计级配的阶段，但离散元仿真显示此时层内颗粒空间分布仍不均匀。针对3种级配的混合料的I_U在各级配条件下分别计算，在振动30 s时3种级配对应的I_U分别为0.486、0.449和0.489，振动至120 s时I_U增大至0.502、0.520和0.529，其随振动时间的变化趋势与离散元仿真中颗粒分布状态一致。【结论】 构建的I_S、 Iv与I_U指标可从连续性与分散性2个维度综合评估颗粒材料的均匀性，可定量分析颗粒体系混合质量。

关键词： 道路工程； 混合材料； 离散单元法； 均匀性

Abstract

Objective The performance stability of granular material is a critical factor influencing its service. To achieve quantitative analysis and evaluation of the mixing uniformity of mixture components under vertical vibration conditions， and to address the limitations of traditional zone-division evaluation methods，including their susceptibility to gradation segregation and strong subjectivity， a quantitative evaluation method for mixture uniformity is proposed based on two dimensions： the continuity and dispersity of particle distribution.

Methods The segregation degree of a specific aggregate fraction in a mixture can be characterized from two dimensions. First， it relates tothe rationality of interparticle spacing， which reflects whether particles within that size range exhibit a uniform and continuous spatial distribution in the mixture.Second，it concernsthe sufficiency of dispersion，which is the extent and severity of local agglomeration for that aggregate fraction. Based on these two dimensions， corresponding quantitative segregation evaluation indicators for each aggregatefractionweredevelopedusing spatial location information， ultimately enablinga comprehensive evaluation of the overall segregation degree of the mixture. Initially， the three-dimensional spatial distribution of particles was investigated， and the minimum particle number threshold for clusteringwas determined， typically set as twice the spatial dimension （i.e.， 6 for three-dimensional space）. By treating the DBSCAN search radius ε as a variable parameter， a functional relationship between ε and the number of clusters was established. The differences between the non-uniform state and the ideal uniform state （where the number of clusters was always 1） were quantified using a definite integral.On this basis， the self-uniformity degree index （I_S）was proposed. Large-scale numerical experiments were conducted to validate the correlation between I_S and particle distribution uniformity. Three-dimensional point sets were randomly generated within a unit cube， and the I_S values for each set of 100 points were calculated.The process wasrepeated 10 000 times. The results were consistent with natural distribution characteristics， confirming a linear relationship between I_S and particle distribution uniformity.Subsequently， the triangular mesh method was used to construct surface contour models for single-grade aggregates and the overall mixture， and their volumes were calculated. The surface contour volume ratio （I_V） was defined as the ratio of the surface contour volume of a single-grade aggregate volume to that of the total mixture volume. When evaluating mixture uniformity， considering the significant impact of particles with larger mass fractions on the overall performance of the mixture， the uniformity degree index （I_U） was calculated as a comprehensive evaluation indicator by integrating I_S and I_V based on the mass-weighting principle. Finally， the simulation model was validated through vertical vibration segregation tests.

Results and Discussion Simulation results conducted using the EDEM softwaredemonstrated that traditional evaluation methods， such as those based on fractal dimension analysis，could not fully characterize particle uniformity. Moreover， these methods relied on grid partitioning to assess the spatial distribution of aggregates， where determining an appropriate grid size is challenging and the evaluation results aresensitive to both grid configuration and positioning.As aresult， such methods often failed to accurately reflect the actual distribution state of particles. To address these issues， the uniformity evaluation method proposed in this study， based on I_S， I_V， and I_U， did not depend on grid partitioning during computation. It objectively characterized the true distribution characteristics of particles from the perspectives of continuity and dispersion， thereby offering better universality and applicability formixtures with arbitrary shapes. In a simulation of particle layer paving underhorizontal vibration mixing conditions， particles of the same type were stacked in cubes at equal spacing intervals.Under these conditions， the I_S value consistently equaled 1， indicating no spatial overlap between particles. However， when the spacing between particles changed， the I_V value deviated from 1 and varied accordingly. The calculated I_U value reached 0.91， which was very close to 1， demonstrating that this method provided a reasonable evaluation of the gradation uniformity of uniformly distributed mixtures. Additionally， comparisons with experimental data from vertical vibration segregation tests under the same conditions showed high consistency with the simulation results. This confirmed that the particle segregation evaluation indices established in this study reliably reflectactual segregation behavior.

Conclusion I_S， developed based on the DBSCAN clustering algorithm， effectively evaluates the continuity of particle distribution. I_V quantitatively characterizes the dispersion degree of single-grade particles through the external contour volume ratio. I_U， obtained through mass-weighted integration of I_S and I_V， accurately reflects the overall uniformity of the mixture.However， it should be noted that this method only considers the influence of volume during particle mixing， and factors such as particle density differences and interparticle interaction effects are not included in the weighting of index calculations.

Keywords： road engineering； mixture materials； discrete element method； uniformity

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