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

Get Citation: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.

Received:2025-11-05, Revised: 2025-12-24, Online: 2026-01-23.

Funding： The research was supported by the Key Program of the National Natural Science Foundation of China (Grant No. 211021200570) and the 2023 Transportation Scientific Research Project of the Department of Transport of Shaanxi Province (Grant No. 23-80X).

DOI：10.13732/j.issn.1008-5548.2026.02.003

CLC No:U414； U416.0； TB4          Type Code: A

Serial No:1008-5548（2026）02-0001-14