Quantitative evaluation methods for mixture uniformity under vertical vibration conditions

LI Zhenjie; HU Liqun; CHU Jiawei; CHENG Gaoli

doi:10.13732/j.issn.1008-5548.2026.02.003

Abstract：Objective The performance stability of granular material is a critical factor influencing its service.To achieve quantitative analy-sis and evaluation of the mixing uniformity of mixture components under vertical vibration conditions,and to address the limita-tions of traditional zone-division evaluation methods,including their susceptibility to gradation segregation and strong subjectiv-ity,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 con-tinuous 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 evalua-tion 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 dimen-sion(i.e.,6 for three-dimensional space).By treating the DBSCAN search radius ε as a variable parameter,a functional rela-tionship between ε and the number of clusters was established.The differences between the non-uniform state and the ideal uni-form state(where the number of clusters was always 1)were quantified using a definite integral.On this basis,the self-uniformity degree index(IS)was proposed.Large-scale numerical experiments were conducted to validate the correlation between IS and particle distribution uniformity.Three-dimensional point sets were randomly generated within a unit cube,and the IS 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 IS and particle distribution uniformity.Subse-quently,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(IV)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(IU)was calculated as a comprehensive evaluation indicator by integrating IS and IV based on the mass-weighting prin-ciple.Finally,the simulation model was validated through vertical vibration segregation tests. Results and Discussion Simulation results conducted using the EDEM softwaredemonstrated that traditional evaluation meth-ods,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 challeng-ing 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 IS,IV,and IU,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 condi-tions,particles of the same type were stacked in cubes at equal spacing intervals.Under these conditions,the IS value consis-tently equaled 1,indicating no spatial overlap between particles.However,when the spacing between particles changed,the IV value deviated from 1 and varied accordingly.The calculated IU 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 IS,developed based on the DBSCAN clustering algorithm,effectively evaluates the continuity of particle distribu-tion.IV quantitatively characterizes the dispersion degree of single-grade particles through the external contour volume ratio.IU,obtained through mass-weighted integration of IS and IV,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 den-sity differences and interparticle interaction effects are not included in the weighting of index calculations.